Math is Figure-Out-Able!

#MathStratChat - July 1, 2026

Wed, 01 Jul 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 1, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Developing Mathematical Reasoning FREE workshop

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 315: "Best of", for Leaders

Tue, 30 Jun 2026 00:00:00 -0500

Shout out to our leaders! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.

Talking Points:

Ep 65: The power of shared math and teaching experiences
Ep 104: What is Math Is Figure-Out-Able?
Ep 165: Caution with manipulatives
Ep 201: Are algorithms bad?

Developing Mathematical Reasoning FREE workshop

Check out Pam's Books
Math is FigureOutAble Blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 24, 2026

Wed, 24 Jun 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 24, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 314: "Best of" 9-12

Tue, 23 Jun 2026 00:00:00 -0500

Shout out to our 9-12 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.

Talking Points:

Ep 294: Introducing Logarithms
Ep 69: Equations of Lines are Figureoutable!
Ep 6: Developing Functional Reasoning

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 17, 2026

Wed, 17 Jun 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 17, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 313: Best of 6-8

Tue, 16 Jun 2026 00:00:00 -0500

Shout out to our 6-8 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.

Talking Points:

Ep 45 - 5 Interpretations of Rational Numbers
Ep 183 - Integer Subtraction
Ep 266 - Solving Proportions - Within & Between

#MathStratChat - June 10, 2026

Wed, 10 Jun 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 10, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 312: Best of 3-5

Tue, 09 Jun 2026 00:00:00 -0500

Shout out to our 3-5 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.

Talking Points:

Ep 174 - Double/Half: The Most Sophisticated Multiplication Strategy
Ep 29 - Ratio Tables!
Ep 34 - Knowing vs Memorizing Multiplicaiton Facts

#MathStratChat - June 3, 2026

Wed, 03 Jun 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 3, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 311: Best of K-2

Tue, 02 Jun 2026 00:00:00 -0500

Shout out to our K-2 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.

Talking Points:

Ep 16 - Names of Teens
Ep 85 - Moving Past Counting
Ep 195 - Main Strategies for 1st Grade
Ep 281 - How Strategies Grow Up

Check out Pam's Books

Math is FigureOutAble Blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 27, 2026

Wed, 27 May 2026 15:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 27, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 310: More On Letting The Students Play

Tue, 26 May 2026 14:00:00 -0500

How would you describe the difference between a classroom that emphasizes memorization and a classroom that develops mathematical reasoning? In this episode, Pam and Kim wrestle with an analogy for math classrooms.

Talking Points:

Importance of letting students play with what they know to learn the real game of math
The significance of choice in math class
Pitfalls of labeling students
Value of providing equal opportunities in math class
What does "natural talent" mean in math?

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out Pam's Books

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 20, 2026

Wed, 20 May 2026 17:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 20, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 309: Classroom Takeaways: Aha Moments, Math Trauma, Differentiation, Tasks

Tue, 19 May 2026 16:00:00 -0500

What benefits have you found from teaching reasoning and mathing in your classroom? In this episode, Pam shares with Kim things she learned in her recent trip to South Korea.

Talking Points

Learning with your students
Importance of turn and talks to capture internal "aha" moments
Value of vulnerability and openness in the classroom
Math content vs math content for teaching
How open-ended problems and real math-ing naturally differentiates

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 13, 2026

Wed, 13 May 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 3, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 308: Fraction Multiplication, What?!

Tue, 12 May 2026 00:00:00 -0500

Can your students confidently reason about fraction multiplication? In this episode, Pam and Kim facilitate a Problem String that develops two strategies for fraction multiplication and discuss the thoughts that went into designing the string.

Talking Points:

#TryThisTuesday and #TryThisThursday
Scaling with fractions
Building fraction relationships
Goal of math is to build mathematical reasoning, not just get answers.
Reasoning is the reason!
Designing Problem Strings for multiple outcomes

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 6, 2026

Wed, 06 May 2026 12:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 6, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 307: Naming Fractions

Tue, 05 May 2026 00:00:00 -0500

Is there a 'correct' way to name math concepts? In this episode, Pam and Kim discuss different naming conventions for fractions from different cultures.

Talking Points:

Cultural difference in how fractions are expressed in Korean, where the denominator is said and written first.
Cultural convention influences the way students think about and express fractions.
Social conventions can influence mathematical understanding and the importance of being aware of these differences.
Many languages use a part-whole approach, while others use a whole-part approach.
Importance of being flexible in how we express fractions to support students' understanding and avoid confusion.

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 29, 2026

Wed, 29 Apr 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 29, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 306: Which Algorithm Would You Use: Fractions?

Tue, 28 Apr 2026 00:00:00 -0500

Can you use an algorithm to solve every type of problem, or are there some problems for which algorithms leave you stranded? In this episode, Pam and Kim answer that question and share a Problem String to build fractional fluency.

Talking Points:

Importance of understanding the relationships between different fractions.
Making sense of equivalent fraction values through experiences rather than memorized procedures.
Problem Strings provide continual building and strengthening of relationships and skills.
Problems Strings send the message it is not about one and only one way.

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 22, 2026

Wed, 22 Apr 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 22, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 305: Guiding Principles for What We Recommend

Tue, 21 Apr 2026 00:00:00 -0500

Looking for useful games and materials for your classroom? In this episode, Pam and Kim discuss some of the classroom materials and games they love and what makes them great.

Talking Points:

Games and resources that do NOT lead towards an algorithm
The value of games with strategy choice and without time/speed
Hand2mind Foundations for Strategies
Number Hive games for differentiation and to practice facts
Math For Love games
NumberClub games to build understanding
Wipebooks for Rich Tasks

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 15, 2026

Wed, 15 Apr 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 15, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 304: Context, Models, and Strategy for a Better CRA

Tue, 14 Apr 2026 00:00:00 -0500

How should context and models be used to build strategy? In this episode, Pam and Kim share a sequence of tasks regarding area to demonstrate a better approach for building understanding, abstraction, and strategy as a natural outcome.

Talking Points

Hand2mind Foundations for Strategies
Use of manipulatives to feel the meaning of area
Guiding students to become more sophisticated, both in models and in strategies
The importance of context for clarity and developing strategy
Moving from concrete, to representational, to abstract to deepen understanding, strategy, and independence, NOT to apply an algorithm

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 8, 2026

Thu, 09 Apr 2026 11:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 8, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 303: Product Approach to Multiplication Facts

Tue, 07 Apr 2026 00:00:00 -0500

If multiplication facts are so fundamental, why do students who memorize them struggle with multiplicative reasoning? In this episode, Pam and Kim take a hard look at what students need to succeed multiplicatively.

Talking Points

What does it mean to 'know' multiplication facts?
Using multiplication to solve subtraction problems
Memorizing facts doesn't build complex multiplicative reasoning
Redefining the mathematical 'basics'
Applications to algebra
How "productive practice" engages students in meaningful activities to build knowledge

Ep.139: Factor to Add and Subract!?

Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 1, 2026

Wed, 01 Apr 2026 14:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 1, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 302: Factor Puzzles 3: Expressions

Tue, 31 Mar 2026 00:00:00 -0500

How can we prepare students to grapple with algebraic concepts? In this episode, Pam and Kim further adapt factor puzzles for developing understanding of both decomposing and combining expressions.

Talking Points:

Helping students understand algebraic expressions
Differences in adding and multiplying variables
Relationships between terms in algebraic expressions
The need for multiplicative reasoning in algebra
Advanced Factor Puzzles for high school

Links:

1) Ep.139: Factor to Add and Subract!?
2) Factor Puzzle Blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 25, 2026

Wed, 25 Mar 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 25, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 301: Factor Puzzles 2: Integers

Tue, 24 Mar 2026 00:00:00 -0500

Why is practice sometimes not enough for students to become comfortable multiplying and adding integers? In this episode, Pam and Kim explore more with Factor Puzzles, this time with integers!

Talking Points:

Gaining experience multiplying and adding with negative integers
Purposefulness of keeping certain numbers constant in the factor puzzles
Practical applications of when to do Factor Puzzles
Importance of understanding the absolute value of numbers
Connection between Factor Puzzles and factoring quadratic trinomials

Link to Blog: https://www.mathisfigureoutable.com/blog

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 18, 2026

Wed, 18 Mar 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 11, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 300: Factor Puzzles 1: Whole Numbers

Tue, 17 Mar 2026 00:00:00 -0500

What is a great way for student's to increase their factor fluency and move from additive reasoning to multiplicative reasoning? In this episode, Pam and Kim play with factor puzzles and describe their many benefits.

Talking Points:

Kim loves podcast reviews!
Factor Puzzles routine
Generalizing patterns to develop algebraic reasoning
Building multplicative reasoning
Fluency with factor pairs
Ties to factoring quadratics

Link to Blog: https://www.mathisfigureoutable.com/blog

Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 11, 2026

Wed, 11 Mar 2026 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 11, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 299: Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in 3-5

Tue, 10 Mar 2026 00:00:00 -0500

What does the day-to-day of a math is figureoutable classroom look like? In this episode, Pam and Kim discuss the new book for teachers of Grades 3-5 to transform their teaching.

Talking Points:

New book release for Grades 3-5!
Development of Mathematical Reasoning
Additive Reasoning
Multiplicative Reasoning
Problem String walkthroughs and videos
Rich tasks, routines, models and modeling
Next steps for teachers, specific to their needs and experience

Shark Metaphor Podcast episode: Ep 245: Three Distortions that Ruin Math Teaching

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 4, 2026

Wed, 04 Mar 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 4, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 298: Who Gets to Math? One thing that Opens or Closes the Gate

Tue, 03 Mar 2026 00:00:00 -0600

Using strategies to solve problems sounds good, but what if my students don't know the basics? In this episode, Pam and Kim dispel the myth that "the basics" needed for mimicking algorithms are the same as the fundamentals for math-ing.

Talking Points

The limitations of rote memorization and the benefits of strategic thinking
The challenges of shifting away from traditional math teaching methods
Redefining what constitutes "basic math knowledge"
"The basics" needed for mimicking algorithms are not the same as "the basics" for math-ing.
Students need to understand underlying properties and relationships rather than isolated facts
Putting algorithms before reasoning gatekeeps who gets to reason

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 25, 2026

Wed, 25 Feb 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 25, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 297: What Makes Good Shifts in a School's Math Teaching?

Tue, 24 Feb 2026 00:00:00 -0600

What does it take to make real change in a school's math program? In this episode, Pam and Kim share what does and doesn't work to make lasting, systemic change in mathematics teaching for schools and school districts.

Talking Points:

Teachers should not have to be expert teachers and expert curriculum writers at the same time.
Good curriculum change alone is not enough
Lock-step plans backfire
Teachers need math-ing experiences
Teachers need to analyze mathematics for teaching
Teachers need bite-off-able tasks
Gradual, differentiated shifts over time last
Get in touch with us to make lasting impact in your schools at https://www.mathisfigureoutable.com//solution

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 18, 2026

Wed, 18 Feb 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 18, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 296: Live at NCTM Spring

Tue, 17 Feb 2026 00:00:00 -0600

It's great to learn from other educators. In this episode, Pam and Kim relay their experience at NCTM Spring 2026, giving their unique perspective of modern teaching trends.

Talking Points:

The need to define the terms curriculum, resources, scope and sequence, standards, content
Clarity before competence
Mathematics as both a noun and a verb
Caution around "research" and the "science of math"
The micro-routine "Interpret with Intention"
Different types of strategies

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 11, 2026

Wed, 11 Feb 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 11, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 295: Differentiating Problem Strings for your Grade Level: Over Subtraction

Tue, 10 Feb 2026 00:00:00 -0600

How can you tweak a Problem String to work perfectly for your class? In this episode, Pam and Kim share a subtraction Problem String, and then unpack what changes they'd make for different audiences.

Talking Points:

A subtraction Problem String with the Over strategy
The purpose of "what could a Helper be"?
When to provide a Helper problem
Adult-ish Problem Strings can cover more content
Making a Problem String appropriate for your grade level

Link to blog: Differentiating Problem Strings for Your Grade Level

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 4, 2026

Wed, 04 Feb 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 4, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 294: Introducing Logarithms

Tue, 03 Feb 2026 00:00:00 -0600

Introducing new math concepts can be tricky. In this episode, Pam and Kim do a Problem String to introduce logarithms in a natural, figureoutable way.

Talking Points

Problem String to introduce students to logarithms
Differences between logarithms and algorithms
Relationship between logarithms and exponents
Developing exponential equations

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 28, 2026

Wed, 28 Jan 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 28, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 293: What Makes a Good Number Talk?

Tue, 27 Jan 2026 00:00:00 -0600

Are your Number Talks purposeful? In this episode, Pam and Kim discuss the when, how, and why of Number Talks, which they call Problem Talks.

Talking Points:

Problem Talk vs. Problem String
When and why to use a Problem Talk
Example Problem Talk of 15 x 36
Deciding whose strategy to represent
Problem Talks are still instructional
How many students to choose
Choosing a rich problem

For more about Problem Talks and Problem Strings, check out episodes 33 and 241. Episode 33 , Episode 241

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 21, 2026

Wed, 21 Jan 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 21, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 292: Playing With Division and Fractions

Tue, 20 Jan 2026 00:00:00 -0600

There is much more to fractions than "cross multiply and divide". In this episode, Pam and Kim facilitate a Problem String to explore the partitive meaning of fractions.

Talking Points:

Fractions and division
The partitive meaning of fractions
Equivalent fractions
Relational reasoning in understanding fractions
Scaling up or down to find equivalent, simpler problems

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 14, 2026

Wed, 14 Jan 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 14, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 291: Starting the Year Grounded

Tue, 13 Jan 2026 00:00:00 -0600

Part of being a good teacher is teaching with integrity and consistency. In this episode, Pam and Kim discuss the importance of knowing your beliefs about teaching and learning math to guide your choices and decision making.

Talking Points:

Mathematics is hierarchical
Development of Mathematical Reasoning framework
Know your content, know your kids
Success Map framework
Developing a cohesive vision for math and math teaching
Decision making about the what and how of teaching math

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 7, 2026

Wed, 07 Jan 2026 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 7, 2026.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 290: Looking Ahead to 2026

Tue, 06 Jan 2026 10:00:00 -0600

How did you grow in 2025? What are your goals for 2026? In this podcast, Pam and Kim reflect on 2025 and share the exciting things they are working towards in 2026.

Talking Points:

Recapping highlights of 2025
Problem String book series completed
Development of Mathematical Reasoning anchor and companion books
Foundations for Strategies
New workshops in 2025 and 2026
Free opportunities in 2026
Conferences in 2026

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 31, 2025

Wed, 31 Dec 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 31, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 289: Pedagogical Moves vs Personality

Tue, 30 Dec 2025 00:00:00 -0600

All teachers are different, but we should all teach intentionally. In this episode, Kim surprises Pam with a collection of favorite "Pam-isms" and asks Pam to elaborate on whether each one is an intentional teacher move and why it is important, or if it is just her personality.

Talking Points

Ninety-niiiiiiiiine...
Is that legal?
Isn't it nice, when the answer is the question?
Sit up tall, you just mathed!
Math is Figure-Out-Able!
Bam!
Could I invite you to consider...
I know you didn't, but could you?
Tell us more about that.
Who wants their brain to think like that?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 24, 2025

Wed, 24 Dec 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 24, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 288: 12 Days of Free Part 2

Tue, 23 Dec 2025 09:00:00 -0600

In the season of giving, Math is Figure-Out-Able is giving some free stuff to you! In this episode, Pam and Kim discuss free opportunities to learn and grow as a teacher.

Talking Points:

Join the Teacher Facebook Group
Podcast Episodes 156 "Start Here"
Development of Mathematical Reasoning Episodes 5, 6, 67, 68
Focus on Fluency in Episode 277
Math is FigureOutAble Blog
Problem String Videos
Numberclub Webinar
Our Free Developing Mathematical Reasoning Workshop

Link to all 12 Days of FREE: https://www.mathisfigureoutable.com/blog/12-days-of-christmas-math-is-figureoutable

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 17, 2025

Wed, 17 Dec 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 17, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 287: 12 Days of Free, Pt 1

Tue, 16 Dec 2025 00:00:00 -0600

Who does not love free? We do, and know you do too!
In this episode, Pam and Kim kick of the 12 Days of Free, Math is Figureoutable style! Tune in to hear the first 6 FREE opportunities for supporting your math teaching.

Talking Points:

The Most Important Numeracy Strategies ebook
#MathStratChat
TryThisTuesday/Thursday
Problem Strings Guide
Math if Figure-out-Able Podcast favorite 3 episodes
How to receive our weekly email newsletter
Instructional Routines Hub

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

FREE Resources:

Most Important Numeracy Strategies https://www.mathisfigureoutable.com/big

Problem Strings Guide https://www.mathisfigureoutable.com/problem-string

Instructional Routines Hub https://www.mathisfigureoutable.com/instructionalroutines

Podcasts https://podcast.mathisfigureoutable.com/ (Check out episodes #245, #276, #277)

#MathStratChat - December 10 , 2025

Wed, 10 Dec 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 10, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 286: Listening Is Not Enough

Tue, 09 Dec 2025 00:00:00 -0600

Why do we listen to student thinking? In this episode, Pam and Kim discuss how listening is a powerful tool for both coaching and teaching.

Talking Points:

Why do we listen?
What do we do after listening?
Listening in service of moving the student or teacher forward
The Success Map and Developing Mathematical Reasoning
Affirming Learning Walks
Distinguishing methods from end goals
Mathematical and Community Building purposes for listening

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 3 , 2025

Wed, 03 Dec 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 3, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 285: Small Shifts, Big Impact

Tue, 02 Dec 2025 00:00:00 -0600

Sometimes a little shift makes all the difference. In this episode, Pam and Kim describe the new mini workshop for introducing secondary teachers to the small shifts in their teaching that can bring reasoning into their classrooms.

Talking Points:

Cathy Fosnot's 'Young Mathematicians At Work'
Introducing new 'mini' workshops on Transforming Teaching 6-12
Bridging the gap between K-5 and secondary teachers
How these workshops are accessible and affordable for both teachers and leaders.
The importance of small shifts and manageable chunks of information

Register for the workshop that's right for you at: https://mathisfigureoutable.com/mini-hub

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 26, 2025

Wed, 26 Nov 2025 12:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 26, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 284: Grateful for...

Tue, 25 Nov 2025 00:00:00 -0600

As the end of the year gets closer, it's a great time to reflect what and who we are grateful for! In this episode, Pam and Kim pause to give thanks for the wonderful work being done around the world to make math more figureoutable.

Talking Points:

Grateful for YOU, listeners!
Grateful for our amazing teacher Facebook group
Grateful for our Journey and JourneyLeader communities
Grateful for the Math is FigureOutAble team
Grateful for hard questions
Grateful for each other
Grateful for the journey!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 19, 2025

Wed, 19 Nov 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 19, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 283: Are Equations Ever the Best Model?

Tue, 18 Nov 2025 00:00:00 -0600

With so many models, what role do equations play? In this episode, Kim takes Pam through a Problem String that can only be modeled with equations and shares why.

Talking Points:

Fibonacci Day
Utilizing choice is a mathematical behavior
Differentiating instruction through strategies
Swapping, not a major strategy, but a fun one
Models vs. Strategies
Equations as models for equivalance strategies

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 12, 2025

Wed, 12 Nov 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 12, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 282: Playing With Math

Tue, 11 Nov 2025 00:00:00 -0600

Understanding math is important, and fun. In this episode, Pam and Kim discuss the necessity of play in mathematics education and share when, where, and why they each play differently with math.

Talking Points:

Dr. Brad Ballinger's view that algorithms are...playful??
The fun and educational value of simply playing with mathmatics
How Pam and Kim differ in their purposes and preferences when playing with math
How #MathStratChat can help you!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 5, 2025

Wed, 05 Nov 2025 00:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 5, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 281: Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in K-2

Tue, 04 Nov 2025 00:00:00 -0600

There's a brand new book for K-2 teachers! In this episode, Pam and Kim discuss how strategies in early mathematics build upon each other and increase in sophistication for future learning.

Talking Points:

Strategies build on each other, algorithms do not
The importance of building relationships and mental actions in students' brains
Get to Ten grows up to Get to a Friendly Number
Add Ten grows up to Add a Friendly Number
How the Over and Give and Take strategies help students think outside the problem
Ways developing strategies allows for differentiation

Purchasing Information: Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in K-2 https://www.mathisfigureoutable.com/dmrk2

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 29 , 2025

Wed, 29 Oct 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 29, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 280: Rapid Fire Math Pedagogy Questions

Tue, 28 Oct 2025 00:00:00 -0500

How can we adjust our teaching to meet the needs of our students? In this episode, Pam proposes a series of rapid-fire pedagogical scenarios for Kim to respond to with her best advice. What will Kim say in 90 seconds or less?

Talking Points:

What to do about a student who only solves addition problems left to right?
How to handle a student who always signals to pass during Problem Strings?
Ways to encourage students to use strategies learned in Problem Strings when doing independent math work.
Managing students who always yell out answers.
Using Hint Cards/Clue Cards effectively
Suggestions for students who have additional time accommodations
The importance of knowing your students

For additional information on Hint Cards, listen to Podcast Episode 38: Multiplication Facts: The Good, the Bad, and the Ugly Pt. 5

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 22, 2025

Wed, 22 Oct 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 22, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

NCSM/NCTM Reflections: What We Are Thinking About!

Tue, 21 Oct 2025 00:00:00 -0500

Pam and Kim went to NCSM and NCTM in Atlanta! In this episode, they share some of their favorite moments, biggest take-aways, and new insights gleaned from the sessions they attended and the people they met.

Talking Points:

Discussing the meaning of "algorithm" with Sarah Bush and Karen Karp, authors of The Math Pact
Importance of talk moves and listening moves, with Elham Kazemi and Allison Hintz, authors of Intentional Talk And Listening
The joy of celebrating someone else's learning from Vanessa Vakharia
How the Science of Reading does not correlate or correspond with what the people who call themselves the Science of Math are suggesting
The importance of Affirming Learning Walks
Clarifying the meaning of the word "procedural", as in "procedural fluency"
The misleading nature of much of the math research currently being approved by What Works Clearinghouse
Shout-out to James Tanton for being intellectually curious!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 15 , 2025

Wed, 15 Oct 2025 10:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 15, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 278: Benefit from Solving Equations Graphically

Tue, 14 Oct 2025 00:00:00 -0500

What role can technology play in mathematics education? In this episode Pam and Kim explore a Problem String for solving systems of equations using Desmos.

Talking Points:

Graphing systems of equations
Where lines intersect with different parent functions
Using graphing to understand the behavior of a cubic function and more
Using technology as a tool to understand what's happening, not as a crutch just to get answers.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 8, 2025

Wed, 08 Oct 2025 13:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 8, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 277: Memorize the Facts - It Makes All the Difference

Tue, 07 Oct 2025 13:00:00 -0500

What is the difference between "knowing" and "owning" facts? In this episode Pam and Kim discuss how to help all students make the most of multiplication facts.

Talking Points:

How different people respond when asked to "memorize facts"
"Own the facts" versus "Know the facts" - Do they mean the same thing?
Napkin Math
Using Problem Strings to teach facts and more
How reasoning about facts builds important multiplicative relationships
How reasoning in Problem Strings supports reasoning in word problems
Redefining what "memorization" means
Teaching for operational fluency

Facts Problem Strings: www.mathisfigureoutable.com/factsps

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 1, 2025

Wed, 01 Oct 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 1, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 276: Facilitating Pam's Favorite Problem String

Tue, 30 Sep 2025 00:00:00 -0500

Facilitating a Problem String is much more than providing a list of problems. In this episode Pam shares the moment to moment decisions she makes when facilitating a "Sticks of Gum" proportional realtionship building Problem String.

Talking Points:

Setting the stage
How to pull out thinking
Using this string to math with teachers in professional development
Reinforcing mathematical behaviors
Strategically determining wait time
Using potential misunderstandings as learning opportunities
Applying models to student thinking
Deciding the order of strategies to elicit
Choosing the numbers in the Problem String

Check out the Sticks of Gum Problem String here:
https://www.mathisfigureoutable.com/ratio-tables

Check out our social mediaTwitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 24, 2025

Wed, 24 Sep 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 24, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 275: Playing with Mathematical Relationships in Life

Tue, 23 Sep 2025 00:00:00 -0500

Mathematics is everywhere, but if students don't know how to reason they may not want to engage and play with numbers or see all the opportunities to do so. In this episode Pam and Kim discuss scenarios where they play with mathematical concepts in their daily lives.

Talking Points

Playing with numbers...double, half, factors, multiples, etc.
What numbers do they play with? House numbers, license plates, time, prices, interstate signs
I Have, You Need with time and distance
Which is a better deal? Cost per ounce
Mindset to engage in play with math

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 17, 2025

Wed, 17 Sep 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 17, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 274: Best Way to Teach Word Problems

Tue, 16 Sep 2025 00:00:00 -0500

Have students that struggle with word problems? In this episode Pam and Kim discuss the best way to help students succeed when faced with a word problem.

Talking points:

Why mimicking makes word problems harder
Reasoners develop greater stamina
Developing the feel of actions of the operations

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 10, 2025

Wed, 10 Sep 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 10, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 273: Conceptual Understanding... Then Algorithms

Tue, 09 Sep 2025 00:00:00 -0500

Is the goal of math class all about getting answers? In this episode Pam and Kim discuss how their work differs from those who promote traditional math classrooms and even some conceptual inquiry based classrooms.

Talking Points:

Teaching algorithms as the goal is detrimental
What is the goal?
Teachers need their own math learning experiences
We want students to own relationships to develop strategies that they will use in math class and throughout life

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 3, 2025

Wed, 03 Sep 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 3, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 272: What is Fluency Anyway?

Tue, 02 Sep 2025 00:00:00 -0500

How does the definition of fluency change when your goal for math class changes? In this episode Pam and Kim discuss in some areas of mathematics they aim for fluency and how students use those relationships to build from.

Talking Points:

Buzzwords
What are our goals?
Does automaticity need to be drilled or can it develop naturally?
Strategies are synergistic
Fluency with decomposing numbers
Functional fluency
Fluency with prime and square numbers
Fluency in mathematical behaviors

Check out these episodes to learn more about "working with multiplication facts".

Ep 97: If Not the Multiplication Algorithm, Then What?
Ep 34 - 38: Multiplication: The Good, The Bad, And the Ugly

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 27, 2025

Wed, 27 Aug 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 27, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 271: Direct Variation

Tue, 26 Aug 2025 00:00:00 -0500

How can we bridge from proportional reasoning to functional reasoning? In this episode Pam and Kim talk through a Problem String that moves students from proportional reasoning into linear functions.

Talking Points:

Building Proportions Problem String
Thinking about "between" and "within" relationships in a ratio table
Slope, rate of change, similar triangles, equivalence: all figure-out-able
Ratios and proportional reasoning to functional reasoning
Slope is a ratio

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 20, 2025

Wed, 20 Aug 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 20, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 270: Mathematical Behaviors

Tue, 19 Aug 2025 00:00:00 -0500

How do mathy people approach mathematics? In this episode Pam and Kim discuss different mathematical behaviors and the value of engendering them in students.

Talking Points:

Reflecting about what else you could have done that might be more sophisticated
Seeking the "ooh" factor or the "aha" moment
Compare strategies and make connections
Making choices based on numbers or the structure
Seeking efficiency and making generalizations
Start with "What do I know?"
Seek understanding and asking for more
The importance of acknowledging mathematical behaviors

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 13, 2025

Wed, 13 Aug 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 13, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 269: Why the Debate between Inquiry and Direct Instruction, Developing Reasoning and Teaching Procedures.

Tue, 12 Aug 2025 00:00:00 -0500

Does inquiry mean leaving students to their own devices? In this episode Pam and Kim share their thoughts on the debate teaching reasoning vs. teaching procedures.

Talking Points:

We all want what's best for students
Sometimes educators talk past each other, using words without examples to give meaning
Experiencing mathing is different from helping students learn to do the mental actions of mathing
Is there a continuum of how to teach?
Examples of "direct" and "inquiry based" instruction
Should we ever be explicit?
Why is it so important to have a common experience?

See the debate here: https://www.youtube.com/watch?v=CANtr9OHAvU

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 6, 2025

Wed, 06 Aug 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 6, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 268: Connecting Strategies, Properties, and Models in Addition

Tue, 05 Aug 2025 00:00:00 -0500

How can teachers help students be more sophisticated additive reasoners? In this episode Pam and Kim discuss the major addition strategies, what properties they use, and how to model student thinking.

Talking Points:

Addition strategies and models
Addition strategies modeled with equations
Proporties that the addition strategies are based on
When manipulatives are appropriate
Why teachers need to own the major strategies addition

Get the free ebook of Major Strategies at: https://www.mathisfigureoutable.com/big

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LL

#MathStratChat - July 30, 2025

Wed, 30 Jul 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 30, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 267: Connecting Strategies, Properties, and Models in Multiplication

Tue, 29 Jul 2025 00:00:00 -0500

If your only focus is answer getting, students may never experience and grapple with and understand multiplicative properties. In this episode Pam and Kim discuss how to use models to help students progress to more sophisticated strategies using multiplicative properties.

Talking Points:

Modelling different strategies on area models, ratio tables, and equations
Using models to visualize properties
Strategies that use the associative property are more multiplicative than the those that use the distributive property

Get the free ebook of Major Strategies at: https://www.mathisfigureoutable.com/big

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting

#MathStratChat - July 23, 2025

Wed, 23 Jul 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 23, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 266: Solving Proportions - Within & Between

Tue, 22 Jul 2025 00:00:00 -0500

How does proportional thinking prepare students for reasoning with variables? In this episode Pam and Kim explore the transition from proportional reasoning to functional reasoning.

Talking Points:

Connecting proportional reasoning to linear functions
Scaling triangles
Proportions "within" and "between"
Introducing tricks stifles students' opportunity to build sophisticated reasoning
Rich task with non-unit rates

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 16, 2025

Wed, 16 Jul 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 16, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 265: Show Your Work

Tue, 15 Jul 2025 00:00:00 -0500

Should you require student's to show their work in mathematics? Whose work? When? How much work? For what purpose? In this episode Pam and Kim discuss classroom culture and the importance of communication in mathematics, diving into these questions and more.

Talking Points:

Whose work are you asking student to show?
Motivations for showing work
Don't fix the math, mentor the mathematician - Cathy Fosnot
Communication is a mathematical behavior
Determining 'just enough' is a mentoring opportunity

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 9, 2025

Wed, 09 Jul 2025 00:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 9, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 264: Facilitating an Equivalence Structure Problem String - Multiplicative Reasoning

Tue, 08 Jul 2025 00:00:00 -0500

How can Problem Strings help build big ideas? In this episode Pam and Kim walk through a Problem String that helps students dig into area and multiplicative equivalence and help you know how to expertly facilitate.

Talking Points:

Facilitating the string
Teacher moves during the string
Modeling the string
Equal products means total area is the same
Why we want students to have lots of experience with concepts rather than just direct teaching.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 2, 2025

Wed, 02 Jul 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 2, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 263: Facilitating an Equivalence Structure Problem String - Additive Reasoning

Tue, 01 Jul 2025 00:00:00 -0500

How does a Problem String look in front of real students? In this episode Pam and Kim give a play by play for how a Problem String could be facilitated.

Talking Points:

When to circulate and when to ask for choral response
Helping students communicate thinking
How and when to engage students in conversations
When to anchor strategies
When to be intentionally curious to solidify thinking

Check out our grade level Problem String books!

Grade 1 Problem Strings: https://www.mathisfigureoutable.com/nps-1

Grade 2 Problem Strings: https://www.mathisfigureoutable.com/NPS-2

Grade 3 Problem Strings: https://www.mathisfigureoutable.com/nps-3

Grade 4 Problem Strings: https://www.mathisfigureoutable.com/nps-4

Grade 5 Problem Strings: https://www.mathisfigureoutable.com/nps-5

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 25, 2025

Wed, 25 Jun 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 25, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 262: Code Switching in Mathematics

Tue, 24 Jun 2025 00:00:00 -0500

What if finding equivalence between fractions, decimals, and precents wasn't just a task for students to do, but a tool making them more efficient in rational number computations? In this episode Pam and Kim talk about code switching with rational numbers to make complex problems more figure-out-able.

Talking Points:

What is code switching in rational numbers?
A Problem String using equivalence to think about multiplication
Tasks that use equivalency to solve problems rather than just practicing conversions

See episode 219 for learning about finding the mean: https://www.buzzsprout.com/1062400/episodes/15561786

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 18, 2025

Wed, 18 Jun 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 18, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 261: Five Year Anniversary Episode

Tue, 17 Jun 2025 00:00:00 -0500

Five years of important conversations, lots of laughs and a blooper every once in a while. In this episode Pam and Kim revisit some important moments of the podcast from the last 5 years.

Talking Points:

Clips from the past 5 years!
Types of questioning
Student compliance
Problem Strings vs Problem Talks
Math distortions
Wait time and Private signals

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 11, 2025

Wed, 11 Jun 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 11, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 260: Refining And Extending I Have, You Need

Tue, 10 Jun 2025 00:00:00 -0500

How can you get the most out of I Have, You Need in your classroom? In this podcast Pam and Kim answer some common questions and dig deeper into one of their favorite routines, I Have You Need.
Talking Points:

Do cars speak the language of fractions?
I Have, You Need (See also Ep 7 and 164)
Why it is helpful to know partners of 1, 10, 100, 1000, etc.
Common misconceptions
Why it is important for the teacher to call the numbers
Is it about creativity or efficiency?
Discussing strategy is a big part of I Have, You Need

Get the free download at:
https://www.mathisfigureoutable.com/youneed

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 4, 2025

Wed, 04 Jun 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 4, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 259: Universal Screeners: The Good, Bad, and Ugly - Part 2

Tue, 03 Jun 2025 00:00:00 -0500

We've got a lot to say about screeners! In this episode Pam and Kim dig a bit more into why we screen and what we do with the results.

Talking Points:

Are screeners useful for diagnosing and grouping students?
Are assessments important?
What would be a helpful way to spend the first few weeks of school with students?
What to do with required screeners
Some recommended screeners

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 28, 2025

Wed, 28 May 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 28, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 258: Universal Screeners: The Good, Bad, and Ugly - Part 1

Tue, 27 May 2025 00:00:00 -0500

Are Universal Screeners worth the time and effort? What do we gain? In this episode Pam and Kim begin their discussion about using Universal Screeners and raise some wonders for consideration.

Talking Points:

Defining screeners
Limitations of screeners
What we screen reveals what we value
Screeners don't always reflect the content in the classroom

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 21, 2025

Wed, 21 May 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 21, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep257: Are Problem Strings the Same as Thin Slicing? Pt 2

Tue, 20 May 2025 00:00:00 -0500

Do Problem Strings and Thin Slicing achieve the same results? In this episode Pam and Kim discuss the differences between Problem Strings and Dr. Liljedahl's Thin Slicing.

Talking Points:

Different purposes, different facilitation
The importance of recording student thinking
When non-permanent surfaces can be helpful
Problem Strings are strategically planned sequences and not always 'easy to more complex'
Differences in the teacher's role, questioning, math relationships
Word problems are natural extensions of Problem Strings
Problem Strings and Thin Slicing: Some similarities, but not the same.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 14, 2025

Wed, 14 May 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 14, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 256: Are Problem Strings the Same as Thin Slicing? Pt 1

Tue, 13 May 2025 00:00:00 -0500

Are Problem Strings the same thing as Thin Slicing? In this episode Pam and Kim talk about the similarities between Problem Strings and Dr. Peter Liljedahl's Thin Slicing.

Talking Points:

Example Problem String:
- Calling on students strategically in a Problem String
- Strategic seating arrangements for partner talk
Similarities between Problem Strings and Thin Slicing:
- Purposefully designed sequence of related problems
- Problems given one at a time
- Increasing challenge
- Critical teacher planning
- Open access for all students
- Purposeful variation to keep students challenged

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 7, 2025

Wed, 07 May 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 7, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 255: After a Problem String

Tue, 06 May 2025 00:00:00 -0500

You facilitated a Problem String! ... Now what? In this episode Pam and Kim share they think about after facilitating a Problem String and what their next steps for their classroom might be.

Talking Points:
Ways to up the ante

Echo strings
How much to change at once
Next Step strings
When to move on
When to anchor

Get Problem String books here: https://www.mathisfigureoutable.com/books

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 30, 2025

Wed, 30 Apr 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 30, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 254: Preparing for a Problem String

Tue, 29 Apr 2025 00:00:00 -0500

You've chosen a Problem String to teach, but does it need any preparation? In this episode Pam and Kim discuss how they prepare to facilitate a Problem String.

Talking Points:

Is it ok to adjust a pre-written Problem String?
What should you include in your 'Kim's Notes'?
What will your final board layout look like?
Naming specific teacher moves
Practice using models ahead of time
Are pre-created models ok?
Where can you find pre-written strings complete with facilitation notes and final display? https://www.mathisfigureoutable.com/big

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 23, 2025

Wed, 23 Apr 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 23, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 253: Choosing a Problem String

Tue, 22 Apr 2025 00:00:00 -0500

Which Problem Strings are appropriate for your students? In this episode Pam and Kim discuss what they consider when choosing a Problem String for a classroom.

Talking Points:

A fraction addition example string
Things to consider when choosing a Problem String:
- Prewritten vs write your own
- Time of year
- Strategies students already own
- Building a model vs building a strategy
- Order of sophistication of strategies
- Building a model vs strategy
- New content versus review/reteach

See episodes 33, 71, 72, 163, 226, 241 for more on Problem Strings!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 16, 2025

Wed, 16 Apr 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 16, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 252: Foundations for Multi-Digit Multiplication & Division Strategies

Tue, 15 Apr 2025 00:00:00 -0500

What kinds of tasks help students build multi-digit multiplication and division strategies? In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for multi-digit multiplication and division: Scaling, Over and Adjust, Partial Products, Factoring

Talking Points:

Benefits of using diverse task types
Sample of three "messy" tasks to develop:
Ratio tables
Area model
2 different kinds of division
Relationship between multiplication and division
Practice ideas

Get your kit from Hand2mind here: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-multiplication-division-small-group-kit

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 9, 2025

Wed, 09 Apr 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 9, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 251: Foundations for Multi-Digit Addition & Subtraction Strategies

Tue, 08 Apr 2025 00:00:00 -0500

What kinds of tasks help students build multi-digit addition and subtraction strategies? In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for multi-digit addition and subtraction: Friendly numbers, place value, adjusting, the commutative property, decomposing

Talking Points:

Sequencing tasks is more than just moving from one page to the next in the teacher guide
Sample of three "messy" tasks to:
- develop number lines
- make connections between addition and subtraction
- analyze strategies
- solidify a strategy

For more sequences, check out the Foundations for Strategies from Hand2mind!: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 2, 2025

Wed, 02 Apr 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 2, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 250: Foundations for Single Digit Multiplication & Division Strategies

Tue, 01 Apr 2025 00:00:00 -0500

Math class is richer and more fun when the goal is more than answer-getting!

In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for single digit multiplication and division: doubling, making use of ten, and partial products/quotients.

Talking Points:
Three sample sequence of tasks that use:

A product approach
Student exploration of patterns
Just in time vocabulary
Differentiation
Foundations of multiplicative reasoning, area, geometry
Contexts to develop 3 major models
Useful fact practice
Anchoring the learning

For more sequences, check out the Foundations for Strategies from Hand2mind!: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 26, 2025

Wed, 26 Mar 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 26, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 249: Foundations for Single Digit Addition & Subtraction Strategies

Tue, 25 Mar 2025 00:00:00 -0500

What should the bulk of math class look like? In this episode Pam and Kim discuss sequencing tasks to build foundational relationships that develop into major strategies.

Talking Points

Major relationships that build the major strategies
Problem Strings are one kind of task
Foundational Relationships for young learners
Rich tasks that get kids messing with relationships
What does practice look like? (See Episode 38 for more information on Hint Cards)
Check out pre planned sequence of tasks in the Foundation for Strategies small group kit

Order information for Foundation for Strategies here: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit

Order your copy of Avoiding the Trap of Algorithms here: https://www.mathisfigureoutable.com/avoidthetraps

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 19, 2025

Wed, 19 Mar 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 19, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 248: Avoid the I'm Not A Math Person Trap

Tue, 18 Mar 2025 00:00:00 -0500

Why do students give up on learning math? In this episode Pam and Kim discuss how using algorithms as teaching tools is distorting students' perception of what the definition of math is, which results in a poor mathematical identity.

Talking Points:

A mysterious five pound bag
A proportional reasoning Problem String
Trap #1 and #2 (see Ep 246 and 247 for more details)
Trap #3 a false definition of math that leads to Identity Definition of Math Trap
Read Pam's new book for more information: Developing Mathematical Reasoning: Avoiding the Trap of Algorithms

Purchase Book here: http://www.mathisfigureoutable.com/avoidthetraps

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 12, 2025

Wed, 12 Mar 2025 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 12, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 247: Avoid the Digit Trap

Tue, 11 Mar 2025 00:00:00 -0500

Why do students not realize their incorrect answers are completely unreasonable? In this episode Pam and Kim discuss another trap students fall into when taught to mimic algorithms as 'the way' to solve problems.

Talking Points:

The patterns in Remove a Friendly Number Over strategy
Important place value conversations
How students can be stuck dealing with only digits rather than magnitude
Reasonableness, or "Ish", numbers
Parsing out polynomials into too many pieces

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 5, 2025

Wed, 05 Mar 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 5, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 246: Avoid the Trap of Using Less Sophisticated Reasoning

Tue, 04 Mar 2025 00:00:00 -0600

If a student can perform an algorithm, have they developed the mathematical reasoning that operation calls for? Or are they answer-getting? In this episode Pam and Kim discuss a major trap students fall into when we teach mathematics as a series of steps to rotely memorize.

Talking Points:

A closer look at the multiplication algorithm and a major trap.
Problem String that helps give students a high does of patterns for a multiplicative strategy.
Algorithms disregard reasonableness.
Memorizing an algorithm is forgetable but every strategy learned helps build mental maps to the make subsequent strategies easier to develop.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 26, 2025

Wed, 26 Feb 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 26, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 245: Three Distortions that Ruin Math Teaching

Tue, 25 Feb 2025 00:00:00 -0600

If math is figure-out-able why does the world not always teach it that way? In this episode Pam and Kim discuss the three major distortions holding back math education today.

Autostereograms as a metaphor
How the distortions are learned
How the distortions create frustration
How classrooms transform without distortions
We want all kids to "see the shark"!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 19, 2025

Wed, 19 Feb 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 19, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 244: Opportunities for Awareness of Current Math Teaching Topics

Tue, 18 Feb 2025 00:00:00 -0600

There are so many way to participate in math professional learning! In this episode Pam and Kim discuss some benefits of choosing your own learning and engaging in free opportunities.

Talking Points:

Traditional forms of professional development
Benefits of multi-day online summits/conferences
The value of a shared experience
Join in on these great math summits from other fantastic educators!

Bulid Math Minds Free Virtual Math Summit, sponsored by Christina Tondevold: https://virtualmathsummit.com/

Make Math Moments FREE Virtual Summit sponsored by Jon Orr and Kyle Pearse: https://makemathmoments.com/summit/

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 12, 2025

Wed, 12 Feb 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 12, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 243: Integer Division

Tue, 11 Feb 2025 00:00:00 -0600

In this episode Pam and Kim use what students know about integer multiplication to tackle integer division (without mismatching rules or randomly switching signs).

Talking Points:

Reasoning about integer multiplication is ground work for integer division
An integer division Problem String
Teacher move: time to pause and consider
Using the quotative meaning of division
Thinking about opposites and reflection
Using the partitive meaning

See episode 64 for the equivalent ratio strategy

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 5, 2025

Wed, 05 Feb 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 5, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 242: Integer Multiplication

Tue, 04 Feb 2025 00:00:00 -0600

One of our most requested topics! In this episode Pam and Kim discuss integer multiplication without mismatching rules or randomly switching signs.

Talking Points:

Whole number multiplication strategies + meaning of integers leads to integer multiplication.
The meaning of integers (See episodes 169, 181, 182, 183, 186)
An integer multiplication Problem String and how to model
Important noticings about modeling and context
The importance of distance, reflection and opposites
The importance of equivalence and commutative property

Free downloads!
https://www.mathisfigureoutable.com/factsps
https://www.mathisfigureoutable.com/big

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 29, 2025

Wed, 29 Jan 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 29, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 241: Algorithm vs Problem Talk vs Problem String

Tue, 28 Jan 2025 00:00:00 -0600

Is mathing just about allowing students to solve problems their way? Aren't Probem Strings and Problem Talks really just the same routine? In this episode Pam and Kim discuss how Problem Strings move beyond Problem Talks to develop student's mathematical reasoning at a more sophisticated level.
Talking Points:

Example of a Problem Talk
What do we gain from Problem Talks?
Example of a Problem String
Problem Strings are more focused conversations
Problems Strings allow for constant feedback, a high dose of patterning

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 22, 2025

Wed, 22 Jan 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 22, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 240: Real Math, Fake Math?

Tue, 21 Jan 2025 00:00:00 -0600

Math may be figureoutable, but communication can be tricky! In this episode Pam and Kim discuss things to consider in order to be clear in the message we send when we speak about mathematics education.
Talking Points:
Duking it out!

Are algorithms fake math?
A better word than mathing?
What do mathematicians think about algorithms?
Do the math in mathematics education discussions so we have a common experience.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 15, 2025

Wed, 15 Jan 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 15, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 239: Counted Out

Tue, 14 Jan 2025 00:00:00 -0600

People across the world are changing math education. In this episode Pam and Kim discuss the documentary Counted Out that they were fortunate to see. They spotlight some of the thoughts of a few of the great researchers and add their thoughts about affecting change.
Talking Points:

Spoilers!
The effects of algorithms today
What needs to change?
How do we contribute to change?
Math is everywhere
Giving students choice
Jo Boaler will be on the January 2025 Math is Figureoutable Challenge!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

Ep 239: Counted Out (SPOILER FREE)

Mon, 13 Jan 2025 00:00:00 -0600

Spoilers!
The effects of algorithms today
What needs to change?
How do we contribute to change?
Math is everywhere
Giving students choice
Jo Boaler will be on the January 2025 Math is Figureoutable Challenge!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 8, 2025

Wed, 08 Jan 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 8, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 238: Inverse Variation Pt 2

Tue, 07 Jan 2025 00:00:00 -0600

Are inverse functions figureoutable? In this episode Pam and Kim go more into the nuance of when and how we want students to tackle inverse relationships.
Talking Points:

When to introduce inverse proportions
Experience versus instruction
Allowing students to grapple to in order to experience those aha moments
Problem String design

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 1, 2025

Wed, 01 Jan 2025 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 1, 2025.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 237: Inverse Variation Pt 1

Tue, 31 Dec 2024 00:00:00 -0600

What does it mean for something to be an inverse, or to be inversely proportional? In this episode Pam and Kim look at a specific kind of proportional reasoning.
Talking Points:

It's worth thinking before doing
Inversely proportional vs direct variation with non-unit scaling
Common misunderstandings

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 25, 2024

Wed, 25 Dec 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 25, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 236: Exponent Relationships Pt 5

Tue, 24 Dec 2024 00:00:00 -0600

Did you know that students can understand negative exponents without being told what they mean? In this episode Pam and Kim wrap up their series on exponent relationships.
Talking Points:

New listeners, where to start? Episode 156 Start Here
Discovering Negative Exponents
Give students experiences first and let them make sense of it
Using equivalent expressions to help students visualize and make generalizations
What grade levels are these strings for?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 18, 2024

Wed, 18 Dec 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 18, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 235: Exponent Relationships Pt 4

Tue, 17 Dec 2024 00:00:00 -0600

What if students actually understood using common factors to simplify complex division expressions? In this episode Pam and Kim divide exponents without reciting a rule.
Talking Points:

Thinking versus reasoning
Problem String Dividing Exponents
"Canceling" vs "Dividing out to equal 1"
Focus on left over factors vs mimicking a rule
Why start with smaller bases?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 11, 2024

Wed, 11 Dec 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 11, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 234: Exponent Relationships Pt 3

Tue, 10 Dec 2024 00:00:00 -0600

When variables and exponents start mixing, we need to memorize the rules, right? In this episode Pam and Kim develop exponential relationships, not rules.
Talking Points:

How "Kim's Notes" became "Half Sheets"
Problem String to explore multiplicative relationships when working with exponents.
Generalizing multiplication of exponents

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 4, 2024

Wed, 04 Dec 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 4, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 233: Exponent Relationships Pt 2

Tue, 03 Dec 2024 00:00:00 -0600

Would you believe I'm more comfortable dealing with exponents because I haven't memorized the rules? In this episode Pam and Kim continue building exponentiation with a great problem string
Talking Points:

Problem string to help build exponentiation
When and how to introduce vocabulary
Teacher move: Choosing who shares, and in what order
More confident reasoning without the rules
Teacher Move: Generalizing

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 27, 2024

Wed, 27 Nov 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 27, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 232: Exponent Relationships Pt 1

Tue, 26 Nov 2024 00:00:00 -0600

Can we prepare students for really hairy exponent problems without resorting to memorized rules? In this first episode of a series, Pam and Kim share a task that could get kids and teachers thinking more and more multiplicatively and understandably about exponents.
Talking Points:

Can a task have too many layers for students to be successful?
Can we sequence a task that works for 3rd grade to Algebra?
Problem String to connect prime factorization to exponents.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 20, 2024

Wed, 20 Nov 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 20, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 231: Systems of Equations with Substitution

Tue, 19 Nov 2024 00:00:00 -0600

Should high school mathematicians be given choice of which strategy to use? In this episode Pam and Kim wrap up their exploration of systems of equations.
Talking Points:

What is needed to understand 3x?
Where students mess up using substitution
How do different systems lend themselves to different strategies?
Ketchup problems
Next step Problem Strings and comparing strategies
Giving students choice

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 13, 2024

Wed, 13 Nov 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 13, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 230: Systems of Equations with Elimination (with sandwiches and cookies)

Tue, 12 Nov 2024 00:00:00 -0600

Don't you think math needs more cookies in it? In this episode Pam and Kim use Desmos graphing calculator to go through a routine to make sense of systems of equations before doing any elimination or substitution.
Talking Points:

Kim going to a Cafe for sandwiches and cookies
Graphing on Desmos graphing calculator
Understanding x and y intercepts
Understanding where the lines intersect
Relating systems of equations to each other

Link to Desmos Graphing Calculator: https://www.desmos.com/calculator/qq59ey0bub

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 6, 2024

Wed, 06 Nov 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 6, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 229: Solving Inequalities

Tue, 05 Nov 2024 00:00:00 -0600

Do we flip the sign when its negative? Or is it we keep the sign and flip the minus? I'm confused! In this episode Pam and Kim avoid all that confusion and make solving inequalities figureoutable!
Talking Points:

Open Number Lines for Inequalities
Using "Reflecting the inequality" vs "flipping the sign"
Reasoning about balancing the equation

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 30, 2024

Wed, 30 Oct 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 30, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 228: Solving Equations Pt 2

Tue, 29 Oct 2024 00:00:00 -0500

Solving equations is figureoutable! In this episode Pam and Kim do a follow up string to last week's episode to further develop algebraic reasoning.
Talking Points

Using a double open number line to build proportional reasoning
Using what you know to find x and explore multiple relationships
Understanding equations vs mimicking steps
Simultaneity can be tricky
Additive vs Multiplicative thinking showing up
Operator meaning of fractions comes into play

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 23, 2024

Wed, 23 Oct 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 23, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 227: Solving Equations Pt 1

Tue, 22 Oct 2024 00:00:00 -0500

Do we need to memorize a bunch of rules to solve linear equations or can we reason about them? In this episode Pam and Kim use a model to make thinking visible and keep students reasoning!

Talking Points:

Modeling on a double open number line
Finding where x lies on a double open number line.
Grappling with the opposite of x
Building integer sense as well as building equation solving sense
Reasoning about an equation versus balancing an equation

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 16, 2024

Wed, 16 Oct 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 16, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 226: Choosing Problem Strings

Tue, 15 Oct 2024 00:00:00 -0500

How can we help students who have always mimicked learn to reason through the content we need to teach? In this episode Pam and Kim lay out their approach to getting students up to speed while preparing them for the content of the day.
Talking Points:

How to avoid students feeling belittled
Using a 1/3, 2/3 mindest to planning
Planning with the entire year in mind
Layering in complexity to build a single strategy
Only change one thing at a time
It may take longer in the beginning or when you switch a strategy

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 9, 2024

Wed, 09 Oct 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 9, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 225: Place Value Tasks

Tue, 08 Oct 2024 00:00:00 -0500

Do your students struggle with place value? In this episode Pam and Kim discuss great tasks to build real place value understanding for students of all ages.
Talking Points:

"Adding a zero" vs shifting place value
Place Value versus Place Labeling
Avoiding rules that expire
Build a Number activity
Place Value Mini-Workshop!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 2, 2024

Wed, 02 Oct 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 2, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 224: NCTM NCSM Takeaways

Tue, 01 Oct 2024 00:00:00 -0500

We love the math teaching community! In this episode Pam and Kim are live from NCTM and discuss the many things they are learning from other math teaching educators at NCSM and NCTM in Chicago.
Talking Points:

Too many great sessions to list! But here are a few.
Announcing: Developing Mathematical Reasoning: Avoiding the Trap of Algorithms
Announced: Foundations for Strategies Small Group Lessons

Pre order Developing Mathematical Reasoning: Avoiding the Trap of Algorithms here: https://us.corwin.com/books/dmr-289132?srsltid=AfmBOor-iPP6FJaP0vQS7MWXGMzv6U6psI-ZbqBwxYbE_y4rGgPHU4fU

Pre order Foundations for Strategies Small Group Lessons here: https://www.hand2mind.com/supplemental-curriculum/math/math-fluency/daily-math-fluency-foundations-for-strategies-small-group-lessons

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 25, 2024

Wed, 25 Sep 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 25, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 223: Foundations for Strategies

Tue, 24 Sep 2024 00:00:00 -0500

How do you plan for the content you teach? In this episode Pam and Kim discuss task sequencing and a new resource for every classroom.
Talking Points:

Determining the big ideas, strategies, models
Alternating between instructional routines
Leading into and getting out of a rich task
Introducing Foundations For Strategies Small Group Lessons a collaboration with hand2mind!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 18, 2024

Wed, 18 Sep 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 18, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 222: Love Maths Games

Tue, 17 Sep 2024 00:00:00 -0500

You all know we love playing games in the classroom. In this episode Pam and Kim discuss the advantages of playing games to change students attitudes and beliefs about math, and just have some fun.
Talking Points:

The benefits of games
They don't even have to be math games
Multiple Machine by Michael Minas

Check out more of Michael Minas' games at Love Maths: https://www.lovemaths.me/games

Other Games: Cubit, Balance Beans, Quarto, Dimension, Blockus

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 11, 2024

Wed, 11 Sep 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 11, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 221: Geometry Riddles

Tue, 10 Sep 2024 00:00:00 -0500

In this episode Pam and Kim discuss a fun way for students to practice their geometry vocabulary and relationships.
Talking Points:

Geometry riddles
Hierarchies of polygons
Practice vocabulary in a meaningful way, in context

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 4, 2024

Wed, 04 Sep 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 4, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 220: The Important Teacher Move You Are Not Doing Enough

Tue, 03 Sep 2024 00:00:00 -0500

How can you intentionally build a Math is FigureOutAble culture in your classroom? In this episode Pam and Kim discuss Pam's recent month long trip to Australia and the important teacher moves she showcased in the lab lessons while she was there.
Talking Points:

Pam's time Down Under
Wait time
Private Signal
Focus on thinking verses focus on the answer
A challenge for some students: What hint could you give?
Teacher engaged with students the entire time
Does every kid need to finish the problem?
Do you need more time or help?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 28, 2024

Wed, 28 Aug 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 28, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 219: Find the Mean, Median, Mode

Tue, 27 Aug 2024 00:00:00 -0500

Statistics Problem Strings? Yes Please! In this episode Pam and Kim demonstrate a Problem String that helps students develop intuition for the meanings of mean, median, and mode.
Talking Points:

Names are social knowledge, but the feel for what they mean in the data is logical mathematical knowledge
Experience with data helps students develop real understanding of mean, median, mode
Changing the data values and comparing how that affects the measures of central tendency deepen understanding

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 21, 2024

Wed, 21 Aug 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 21, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 218: Finding the Mean

Tue, 20 Aug 2024 00:00:00 -0500

Is statistics figureoutable? In this episode Pam and Kim explore a Problem String to build logical mathematical sense for the meaning of mean.
Talking Points:

What is the mean?
Just in time vocabulary
Social vs Logical Mathematical knowledge
Understanding mean/average is much more than performing an averaging procedure

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 14, 2024

Wed, 14 Aug 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 14, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 217: Slow Reveal Graphs

Tue, 13 Aug 2024 00:00:00 -0500

We were joined by Jenna Laib at our last challenge where she facilitated an amazing routine called Slow Reveal Graphs. In this episode Pam and Kim share that same Slow Reveal Graph and explain along the way why it makes for such an impactful tool to teach data analysis and interpretation for students K-12.
Talking Points:

Shout out to Jenna Laib for currating the Slow Reveal Graphs website
Questions that focus on Strategy vs Answers
High level of engagement
Natural extensions built into the routine
Building thinking to analyze data representations and notice critical information or bias of the creator
The advantages to using routines

Follow along with the podcast with the Slow Reveal Graph here: https://slowrevealgraphs.com/2022/04/22/how-loud-is-too-loud-english-espanol/

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 7, 2024

Wed, 07 Aug 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 7, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 216: Assembling Great Resources With Sembl

Tue, 06 Aug 2024 00:00:00 -0500

Have you ever discoverd a super task or routine online only not be able to find it again when you really need it? In this episode Pam and Kim share Sembl, a curation of free, online math resources for your classroom that are filtered for quaility and organized for ease of use. Resources ready for you to integrate into your own curriculum!
Talking Points:

An amazing tool for finding and organizing tasks and other math content
Great to find new math education creators
App is able to organize and share in and between schools
We probably should mention we don't benefit monetarily from promoting tools like this, we just like them :)

Check out Sembl! https://www.sembl.app/

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 31, 2024

Wed, 31 Jul 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 31, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 215: Making Progress - Advancing The Math

Tue, 30 Jul 2024 00:00:00 -0500

It is helpful to find the particular lens to focus your own learning, in order to make real progress. In this episode Pam and Kim discuss planning and sequencing to keep the math moving forward in your classroom.
Talking Points

The stages help teachers focus their energy
Writing an 'Echo' Problem String
Write an 'Up the Ante' Problem String
Sequencing Strings
Sequencing different routines within a task
Sequencing Tasks
Understand the progression of models
Understand the connections between strategies
Explore the different structures of Problem Strings

Developing Mathematical Reasoning Free workshop: http://mathisfigureoutable.com/freeworkshop

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 24, 2024

Wed, 24 Jul 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 24, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 214: Making Progress - Your Teacher Moves

Tue, 23 Jul 2024 00:00:00 -0500

You've worked hard to build your numeracy and already own the strategies and models for your operation that you're working on. What's next?

In this episode Pam and Kim discuss Teacher Moves, the fourth stage on the Success Map.

Talking Points:

Differentiate for teachers' needs like they differentiate for students
Great teacher moves are only helpful when there's great math conversations happening
Model teacher moves in professional development
Using a private signal
Using a neutral response
Using focusing patterns for questions vs funneling patterns
Using partner talk appropriately
Using teacher moves appropriately

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 17, 2024

Wed, 17 Jul 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 17, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 213: Making Progress - Representing Your Students' Thinking

Tue, 16 Jul 2024 00:00:00 -0500

Ready to chat about the next layer of the Success Map?

In this episode Pam and Kim discuss using your understanding of the relationships to represent student thinking.

Talking Points:

The stages layer and build on each other
Different stages for different areas of math you are working on
Use your own understanding of relationships to choose the best model to represent relationships
Problem String vs Problem Talk, with purpose
Learn to listen to, elicit, and represent thinking at every opportunity
Share your experiences in the Math is Figureoutable Facebook group!

The How Do You Reason? free downloadable: https://www.mathisfigureoutable.com/reason

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 10, 2024

Wed, 10 Jul 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 10, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 212: Making Progress - Modeling Your Strategies

Tue, 09 Jul 2024 00:00:00 -0500

What's next on the landscape for teachers after they've built their own math understanding in a particular area? In this episode Pam and Kim discuss math for teaching, the next layer on the Success Map that teachers should consider as they are learning how to make math more figure-out-able for themselves and their students.

Talking Points:

Math for teaching is different body of math than the math anyone does
Understanding and naming the major strategies and models for each operation
Judiciously using the major strategies and models
Crafting rich problems
Build understanding in this stage alongside your students

Register for a workshop: https://www.mathisfigureoutable.com/workshops
Register for free Developing Mathematical Reasoning Workshop: https://www.mathisfigureoutable.com/freeworkshop
Download the free Major Strategies ebook: https://www.mathisfigureoutable.com/big

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 3, 2024

Wed, 03 Jul 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 3, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 211: Making Progress - Building Your Numeracy

Tue, 02 Jul 2024 00:00:00 -0500

What does a landscape look like for teachers trying to develop their skills to facilitate real math? In this episode Pam and Kim discuss one stage of the Success Map.
Talking Points:

Teachers, like students, are in different places in their journey in teaching real math.
Designing the Success Map was not trivial
Building your own Numeracy - a starting point
The Success Map journey is cyclical
What are the major milestones in develping numeracy?
- Solving problems using relationships
- Understanding models versus strategies
- Owning partners of 10, 100, 1000, and 1
- Describing mathematical relationships correctly
Developing Mathematical Reasoning free online workshop is a great place to begin

Check out the free Developing Mathematical Reasoning workshop at mathisfigureoutable.com/freeworkshop

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 26, 2024

Wed, 26 Jun 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 26, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 210: Number Hive

Tue, 25 Jun 2024 00:00:00 -0500

How can students gain fact fluency in a productive, fun way? In this episode Pam and Kim discuss Number Hive, a game that builds students multiplication fact fluency.
Talking Points:

Product Game is great, but Number Hive is even better
How to play Number Hive
Who will win? Kim or Pam?
A product approach to multiplication by considering factor pairs
Opportunities for great classroom discussion
Low cost of failure
Number Hive is flexible with lots of variety and levels

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 19, 2024

Wed, 19 Jun 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 19, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 209: Stick and Split

Tue, 18 Jun 2024 00:00:00 -0500

Developing multiplicative reasoning, let alone learning multiplication facts, has never been more fun. In this episode Pam and Kim discuss Stick and Split, a simple digital game your students or own kids can explore to learn multiplication in a whole new way.
Talking Points:

We don't recommend products lightly - Stick and Split is amazing!
Taking the product approach - How is that different?
Noticing the commutative property
Using common factors as tools
What do the levels look like?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 12, 2024

Wed, 12 Jun 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 12, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 208: Fraction Multiplication Part 3

Tue, 11 Jun 2024 00:00:00 -0500

What does it look like when students confidently and efficiently reason through fraction multiplication problems? In this episode Pam and Kim discuss more sophisticated and efficient strategies for solving fraction multiplication problems.
Talking Points:

How to model the commutative property in fraction multiplication.
How to reasoning through "slash and burn".
In a classroom, we would expect for students to have a variety of strategies to solve a rich problem.
It's not about multiple representations but about connections between multiple representations so that kids have a series of connections in their head.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 5, 2024

Wed, 05 Jun 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 5, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 207: Fraction Multiplication Part 2

Tue, 04 Jun 2024 00:00:00 -0500

Can students reason through fraction multiplication beyond unit fractions? In this episode Pam and Kim finish out last week's Problem String and build on those relationships to reason through more complex fraction multiplication problems.
Talking Points:

Can building Additive and Multiplicative reasoning with whole numbers help with fraction multiplication?
Does the area model just explain a procedure or can you actually reason with it?
How does building reasoning about multiplying fractions using scaling impact future learning (like slope)?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 29, 2024

Wed, 29 May 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 29, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 206: Fraction Multiplication Part 1

Tue, 28 May 2024 00:00:00 -0500

This week we're kicking off our series on fraction multiplication! In this episode Pam and Kim describe a classroom's experience discovering unit fraction multiplication.
Talking Points:

We sometimes have to hear something multiple times for it to "click"
What is 1/4 of 1/5?
Suggestions for modeling fractions and why
Layers of Reunitizing
How memorized procedures can work against students
Explicit teaching the use of a model is actually teaching a procedure

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 22, 2024

Wed, 22 May 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 22, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 205: Beat the Calculator

Tue, 21 May 2024 00:00:00 -0500

When should students use calculators? In this episode Pam and Kim discuss how to help students determine when and for what reasons to turn to technology.
Talking Points

Help students learn judicious use of technology
Great game: Beat the Calculator
Do you know enough to put that in your calculator?
What about competition?
What about speed?
An easy extension for Beat the Calculator

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 15, 2024

Wed, 15 May 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 15, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 204: Building a Community

Tue, 14 May 2024 00:00:00 -0500

Is your classroom a place where students' thinking is valued? In this episode Pam and Kim discuss building a healthy classroom culture.
Talking Points:

Know your content, but also know your kids
Me versus us statements
Walking the line of planning for the community and being part of the community
A great place to start is recognizing 'hidden' students
Names are important, learn them, use them

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 8, 2024

Wed, 08 May 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 8, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 203: Instructional Routines

Tue, 07 May 2024 00:00:00 -0500

What kind of instructional routines should you use in your classroom? In this episode Pam and Kim describe why instructional routines are useful and what makes some of their favorites shine.
Talking Points:

Unlocking creativity and reasoning with routine
Content flexibility within routines
The downside to one and done routines
How to decide which routines are worth establishing
What makes Problem Strings a great routine
Are games routines?
Each of our 3 favorite routines

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - May 1, 2024

Wed, 01 May 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 1, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 202: You Could Have Understood Trigonometry (Radian Measure)

Tue, 30 Apr 2024 00:00:00 -0500

All students can learn more math when it is taught as figure-out-able! In this episode Pam and Kim wade into trigonometry and make sense of it as they go.
Talking Points:

Making sense of Pi and angle measure of a circle

Defining radians
Understanding the unit circle
A Problem String using a unit circle
The importance of modeling
I Have, You Need with angles

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 24, 2024

Wed, 24 Apr 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 24, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 201: Clearing Up Misconceptions

Tue, 23 Apr 2024 00:00:00 -0500

Got questions about the Math Is Figureoutable movement? In this lightning round episode, Pam and Kim answer questions and address misconceptions they've heard people have.
Talking Points:
Is it only about Problem Strings?

Does math-ing have be done in all in your head?
Is "one and done" desirable?
Are we doing "Pam Harris Math"?
Are algorithms bad?
Is Math is Figuroutable appropriate for all grades K-12?
Is Math is Figuroutable only numeracy?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 17, 2024

Wed, 17 Apr 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 17, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 200: Mathematicians or Math-ers?

Tue, 16 Apr 2024 00:00:00 -0500

We're so excited to celebrate our 200th episode with you! In this episode Pam and Kim change up their intro and discuss how the things they've learned continue to shape how they spread the Math is FigureOutAble movement today.
Talking Points:
200 Episodes!!!

Is the math mathing?
Pam, a former mimicker
Perspectives versus distortions
Kim, a reasoner who can now share her thinking
Algorithms are amazing historical feats, but not good teaching tools!
The reason for math class

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 10, 2024

Wed, 10 Apr 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 10, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 199: Numberblocks

Tue, 09 Apr 2024 00:00:00 -0500

Real math is never fun and cute, or is it? In this episode Pam and Kim discuss a cartoon they've fallen in love with that builds number sense intuitively and entertainingly.
Talking Points:

What is Numberblocks? What makes it stand our?
Different representations of numbers
Squares
Doubling
Math symbols
Odd and even
Who is Numberblocks for?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - April 3, 2024

Wed, 03 Apr 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 3, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 198: Look Fors for School Wide Vision

Tue, 02 Apr 2024 00:00:00 -0500

What can schools use to create a shared vision for math instruction? In this episode Pam and Kim discuss the New York Department of Education's Look Fors for School-Wide Mathematics Teaching and Learning.
Talking Points

Who is this Look For for?
Specifics for equity around scheduling teachers with an eye on content knowledge and pedagogy
Making space for observing, sharing, and discussing teaching practices that engage students with challenging mathematics
Share the school's vision throughout all parent communication and events
The importance of shared vision about pathways for students to have access to high quality math

Find the Look Fors here:
For Students
For Teachers
For Schools

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 27, 2024

Wed, 27 Mar 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 27, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 197: Look Fors for Teachers

Tue, 26 Mar 2024 00:00:00 -0500

What conversations can teachers and coaches have about improving instruction in the classroom? In this episode Pam and Kim discuss the Look Fors for Teachers provided by the New York Department of Education.
Talking Points:

Coaching requires more than observation or modeling a lesson
Avoid analysis paralysis
Coaching through conversation
How to inform your in-the-moment decisions
Maintain students' opportunities to develop their own ideas and understandings
Creating a shared vision

Find the Look Fors here:
For Students: https://drive.google.com/file/d/1spWxDFP_FRVGFkNmWAjGxKnDscGSctYD/view
For Teachers:
https://drive.google.com/drive/u/0/folders/1zZI4Y1MLr1DzSwtm_EK3KDC6Re3L62zn

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 20, 2024

Wed, 20 Mar 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 20, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 196: Look Fors for Students

Tue, 19 Mar 2024 00:00:00 -0500

What goals do you have for your classroom? How do you measure your success? How to plan to achieve those goals? In this episode Pam and Kim discuss New York City's Look Fors for Students and how they can help us focus on the changes we want to see in our classrooms.
Talking Points:

Kim and Pam have different styles and personalities as the approach planning a lesson or session
Taking time to think deeply about a lesson
New York City's Look Fors
Kim and Pam highlight a Look For
To avoid burnout, innovate in bursts

Find the Look Fors for Students here: https://drive.google.com/file/d/1spWxDFP_FRVGFkNmWAjGxKnDscGSctYD/view

Find other resources from New York City here: https://sites.google.com/view/nyc-math-resources/home

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 13, 2024

Wed, 13 Mar 2024 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 13, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 195: Early Addition Important Relationships

Tue, 12 Mar 2024 00:00:00 -0500

When should you start developing which relationships? In this episode Pam and Kim discuss the important addition relationships for first grade and how to develop them throughout the year.
Talking Points:

When do I teach what?

Download The Most Important Numeracy Strategies Free Ebook!
We want students to understand relationships so that strategies are natural outcomes, not memorized procedures.
Partners of Ten
Doubles
Plus ten
Modeling is super important

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - March 6, 2024

Wed, 06 Mar 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 6, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 194: Quarter Strategy for Multiplication

Tue, 05 Mar 2024 00:00:00 -0600

Can we really be efficient in solving multiplication problems without algorithms? What about the really cranky ones? In this episode Pam and Kim discuss the quarter strategy- a clean, efficient, figureoutable way of solving traditionally difficult multiplication problems.
Talking Points:

Baby strategies! What?!
A problem string for the Quarter Strategy
COMING SOON! Problem String books: A shared vision for how we could develop the major relationships for each operation, with strings for ALL year

Click here for more information on "Using Quarters" https://www.mathisfigureoutable.com/quarters

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 28, 2024

Wed, 28 Feb 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 28, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 193: Compliance Too

Tue, 27 Feb 2024 00:00:00 -0600

What message do we want to send to students about compliance? In this episode Pam and Kim talk about the importance of respecting student dignity and separating math from punishment.
Talking Points:

Senario of compliance
Reasons we seek compliance from students
Math is not a punishment or taking it away, a reward
Pam and Kim reflect on some of their early experiences
Is it about the math or about the compliance?
Do your grades reflect compliance?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 21, 2024

Wed, 21 Feb 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 21, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 192: Compliance - What do you require in a math class?

Tue, 20 Feb 2024 00:00:00 -0600

A huge part of any teacher's life is classroom management, setting expectations, and compliance. In this episode Pam and Kim consider when compliance might or might not be helpful in a math classroom.
Talking Points:

Sucked down the Math Is Figureoutable vortex
Would you rather have compliant students? Or have students who question?
There are times when compliance is important
Kim and Pam's early experiences with compliance
Negative consequences for non-compliance aren't always helpful
Creating a learning atmosphere
Model your expectations
Time for reflection not finger wagging

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 14, 2024

Wed, 14 Feb 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 14, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 191: PEMDAS Is Figureoutable

Tue, 13 Feb 2024 00:00:00 -0600

Thinking and reasoning is always more powerful than rotely memorizing steps. In this episode Pam and Kim demonstrate how to help students reason about Order of Operations.
Talking Points:

Nat Banting's "Oops, I Meant"
Representing a context using the grouping symbols to communicate
Demonstrate how mathematicians communicate with symbols earl
Using the equals sign correctly to mean "equal" vs "Do it""
No more unnecessarily difficult practice

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - February 7, 2024

Wed, 07 Feb 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 7, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 190: The Problem With PEMDAS

Tue, 06 Feb 2024 00:00:00 -0600

Order of operations seems more rote memorizable than figure-out-able, or is it? In this episode Pam and Kim discuss the pitfalls of teaching order of operations as an acronym to memorize, and offer a better alternative.
Talking Points:

It's about communication rather than a thing to memorize.
The notation is social knowledge.
The order is logical mathematical knowledge and therefore figure-out-able!
Open-middle problems for meaningful practice.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 31, 2024

Wed, 31 Jan 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 31, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 189: The Operator Meaning of Fractions

Tue, 30 Jan 2024 00:00:00 -0600

Finding a fraction of something can be a tricky concept. In this episode Pam and Kim run through two strings that help reason about using fractions as operators.
Talking Points:

How are unit fractions related like halves, fourth and eighths?
Scaling and Over Strategy with unit fractions
Fractions as operators
Why is scaling a unit fractions critical? Knowing that three fourths is the same as three 1/4s?
Knowing non-unit fractions from fractions is a precursor.
Thinking of fractions only as part-whole is not sufficient.
A different problem string using the operator meaning of fractions.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 24, 2024

Wed, 24 Jan 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 24, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 188: The Whole Matters

Tue, 23 Jan 2024 00:00:00 -0600

Does it really matter what we call the whole? In this episode Pam and Kim take a closer look at fraction problems where the unit matters.
Talking Points:

Kim and the beach
How can there be 2 possible answers to the question "What is 1/2?"
Focusing on the unit
Naming the unit
What happens when the unit changes?
Help students focus on the unit, changing the unit, and finding a fractional amount of that new unit
Even test writers struggle with fractions
Re-unitizing will support students to reason through fraction multiplication

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 17, 2024

Wed, 17 Jan 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 17, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 187: Getting Answers to Fraction Problems is Not Enough

Tue, 16 Jan 2024 00:00:00 -0600

How many people do you know that shy away from fractions? In this episode Pam and Kim discuss why teaching students to use step by step procedures to solve fraction problems actually leaves them not able to think about fractions at all.
Talking Points:

We love hearing your stories!
What kind of reasoning do fractions engage?
What happens when students learn to mimic steps rather than reason about fractions?
What does reasoning about fractions look like?
Are least common denominators really that important?

See Episode 5, 67, 68 for more about Development of Mathematical Reasoning

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 10, 2023

Wed, 10 Jan 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 10, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 186: Subtracting Integers - Add The Opposite

Tue, 09 Jan 2024 00:00:00 -0600

Minus-minus, plus-plus, or is integer subtraction actually figureoutable? In this episode Pam and Kim use a Problem String to build real understanding of integer subtraction.

Talking Points:

The importance of having multiple contexts
Seeing the negative symbol as "opposite of"
Using distance
Understanding takes time, but is so worth it!

See Episodes 181-183 for more about Integer operations.
See Ep 242 for more information on Integer Multiplication

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - January 3, 2024

Wed, 03 Jan 2024 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 3, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 185: Tracking

Tue, 02 Jan 2024 00:00:00 -0600

Tracking students and sorting them into 'higher'/'lower' tracks is a topic that we have really, really firm feelings about. In this episode Pam and Kim discuss the unintended consequences of tracking students and offer some ideas to consider.

Talking Points

Who does tracking benefit, who does it hurt?
Distaste for the vocabulary used to describe tracks of kids
Everyone can do more real math than fake math
From our experience as a teacher
From our experience as a parent
From a student's perspective

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 27, 2023

Wed, 27 Dec 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 27, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 184: Revisiting - But I'm Required To Teach Algorithms

Tue, 26 Dec 2023 00:00:00 -0600

Happy holidays! Pam and Kim invite you to revisit Ep 87, it's super important! How do you navigate teaching math that is figure-out-able if your standards include the teaching of algorithms?
Talking Points:

All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems.
Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year.
Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and become good mathematicians.
Introduce the algorithm as a study of why the algorithm works for the very end of the year. Introducing the algorithm too early in the year risks giving students the option to turn their brains off.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 20, 2023

Wed, 20 Dec 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 20, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 183: Integer Subtraction

Tue, 19 Dec 2023 00:00:00 -0600

Can integer subtraction feel intuitive without rote memory? In this episode Pam and Kim delve into a Problem String and explore integer subtraction relationships.
Talking Points:

Integer chips?
Students reason about subtracting integers
Distance versus removal
Problem String subtracting integers in context
When context is less helpful
Don't go to rules, stay in reasoning

See Episodes 149 and150 for more about distance vs removal
See Ep 242 for more information on Integer Multiplication

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 13, 2023

Wed, 13 Dec 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 13, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 182: Integer Addition

Tue, 12 Dec 2023 00:00:00 -0600

Mimicking rules for integer operations does not help students become doers of Real Math, and frankly doesn't often stick in their long term memory. In this episode Pam and Kim walk through a Problem String that helps students develop an intuitive understanding of integer addition!
Talking Points:

Exploring the beach as a context
Equations and number lines in context
Carefully chosen numbers to avoid distracting cognitive load
Subtraction symbol or adding a negative? Parentheses or not?
Let students grapple, then support and help make sense of ambiguity

See Ep 242 for more information on Integer Multiplication

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - December 6, 2023

Wed, 06 Dec 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 6, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 181: Integers

Tue, 05 Dec 2023 00:00:00 -0600

How can we help students reason about integers? In this episode Pam and Kim discuss fun and natural ways to explore and understand both positive and negative integers.
Talking Points:

The Pen/Pencil argument continues
5th graders can reason about integers
Games do develp understanding of integers
Clothes line math with integers
Exploring four useful contexts for integers

See Ep 242 for more information on Integer Multiplication

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 29, 2023

Wed, 29 Nov 2023 13:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 29, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 180: Revisit With a Twist - An Important Subtraction Pitfall

Tue, 28 Nov 2023 00:00:00 -0600

How do you label fractions on an open number line? How do you label a fraction of a candy bar? How many cuts do you make to cut a candy bar into fourths? Pam and Kim invite you to revisit episode 138, this time with an ear towards fractions.

Do your students ever get confused about counting obects vs counting distance? In this episode 138 Pam and Kim use a Problem String to help build intuition about everyday subtraction problems.
Talking Points:

Experience a Problem String to build relationships
Fencepost Problems are all over the place
Students can't just pluck numbers out of Fencepost problems
Cathy Fosnot's replacement unit, "Measuring For the Art Show"
Other places these kind of problems show up
Kim explains her strategy

See episode 111 for more about "Measuring for the Art Show"!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 22, 2023

Wed, 22 Nov 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 22, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 179: Fake Math, Not Fake People

Tue, 21 Nov 2023 00:00:00 -0600

What does it mean when we say 'fake math' or 'less sophisticated'? Pam and Kim discuss how learning Real Math is empowering and opens a whole new world of understanding.
Talking Points:

Are squared numbers an important thing to own?
The Matrix
It takes experience to understand perspectives
Martians
Doing 'fake math' or using a 'less sophisticated' way of thinking does not make the person fake or unsophisticated
Real math is empowering and can open up a new reality!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 15, 2023

Wed, 15 Nov 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 15, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 178: Talking Math With Your Kids: Division With Decimals

Tue, 14 Nov 2023 00:00:00 -0600

We can be our own kids' best teachers, even when it comes to gnarly division problems. In this episode Pam and Kim relay their experiences exploring decimal division with their own kids.
Talking Points:

A tool for holding your thinking - a ratio table
It's not about how much you can hold in your head
Help them start with what they know
Problem Strings are not about answering just the last problem
It isn't about being able to solve every problem
It's about owning the major relationships in order to think like a mathematician

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 8, 2023

Wed, 08 Nov 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 8, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 177: NCTM Conference Reflections

Tue, 07 Nov 2023 00:00:00 -0600

Recorded live from NCTM! Pam and Kim discuss some of their experiences and takeaways from the 2023 National Council of Teachers of Mathematics conference.
Talking Points:

Travel stories
As kids grow, teachers grow as well
Know your content know your kids to choose Problem Strings for your students
Tools that focus on answer getting stifle students reasoning
Using a neutral response to keep students and adults continue their thinking
We all need to understand the content - teachers and learning

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - November 1, 2023

Wed, 01 Nov 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 1, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 176: Place Value and Exploding Dots

Tue, 31 Oct 2023 00:00:00 -0500

Place value is so much more than labeling digits. In this episode Pam and Kim dive into place value and common teaching practices that are necessary, but not enough.
Talking Points:

A fascination with the macabre
Typical place value labeling and additional things you can think about to develop place value
Precise questioning yields deeper place value thinking
What are Exploding Dots?
More about our place value system
Practicing expanded notation is not enough

You can register for the Place Value Mini-Workshop now! Don't miss your opportunity to transform your math teaching: https://www.mathisfigureoutable.com/mini

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 25, 2023

Wed, 25 Oct 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 25, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 175: The Most Sophisticated Division Strategy

Tue, 24 Oct 2023 00:00:00 -0500

Division is figure-out-able! In this episode Pam and Kim discuss the most sophisticated strategy for division and precursors that students can begin developing in the fourth grade!
Talking Points:

An Equivalent Ratios Problem String
Precursor relationships
Scaling up or Scaling down
What makes Equivalent Ratios the most sophisticated strategy for division
4th grade can begin to reason about division using the "bigger, smaller thing" to reason about division
5th grade can begin to reason about equivalence
Relational thinking

See Ep 64 and 132 for more on equivalent ratios!
Checkout mathisfigureoutable.com/relational-thinking for free exercises to develop the equivalent ratios strategy..

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 18, 2023

Wed, 18 Oct 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 18, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 174: The Most Sophisticated Multiplication Strategy

Tue, 17 Oct 2023 00:00:00 -0500

Our students can learn to approach math problems like mathematicians! In this episode Pam and Kim look at one of the most sophisticated multiplication strategies that many mathematicians use.
Talking Points:

Creating an equivalent problem by Doubling and Halving.
What makes a problem reasonable to solve without a calculator?
Double/Halve; Triple/Find a Third; Quadruple/Find a fourth
What makes Doubling and Halving one of the most sophisticated multiplication strategies
Flexible Factoring - for more information see Ep 153
Pitfalls of direct teaching and strategy

Check out the Instructional Routine called Relational Thinking at: mathisfigureoutable.com/relational-thinking

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - October 11, 2023

Wed, 11 Oct 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 11, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 173: The Most Sophisticated Subtraction Strategy

Tue, 10 Oct 2023 00:00:00 -0500

Some subtraction strategies can only get you so far, but with a little more sophistication complex problems become really nice to think and reason about! In this episode Pam and Kim build and discuss the Constant Difference strategy for subtraction and use it to solve a really gnarly problem.
Talking Points:

Equivalence strategies are more sophisticated
Hallmarks of sophisticated stategies
Modeling Constant Difference
Relational Thinking Routine

#MathStratChat - October 4, 2023

Wed, 04 Oct 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 4, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 172: The Most Sophisticated Addition Strategy

Tue, 03 Oct 2023 00:00:00 -0500

What makes a strategy sophisticated? In this episode Pam and Kim build the most sophisticated strategy and talk about how and why to develop it with students.
Talking Points:

What are the most sophisticated strategies?
Strategies that require more simultaneity require more time to develop
Simultaneous versus sequential
Representing Give and Take
We need more than one strategy

#MathStratChat - September 27, 2023

Wed, 27 Sep 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 27, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 171: Tips For Parents, Part 2

Tue, 26 Sep 2023 00:00:00 -0500

Kids learn best with support from their parents, and helping with math has never been easier! In this episode, Pam and Kim are excited to share some tips about how to encourage your children as they grow in mathematical thinking and reasoning.
Talking Points:
Wait a little longer

Resist the urge to tell the right answer
Ask questions to cement the thinking
Counting on and back from numbers other than one
Guess my Number
Discuss fractions by their unit fractions
Compare fractions using landmarks

Get all these tips and more at https://www.mathisfigureoutable.com/parenttips

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 20, 2023

Wed, 20 Sep 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 20, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 170: Tips For Parents, Part 1

Tue, 19 Sep 2023 00:00:00 -0500

This one's for all you, parents! How can you support your children in becoming mathematicians? In this episode Pam and Kim go over their favorite ways to explore math at home in fun game-like activities.
Talking Points:
Speak about math positively

Wondering
Doubling and Halving
Using 10s to find 9s and using 10s to find 5s
I Have, You Need

Get the free download: https://www.mathisfigureoutable.com/parenttips

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 13, 2023

Wed, 13 Sep 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 13, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 169: Graphing, Integers, Quadrants, Oh My!

Tue, 12 Sep 2023 00:00:00 -0500

Can you reason about what it means for a point to be within a given quadrant? Can your students? In this episode Pam and Kim discuss weather and geography to develop understanding of the quadrants in the cartesian coordinate system.
Talking Points:

Understanding points relative to their quadrants and the y = x line
Kim's connection to Alaska
What makes Australia so unique
Graphing inequalities is Figure-Out-Able!

See Ep 242 for more information on Integer Multiplication

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - September 6, 2023

Wed, 06 Sep 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 6, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 168: Guessing in Math Class

Tue, 05 Sep 2023 00:00:00 -0500

Let's do some guessing! In this episode Pam and Kim develop some functional reasoning by analyzing the relationships between their guesses and reality.
Talking Points:

Pam's guesses using her pop culture knowledge
How would you know if you are a good guesser?
Graphing guesses and actual age as an ordered pair
Using the data to discuss the meaning of y=x
The parent function for building all functions

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 30, 2023

Wed, 30 Aug 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 30, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 167: How, What, Why to Change Math Class

Tue, 29 Aug 2023 00:00:00 -0500

What does it mean for math to be figure-out-able? What will you teach? How? Why? In this episode Pam and Kim discuss their thoughts to changing the "how" and "what" of math education around the world and explore the "why".
Talking Points:

"What" math we teach should come first
"How" the math should be embedded in the "what"
What Pam and Kim think about "Why" make the change?

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 23, 2023

Wed, 23 Aug 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 23, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 166: Just In Time Vocabulary vs Key Words

Tue, 22 Aug 2023 00:00:00 -0500

What role does terminology have in math teaching? How do we want students to approach problems? In this episode Pam and Kim discuss when to teach vocabulary how we can prepare students to tackle problems with confidence.
Talking Points:

"Just In Case" vs "Just In Time" vocabulary
Social Knowledge vs Logical Mathematical Knowledge
Anchor Charts to cinch learning
Rejecting key words for operations
Wrong answers are opportunities for good teacher feedback

For more about Anchor Charts check out Episode 123

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 16, 2023

Wed, 16 Aug 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 16, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 165: Where Popular Things Go Wrong

Tue, 15 Aug 2023 00:00:00 -0500

There is so much that is good happening in the math teaching community! In this episode Pam and Kim discuss how we can determine how much of which good things to put into our classrooms.
Talking Points:

Going beyond nixing tricks
Social versus logical knowledge
Nixing the tricks is more than explaining the math better
The dangers of going all in on any good teaching practice
- Number Talks
- Exploding Dots
- Manipulatives
Keep asking for clarification and refining your craft in order to create mathematicians in your classroom

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 9, 2023

Wed, 09 Aug 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 9, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 164: I Have, You Need With a Twist

Tue, 08 Aug 2023 00:00:00 -0500

Who does not love a quick, easy routine that gives students useful problem solving relationships? In this episode Pam and Kim revisit I Have, You Need and apply it with different target numbers.
Talking Points:

Kim and Pam play I Have, You Need often with clocks and marathons
It's not about speed
Goal is reducing cognitive load in the midst of solving other problems
Another goal is building fluency
Other important target numbers for early elementary and even middle and high school students

Get the free I Have, You Need download! bit.ly/ihynroutine

See Episode 7 and 121 for more on I Have, You Need

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - August 2, 2023

Wed, 02 Aug 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 2, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 163: A Problem String Is NOT

Tue, 01 Aug 2023 00:00:00 -0500

What exactly is a Problem String? In this episode Pam and Kim dig into that question and give examples of what a problem string is and is not.
Talking Points:

Pam's conversation with Howie Hua - Problem Strings are not strategies
Example of a helper clunker structure Problem String
What is structure vs strategy?
Example of an equivalent structred Problem String
The power of owning multiple strategies

If you want to hear more about Problem Strings, check out Episodes 71, 72 and 260.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 26, 2023

Wed, 26 Jul 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 26, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 162: Comparing Fractions Pt 2

Tue, 25 Jul 2023 00:00:00 -0500

What are some important relationships that students can use to do Real Math with fractions? In this episode Pam and Kim discuss some important relationships that can help develop deeper understanding about fractions for fractional equivalence and comparison.
Talking Points:

A listener's review
Using benchmark fractions to compare
Using a number line to compare fractions
How does understanding unit fractions help compare ugly fractions?
Why we use symbols to represent complex ideas

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 19, 2023

Wed, 19 Jul 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 19, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 161: Comparing Fractions Pt 1

Tue, 18 Jul 2023 00:00:00 -0500

What if your students could think and reason about the relative sizes of fractions? In this episode Pam and Kim think about where fractions go on clotheslines to show how you can help your students compare fractions without a memorized procedure.
Talking points:

A podcast listener shares her perspective of mathematics as a student
Clothesline Math examples using fractions and percents
Connecting fractions and percents
Generalizing about comparing fractions using reasoning
Help students clarify the meaning of numerators and denominators

Take our math perspectives quiz! http://bit.ly/xyzquiz

See Episodes 24-27 for more about The XYZ Math Perspectives

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - July 12, 2023

Wed, 12 Jul 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 12, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 160: Building Thinking Classrooms and Math is FigureOutAble Pt 3

Tue, 11 Jul 2023 00:00:00 -0500

How we teach and what we teach are both really important. In this episode Pam and Kim wrap up their discussion on Peter Liljedahl's book Building Thinking Classrooms and how it meshes with the Math Is Figure-Out-Able movement.
Talking Points:

When we suggest to defront the classsroom
Don't let language hamper the math for students during a Rich Task
Consolidation versus Math Congress
Use hints and extensions to keep students at the edge of the Zone of Proximal development and that requires knowing the math deeply
Teachers need to know both the "how" and the "what" of the math for students to be successful

See Ep 128 for more about students can do more than they can say and say more than they can represent

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - July 5, 2023

Wed, 05 Jul 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 5, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 159: Building Thinking Classrooms and Math is Figureoutable Pt 2

Tue, 04 Jul 2023 00:00:00 -0500

We think Dr. Peter Liljedahl has some great ideas about how to keep students thinking and reasoning in math class. In this episode Pam and Kim continue to discuss some of his ideas and how they align with the Math is Figure-Out-Able mindset.
Talking Points:
Which questions to answer

Get in, get out
Approach groups with your own question
Using neutral responses

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 28, 2023

Wed, 28 Jun 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 28, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 158: Building Thinking Classrooms and Math Is FigureOutAble Pt 1

Tue, 27 Jun 2023 00:00:00 -0500

We love it when students are thinking and reasoning, and it's important to know how best to build and experience sophisticated strategies. In this episode Pam and Kim continue discussing Dr. Peter Liljedahl's work and finetune where it's appropriate to use vertical nonpermanent surfaces, and what other kind of tasks we should be doing whole class with students.

Talking Points:

Randomized Groups at Vertical Non Permanent Surfaces in random groups are great for Rich Tasks that follow your curriculum
Problem Strings are best used whole class to build specific strategies, models, and big ideas

See Episode 157 for Pam and Kim's introductory comments about Dr. Liljedahl's work.

Check out Pam's social media (I changed this to "Pam's" since it doesn't include mine)
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 21, 2023

Wed, 21 Jun 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 21, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 157: Building Thinking Classrooms

Tue, 20 Jun 2023 00:00:00 -0500

We want our students to be confident problem solvers who can think and reason through complex problems. In this episode, Pam and Kim highlight some of Dr. Peter Liljedahl's work on Building Thinking Classrooms to use student's natural inclinations to help them work better and more collaboratively.
Talking Points:
It's about thinking, not mimicking

Thinking Tasks not mimicking tasks
Vertical Non Permanent Surfaces
Visibly random groups
It takes time for kids to accept working in random groups
Pulse of the room: Are student's opting out? What math are groups using?
The "how " is important, but so is the "what"

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC

#MathStratChat - June 14, 2023

Wed, 14 Jun 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 14, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 156: Start Here

Tue, 13 Jun 2023 00:00:00 -0500

We've reached our third anniversary of the podcast! There's a lot that's been said, so we thought we'd highlight some of the quintessential Pam Harris topics from previous episodes that you need to transform your math classroom. In this episode Pam and Kim blitz through what makes the Math is Figure-out-able Movement so important and unique. They also list out which episodes you can listen to for more information about these key concepts.
Talking Points:

The Development of Mathematical Reasoning: Ep 5, 6, 67, 68
Models vs Strategies: Ep 9
Algorithms Are Not the Goal: Ep 2, 94-99
Different Math Perspectives: Ep 24-28
Problem Strings: Ep 33, 71, 72
Everyone Learns, Everyone Grows: Ep 39
Know Your Content, Know Your Kids: Ep 74
Do, Say, Represent: Ep 128

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - June 7, 2023

Wed, 07 Jun 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 7, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 155: Fraction Division Part 0

Tue, 06 Jun 2023 00:00:00 -0500

Can kids reason about fraction division? In this episode Pam and Kim explore the definition of fractions through a Problem String and show how you can help students build experiences so that fraction division is a natural outcome.
Talking Points:

Can students reason about 1/25 divided by 4?
Dividing parts of candy bars Problem String experience
Discovering the definition of fractions
Kids can intuit!

See Episodes 142-144 for more about fraction division.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - May 31, 2023

Wed, 31 May 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 31, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 154: Will Next Year's Teacher Hate Me?

Tue, 30 May 2023 00:00:00 -0500

It's exciting to watch our students gain confidence and mathematize with the best of them, but what about next year? In this episode Pam and Kim discuss how you can communicate expectations to students and teachers alike to embolden your students that math will always be figure-out-able.
Talking Points:

What is your job for this year?
What do students need to know leaving your classroom to prepare for them for next year?
What does the teacher for next year need to know about your kids coming to them?
Communication is the key

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - May 24, 2023

Wed, 24 May 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 24, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 153: Flexible Factoring

Tue, 23 May 2023 00:00:00 -0500

How sophisticated is your multiplicative reasoning? In this episode Pam and Kim build Flexible Factoring and show how powerful understanding can be!
Talking Points:

We love hearing from listeners!
A Problem String
Develping distributive, associative and commutative properties
Where does Flexible Factoring fit into Multiplicative Reasoning?
Why understanding and owning multiplication facts is more powerful than memorization

For more information about the Development of Mathematical Reasoning, see Episodes 5 and 6.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - May 17, 2023

Wed, 17 May 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 17, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 152: Changing Math Habits

Tue, 16 May 2023 00:00:00 -0500

How do you naturally approach math problems? How do you wish you would naturally approach problems? In this episode Pam and Kim discuss how we as teachers and our students can form powerful new habits to become better mathematicians.
Talking Points:

We all have habits based on our own experiences
Can we change our old habits?
Is it easy to change old habits?
Do you have to know the most efficient strategy when you start messing with a problem?
Can you change your mind about which strategy you want to use after you have started working with a problem?
How long does it take a student's numeracy to grow?
Want to change some of your mathematical habits?

You can register for one of our fantastic online workshops now! The brand new Building Powerful Subtraction workshop is available, as well as all of the workshops from previous years. Don't miss your opportunity to transform your math teaching: https://www.mathisfigureoutable.com/workshops

Want to know which workshop is for you? Take this quiz: https://bit.ly/whichworkshop

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - May 10, 2023

Wed, 10 May 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 10, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 151: Subtraction Facts

Tue, 09 May 2023 00:00:00 -0500

How can we help students own subtraction facts? In this episode Pam and Kim describe some basic strategies and then walk us through facilitating two Problem Strings to build subtraction relationships.
Talking Points:

I Have, You Need - see Episode 7 for more on I Have, You Need
Patterns in a subtraction chart
Generalizing about subtracting 9
Noticing differences of 1 or 2
Diagonal patterns of Constant Difference
Subtracting to 10 Problem String
Using Doubles Problem String

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - May 3, 2023

Wed, 03 May 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 3, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 150: Memorizing Subtraction Facts

Tue, 02 May 2023 00:00:00 -0500

We're digging deep into subtraction! In this episode Pam and Kim talk about what they mean by "memorizing" single digit subtraction facts and the relationships that can empower students to own single digit facts and apply the same relationships to more sophisticated numbers as well.
Talking Points:

The different meanings of "memorize the facts"
Relying on rote memory of facts in isolation leaves students with no other recourse
"No timed drills" does not mean no work on facts, but different work
Remove to 10
Using Doubles
Find the Difference
Remove a Friendly Number Over
Relationships are built, not rote-memorized

See episode 149 for more about the two meanings of subtraction

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - April 26, 2023

Wed, 26 Apr 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 26, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 149: Subtraction: The Operation That Will Surprise You

Tue, 25 Apr 2023 00:00:00 -0500

There's so much power to understanding subtraction that extends all the way to higher math. In this episode Pam and Kim discuss beginning steps to help students develop an understanding of subtraction, preparing them for success.
Talking Points:

How does I Have, You Need apply to subtraction?
Subtracting across zeros is a beast! So what do we do?
Where subtraction helps in multiplication, division and beyond
Understanding removal versus difference
Why is this important for higher math?
What happens if we force kids into steps?
What you can do to help your students?

See Episode 150 for more about "Memorizing Subtraction Facts"

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - April 19, 2023

Wed, 19 Apr 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 19, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 148: Not the Area Model

Tue, 18 Apr 2023 00:00:00 -0500

Establishing a strong understanding of the area model also prepares students for more advanced topics all the way into college! In this episode, Pam and Kim describe how useful the area model is as a foundation for further understanding throughout a student's learning career.
Talking Points:

Using the area model builds intuition of the distributive property
Using and understanding the area model for fraction multiplication
Paradigm shift for teachers to think about what students know about whole numbers and apply it to fractions
The area model as a tool, not something that is sketched for every problem
Area model inspired graphic organizer for polynomial multiplication, polynomial division, and conics

See Episodes 146 and 147 for more discussion of the Area Model
Check out the new t-shirt at https://www.mathisfigureoutable.com/merchandise

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - April 12, 2023

Wed, 12 Apr 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 12, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 147: The Area Model to Build Reasoning

Tue, 11 Apr 2023 00:00:00 -0500

The area model can do more than build Spatial Reasoning. It can help make sense of the major multiplication and division strategies! In this episode Pam and Kim use a Problem String to show how reasoning about area can build more sophisticated and efficient multiplicative relationships.
Talking Points:

Multiplication is about grouping groups
The area model can help make sense of multiplicative relationships and properties
Choose and celebrate efficient strategies
Reasoning about area makes relationships pop so that the strategies are natural outcomes!

See this blog for a picture of Pam's model in this episode: https://www.mathisfigureoutable.com/blog/ep147
See Episodes 146 and 148 for more discussion of the Area Model
Check out the new t-shirt at https://www.mathisfigureoutable.com/merchandise

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - April 5, 2023

Wed, 05 Apr 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 5, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 146: (Mis)Understanding the Area Model

Tue, 04 Apr 2023 00:00:00 -0500

The area model is a great tool to help students develop multiplicative and spatial reasoning, but let's get clear on some things. In this episode Pam and Kim discuss some of the common misconceptions about the area model and show how it can be used help students make connections between area and multiplication.
Talking points:

What is an area model?
Common misunderstanding around an area model
Place Value Partial Products vs Smart Partial Products
Rote memorizing perspective vs Math-is-figureoutable perespective
Closed/Discrete versus Open arrays
Area models build spatial reasoning and connections of products to area and factors to dimensions
Ratio Tables are better models for cranky computation problems

See Episodes 129-133 for more about Ratio Tables and 147 and 148 for more about the Area Model.

Check out the new t-shirt at https://www.mathisfigureoutable.com/merchandise

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - March 29, 2023

Wed, 29 Mar 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 29, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 145: Transforming Teaching: Small Shifts, Big Impact

Tue, 28 Mar 2023 00:00:00 -0500

There are a lot of small shifts needed in math education, and they can have huge impacts. In this episode Pam and Kim talk about some of these shifts that will be included in the new mini workshop. This workshop will help you address the most important things to get right as a math teacher.
Talking Points:
Algorithms verses strategies
Models verses strategies
Common vocabulary
A few major relationships lead to the major strategies
Problem Strings versus Problem Talks
Major Strategies ebook

Check out the mini workshop https://www.mathisfigureoutable.com/mini

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - March 22, 2023

Wed, 22 Mar 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 22, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 144: Fraction Division Pt 3

Tue, 21 Mar 2023 00:00:00 -0500

Sure, simple fraction division is figure-out-able, but what about gnarly fractions? In this episode Pam and Kim uncover simple relationships that make division of any fractions figure-out-able!
Talking points:

What happens when the fractions aren't as nice, especially fractions where their denominators are not factors of each other?
Thinking quotitively
The connection between division and fractions
Find common denominators to divide
Use relative size of the fractions to estimate the quotient
We don't teach rules for students to mimic, we develop relationships

See Episodes 142, 143 and 155 for more about fraction division.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - March 15, 2023

Wed, 15 Mar 2023 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 15, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 143: Fraction Division Pt 2

Tue, 14 Mar 2023 00:00:00 -0500

Fraction division does not have to be scary, and it certainly does not have to be memorized. In this episode Pam and Kim show how to reason through non unit fraction division problems.
Talking Points:

What is a unit fraction?
What does it mean to think quotitively about division?
A Problem String building on unit fraction understanding for division of non unit fractions
How to model this Problem String
Using whole number relations among fractions
Fraction division is accessible!

See Episodes 142, 144 and 155 for more about fraction division.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - March 8, 2023

Wed, 08 Mar 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 8, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 142: Fraction Division Pt 1

Tue, 07 Mar 2023 00:00:00 -0600

Is fraction division figure-out-able? You bet! In this episode Pam and Kim tackle another listener submitted topic and reason through a fraction division Problem String.

Talking Points:

A sign of fake math
An old wound for Pam and Kim
A listener's question
Two ways of thinking about division: partitively and quotitively
A Problem String to develop division of fractions
Why it helps to develop reasoning early with whole numbers
Teacher moves to facilitate the string

See Episode 64 for another Problem String and discussion of thinking about quotitive division.
See Episodes 143, 144 and 155 for more about fraction division.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - March 1, 2023

Wed, 01 Mar 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 1, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

Ep 141: Questioning Questioning

Tue, 28 Feb 2023 00:00:00 -0600

As teachers we want to help our students, and often we do that through questioning. In this episode Pam and Kim discuss how maybe there isn't a perfect list of questions, but it's our pattern of questioning that matters.
Talking Points

We love hearing your suggestions
Focusing on a list of questions vs a pattern of questioning
Funneling pattern of questioning vs. Focusing pattern of questioning
Focusing is more like a conversation rather than a list of questions
To focus students you need to know your content, know your kids
Examples through the grade levels

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - February 22, 2023

Wed, 22 Feb 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 22, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 140: Cancel Simplifying

Tue, 21 Feb 2023 00:00:00 -0600

Have you ever noticed how many different meanings there are for the word simplify? Even if you limit it to mathematical meanings, there's a lot. In this episode Pam and Kim discuss how we can better communicate with students what we really want them to do when we say 'simplify.'
Talking Points:

Asking students to 'simplify' can often be a guessing game as to what we really want students to do.
Why not level the playing field?
Some meanings of "simplify" can be contradictory.
There are better ways to ask students what we actually mean for them to do when they see that word "simplify".

See episode 18 "This, Not That" for other examples of unhelpful words sometimes used in math teaching.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - February 15, 2023

Wed, 15 Feb 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 15, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 139: Factor to Add and Subtract!?

Tue, 14 Feb 2023 00:00:00 -0600

Happy Valentines Day! We love math, and we love you, our listeners! In this episode Pam and Kim discuss a less familiar addition and subtraction strategy that they're coming to love more and more.
Talking Points:

A Problem String to build relationships in order to use common factors in addition and subtraction problems
Why is it not a main strategy?
Where and why teach it anyway?

Find our free e-book here! https://www.mathisfigureoutable.com/big

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - February 8, 2023

Wed, 08 Feb 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 8, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 138: To Include or Not: An Important Subtraction Pitfall

Tue, 07 Feb 2023 00:00:00 -0600

Do you ever fall into the "off by one" trap? Do your students ever get confused about counting objects vs counting distance? In this episode Pam and Kim use a Problem String to help build intuition about everyday subtraction problems.
Talking Points:

Experience a Problem String to build relationships
Fencepost Problems are all over the place
Students can't just pluck numbers out of Fencepost problems
Cathy Fosnot's replacement unit, "Measuring For the Art Show"
Other places these kind of problems show up
Kim explains her strategy

See episode 111 for more about "Measuring For the Art Show"!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - February 1, 2023

Wed, 01 Feb 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 1, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 137: ChatGPT Artificial Intelligence in Math Education

Tue, 31 Jan 2023 00:00:00 -0600

The world is changing, and artificial intelligence is going to replace teachers! ...Or not. In this episode Pam and Kim discuss how teaching Real Math is more important now than ever, and we don't have to be afraid of those pesky robots.
Talking Points:

How Chat GPT is different from AI like Photomath
A teacher's paradigm will influnce how much AI will change the way we teach math
Will the future of AI change the way we think about grading and homework?
Does the future if AI promote answer getting or deeper understanding?
Why Real Math is so important
Teachers are going to need a support system to navigate the change.

Try out Chat GPT here: https://chat.openai.com/chat

Registration for our workshops and Journey is now open! Find what help is best for you at https://www.mathisfigureoutable.com/workshops

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - January 25, 2023

Wed, 25 Jan 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 25, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Ep 136: How Helpful is Too Helpful?

Tue, 24 Jan 2023 00:00:00 -0600

When do you offer students help and what kinds of help do you offer? In this episode Pam and Kim discuss the balance of what kinds of help to give students and also where to find just the right help as teachers.
Talking Points:

Encouragement alone isn't enough help
Modeling thinking doesn't mean to take over the thinking
Funneling vs focusing patterns of questioning
Does your help create mathematicians or learned helplessness?
Teachers also need just the right amount and kind of help

Registration for our workshops and Journey is now open! Find what help is best for you at https://www.mathisfigureoutable.com/workshops

See also Episode 113 for more discussion about helping students.

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - January 18, 2023

Wed, 18 Jan 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 18, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 135: The Challenge

Tue, 17 Jan 2023 00:00:00 -0600

What does it take to change our perspectives so we can teach more and more Real Math? In this episode Pam and Kim discuss how they can help YOU when you join the You Can Change Math Class Challenge!
Talking Points:

What is the Challenge anyway?
Is the math you do at home different from the math you do in school? (Thank you John SanGiovanni)
What are the major perspectives and how can I learn more about them?
How does the perspective of how I was taught affect how I teach?

Register for the challenge here! https://www.mathisfigureoutable.com/change
Get the free ebook here! https://www.mathisfigureoutable.com/big

For more on the perspectives we talked about see episodes 24-28, and take the quiz to learn more about your perspective! https://www.mathisfigureoutable.com/xyz

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - January 11, 2023

Wed, 11 Jan 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 11, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 134: How Do You Know You're in a Mathematizing Classroom?

Tue, 10 Jan 2023 00:00:00 -0600

We have heard from both teachers and leaders that it's a struggle to know what to look for in a Math is Figure-out-able classsroom and how to evaluate it, and help each other better our teaching craft. In this episode Pam and Kim go through the NCTM Effective Teaching practices and discuss and suggest conversations about how those standards look in a Math is Figure-out-able classroom.
Talking Points:

What does it mean to "establish mathematics goals to focus on learning"?
What do tasks that "promote reasoning and problem solving" vs direct teaching look like?
What all is entailed in "connecting matematical representations"?
Why is "meaningful mathematical discourse" critical and what does it sound like? (listen to Episode 128 for more about Do, Say, Represent)
What do "purposeful questions" sound like? The difference between funneling vs focusing questions.
How we tweak "build (procedural) fluency with conceptual understanding"?
What is "productive struggle"? Do you need time, or help? (listen to Episode 113 for more about productive struggle)
What do tasks or problems look like that "elicit evidence of student thinking" then "use the thinking" to move the math forward?

Don't forget to join the You Can Change Math Class Challenge! Register at mathisfigureoutable.com/change

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - January 4, 2023

Wed, 04 Jan 2023 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 4, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 133: The Ratio Table, Pt 5

Tue, 03 Jan 2023 00:00:00 -0600

It's our wrap up episode on ratio tables. In this episode Pam and Kim answer some frequently asked questions and talk about how we can take ratio tables into higher math and beyond.
Talking Points:

Why teachers erase and when should students erase?
Do, Say, Represent: how to help students represent what's going on in their heads
Ratio tables aren't a gimmick, they make thinking visiable of how mathematicians and other mathy people think for the masses
Using ratio tables to notice patterns and reason using mathematical relationships in order to write the equation of a line
Using ratio tables to reason about rational functions and transformations

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - December 28, 2022

Wed, 28 Dec 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 28, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 132: The Ratio Table Model Pt 4

Tue, 27 Dec 2022 00:00:00 -0600

It's time to talk equivalent ratios and fractions! In this episode Pam and Kim demonstrate how understanding equivalent ratios leads to powerful reasoning about fraction operation, without the need to memorize steps and rules or algorithms.
Talking Points:

Empowerment is about having choice
Ratio tables aren't a strategy, they're a model/representation of the strategy or strategies being used
If you understand fractional equivalence, you don't need rules for fraction operations
How to add 3/4 and 5/7 thinking and reasoning using a ratio table
Do non-equivalent ratios go on the same ratio table? How do you handle adding non-equivalent ratios?

Note: for more information about the packs and sticks of gum scenario, listen to Episode 131
See Ep 64 and 176 for more on equivalent ratios!

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

#MathStratChat - December 21, 2022

Wed, 21 Dec 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 21, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 131: The Ratio Table Model, Pt 3

Tue, 20 Dec 2022 00:00:00 -0600

Have we convinced you to love ratio tables as much as we do yet? In this episode Pam and Kim tackle another model building Problem String to show what a powerful model a ratio table can be.
Talking Points:

A non-unit ratio Problem String
Ratios must be equivalent in a ratio table
Reasoning proportionally can be much cleaner than cross-multiply-and-divide
Model building strings verses strategy building strings
Start with reasoning and representing thinking then dive deeper into properties
What's next? A strategy building string using a ratio table as a model
Don't forget to post how you represented your ratio table on social media!

#MathStratChat - December 14, 2022

Wed, 14 Dec 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 14, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 130: The Ratio Table Model, Pt 2

Tue, 13 Dec 2022 00:00:00 -0600

We can't get enough of ratio tables! In this episode Pam and Kim go through another division Problem String, highlighting how they model-represent their thinking on ratio tables. They invite listeners to grab a pen or pencil and practice representing their own thinking on a ratio table.
Talking Points:

Noticings from MathStratChat
Does context matter?
Does a ratio table have to be in sequential order?
Does it matter when to erase during the Problem String?
Does it matter when to use brackets or arrows?
Can color help highlight relationships?
How do you introduce a ratio table?
A tool to represent thinking that can lead to new thinking

#MathStratChat - December 7, 2022

Wed, 07 Dec 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 7, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 129: The Ratio Table Model Pt 1

Tue, 06 Dec 2022 00:00:00 -0600

Why are ratio tables so amazing? In this episode Pam and Kim describe ratio tables and what makes it on the favorite mathematical models short list. Then they show it off with a Problem String.
Talking Points:

What is a ratio table?
Can ratio tables be both vertical or horizontal?
Does the context of a ratio table matter?
Should you ever erase when using a ratio table?
What else should students see and use besides a ratio table?
A Problem String to model on a ratio table
Some powerful generalizations from the problem string using a ratio table model
Are we done talking about ratio tables?

Online workshop registration opens in January!

#MathStratChat - November 30, 2022

Wed, 30 Nov 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 30, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 128: Do, Say, Represent

Tue, 29 Nov 2022 00:00:00 -0600

Do your students ever say things like, "I just know" or "I don't know"? What can we do with that? How can we help students have meaningful discussions about their thinking and why is it so important? In this episode, Pam and Kim discuss the challenges of saying and representing our thinking, and how we can help students clarify their thinking in order to be able to discuss their strategies.
Talking Points:

When students say "I just know" because they just don't know what else to say or do
We can do more than we can say and say more than we can represent
Do, Say, Represent
The importance of knowing your content and knowing your students
Helping students grapple with and resolve disequilibruim helps clarify and solidify their learning
Stay tuned for upcoming podcast for more about modeling to make student thinking visible

#MathStratChat - November 23, 2022

Wed, 23 Nov 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 23, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 127: The Over Strategy - Division

Tue, 22 Nov 2022 00:00:00 -0600

We're wrapping up our series on the Over strategy. In this episode Pam and Kim reason through a Problem String to develop the Over strategy for division.
Talking Points:

A Problem String to develop relationships for the Over strategy for division
Great teacher move that we call "the trail off method" to help students generalize and justify the relationships they are using
Calling out the relationships vs direct teaching
Where does the Over strategy fit in the hierarchy for division?
Advantage of using a ratio table to model Partial Products vs 'lucky 7' or 'magic 7'
Over strategy is helpful for addition and subtraction, but it is essential for efficient multiplication and division

Be sure to get the BIG download with all of the major strategies! https://www.mathisfigureoutable.com/big

Plus, get the download specifically for building the Over strategy for all four major operations:
https://www.mathisfigureoutable.com/over

#MathStratChat - November 16, 2022

Wed, 16 Nov 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 16, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 126: The Over Strategy - Multiplication

Tue, 15 Nov 2022 00:00:00 -0600

We are not over with the Over strategy! This week Pam and Kim dive into the Over strategy for multiplication.
Talking Points:

A new name for the Double and Half strategy?
A Problem String to develop relationships for the Over strategy for multiplication
Where Over strategy for multiplication fits in the hierarchy of multiplicative strategies
Using the Over strategy to help students begin to use more Smart Partial Products
Be sure to get the BIG download with all of the major strategies! https://www.mathisfigureoutable.com/big
Plus, get the download specifically for building the Over strategy for all four major operations:
https://www.mathisfigureoutable.com/over

#MathStratChat - November 9, 2022

Wed, 09 Nov 2022 23:00:00 -0600

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 9, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 125: The Over Strategy - Subtraction

Tue, 08 Nov 2022 00:00:00 -0600

We just love the Over strategy! In this episode Pam and Kim go through a Problem String to develop the relationships used to think about the Over strategy for subtraction.
Talking Points:

Over strategy is a great experience for people new to thinking Real Math.
The Over strategy is one of the major relationships that students need to own.
A Problem String to nudge the Over strategy.
The Over strategy can be tricky, so students need lots of experience and contexts.
Modeling student's thinking on a number line helps make thinking visiable as they grapple with the relationships.
Teacher moves to modeling that can help support students' thinking.
Where does over subtraction fit in the hierarchy?
Bonus! The Over strategy "uses" place value (not just place labeling)!

Download free examples of the Over Strategy: mathisfigureoutable.com/over
Download the free ebook of major strategies: mathisFigureOutAble.com/big

#MathStratChat - November 2, 2022

Wed, 02 Nov 2022 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 2, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 124: The Over Strategy - Addition

Tue, 01 Nov 2022 00:00:00 -0500

In case you haven't noticed, Kim has a favorite strategy. In this episode Pam and Kim discuss one of the most important strategies and how to use it for addition.
Talking Points:

Great listener feedback!
A Problem String
Where does the Over Strategy fit in the hierarchy of strategies?
How does the Over Strategy help build place value?
Modeling is super important
Where we find the Over strategy day to day

Download free examples of the Over Strategy: mathisfigureoutable.com/over
Download the free ebook of major strategies: mathisFigureOutAble.com/big

#MathStratChat - October 26, 2022

Wed, 26 Oct 2022 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 26, 2022

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 123: Anchor Charts

Tue, 25 Oct 2022 00:00:00 -0500

How can we help cement students' learning without memorizing steps? In this episode Pam and Kim share the power of anchor charts and how you can make them with your students.
Talking Points:

What is an anchor chart?
Why have students co-create the anchor chart with teacher fascilitation?
Why is "Do, Say, Represent" critical for student learning?
What kinds of things go on an anchor chart? Kim suggests 3 things.
When do you create an anchor chart?
Where does an anchor chart go?
When do you refer to an anchor chart?
How can students use the anchor chart as a tool?
What do meaningful notes look like for students' notebooks?

#MathStratChat - October 19, 2022

Wed, 19 Oct 2022 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 19, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others' strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 122: How to Help Students Choose Which Operation in a Word Problem

Tue, 18 Oct 2022 00:00:00 -0500

When dealing with word problems it can be tricky for students to decide which operation to use, so we need a way to help them memorize what to do in any given situation... right? In this episode Pam and Kim discuss how reasoning empowers students to skip rotely memorized steps to choosing operations and get straight to problem solving!
Talking Points:

Word problems feel unfair to students who have only experienced fake math.
Students with reasoning develop intuition for what relationships a problem requires.
Rich Tasks and Problem Strings with mini-contexts prepare students to apply their reasoning to real world contexts.

#MathStratChat - October 12, 2022

Wed, 12 Oct 2022 23:00:00 -0500

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 12, 2022.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others' strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Ep 121: Is This a Major Strategy?

Tue, 11 Oct 2022 00:00:00 -0500

When we teach Real Math, students come up with all sorts of cool strategies! But which ones are the main strategies, and how do we make the distinction? In this episode Pam and Kim take a listener submitted strategy and discuss where and what its uses are.
Talking Points:

The Most Important Numeracy Strategies are a relatively finite set.
Are there other strategies that work and are mathematically coherent?
Why do some strategies not make the short list?
It's not about memorizing the strategies, it is about building relationships to help students become fluent.
The less sophisticated strategies deal with single digits and partials.
The more sophisticated strategies extend to multi-digit numbers and are more important.
Our goal is to help students move to bigger and bigger chunks using more advanced reasoning.
Teachers need to know the Landscape for Learning to recognize and acknowledge students' strategies.

Check out Episodes 7 and 164 of this podcast for more about I Have, You Need
Check out our free eBook to learn more about these strategies: https://www.mathisfigureoutable.com/big

Ep 120: Rounding

Tue, 04 Oct 2022 00:00:00 -0500

What fun rhymes will best help your students learn to round? Just kidding! In this episode Pam and Kim describe their wholistic approach to rounding that helps kids build relationships like place value!
Talking Points:

No rhymes needed.
Modeling on a number line to reason about how far a number is from a landmark.
Keep students reasoning about number with rich experiences.
Conversations about the number line and rounding help develop students' place value and other mathematical concepts.
Students need to understand the math that is figure-out-able and which is social knowledge.
Context is an important part of rounding conversations.
Clothesline math helps students build better intuition about numbers and their relationship to other numbers and rounding conversation can emerge.
I Have You Need helps students find the greater landmark which is harder for students.

Download the guide to playing I Have, You Need HERE

Ep 119: Elapsed Time on a Number Line

Tue, 27 Sep 2022 00:00:00 -0500

Finding elapsed time can be a tricky concept, but when combined with a number line, we can make it figureoutable! Join Pam and Kim as they discuss using addition strategies to find elapsed time.
Talking Points:

Daily schedule on an open number line
I Have, You Need with combinations of 60
How students might approach elapsed time
Three kinds of elapsed time problems

Ep 118: Time and Elapsed Time

Tue, 20 Sep 2022 00:00:00 -0500

Do your students struggle tracking time or reading an analog clock? In this episode Pam and Kim discuss three simple ways you can help your students internalize time and elapsed time.
Talking Points:

Help students build a feel for benchmark units of time
Notice and tell what time it is a lot with kids
Notice aloud how long things take throughout the day

Ep 117: Math is Figureoutable, Even In High School

Tue, 13 Sep 2022 00:00:00 -0500

A lot of people feel like when it comes to high school math, it's just not possible to think and reason through things anymore. Not true! In this episode Pam and Kim make the transition from Proportional Reasoning to Functional Reasoning and writing the equation of a line using relationships and what students already know.
Talking Points:

Is math always Figure-Out-Able?
How ratio tables prepare students for linear functions
Example Problem Strings
Registration for workshops closes this Friday!

Get a workshop while you can: https://www.mathisfigureoutable.com/workshops

Ep 116: Structuring Your Math Class Examples

Tue, 06 Sep 2022 00:00:00 -0500

What does teaching Real Math look like at your grade level? In the last episode Pam and Kim discussed the One Third/Two Thirds rule to structure math time. In this episode they give specific examples at various grade levels of what it might really look like.
Talking Points:

1st Grade - doubling and halving
3rd Grade - concepts around 100
5th Grade - multiplication and volume
7th Grade - rates (see Episode 112 for Unit Rate Problem String)
Algebra I - exponential functions
Pre-Calculus - functions

Our workshops are open for registration! Take advantage now to change your math classroom! https://www.mathisfigureoutable.com/workshops

Ep 115: Structuring Your Math Class

Tue, 30 Aug 2022 00:00:00 -0500

A listener asked how would we structure our math class. In this episode Pam and Kim discuss the approach they'd take to provide their students with the best math education experience possible to learn Real Math and still meet their required standards and scope and sequence.
Talking Points:

The Two-Third/One-Thirds rule
Rich Tasks - see Episodes 102 and 103
Test Prep?!
Use instructional routines for spiral review
Tune in to the next episode for examples

Registration for our workshops are open now! Sessions for everyone, K-12! Check them out!
https://www.mathisfigureoutable.com/workshops

Ep 114: Moving Students Forward Pt 2

Tue, 23 Aug 2022 00:00:00 -0500

The school year is starting! For this exciting time, Pam and Kim want to discuss what starting strategies can help you and your students to build thinking relationships and strategies rather than simply answer getting.
Talking Points:

Problem Talks are great ways to pre-assess your students
Partial strategies are a great starting place but we have to help students develop more sophisticated strategies
The starting strategies for each major operation
Students need lots of experience developing relationships through Problem Strings and Rich Tasks for strategies to be natural outcomes

Check out our free eBook to learn more about these strategies: https://www.mathisfigureoutable.com/big
And don't miss out on the You Can Change Math Class Challenge! https://www.mathisfigureoutable.com/change
Check out Episodes 10 and 12 of this podcast for more ideas about starting your school year.

Ep 113: Moving Students Forward Pt 1

Tue, 16 Aug 2022 00:00:00 -0500

How can you make changes in your math classroom to help your students do more Real Math? In this episode Pam and Kim describe some first steps, and bigger steps, you can take to transform your math class.
Talking Points:

Creating a safe mathematical community conducive for Real Math to happen
Wait time - "Do you want time or help?"
Where are you on the continuum to make some or lots of changes?
Tips on where to start wherever you are on the continuum
Using Problem Strings, I Have, You Need, MathStratChat and other instructional routines and games
What you celebrate, answers or thinking, is what students will share
How to transform your curriculum if you're super gung-ho

See also Episode 136 for more discussion about helping students.

Don't miss out on the You Can Change Math Class Challenge! Register today at https://www.mathisfigureoutable.com/change

Learn more about I Have, You Need by listening to episode 7, or visit us at https://www.mathisfigureoutable.com/blog/i-have-you-need

Ep 112: The Double Open Number Line Model

Tue, 09 Aug 2022 00:00:00 -0500

We sure loved discussing the open number line model last week, but have you ever heard of the double open number line? In this episode Pam and Kim discuss how the double open number line can be used to develop Proportional Reasoning and to think and reason about rates.
Talking Points:

A Problem String to reason about unit rates and model on a double open number line
When could an double open number line be helpful in middle school and high school?
When is a ratio table more versatile than a double open number line?
What other concepts can a double open number line be helpful for students?
The percent bar is a double open number line?

Check out our free download on Double Number Lines: https://mathisfigureoutable.com/double

Ep 111: The Open Number Line Model

Tue, 02 Aug 2022 00:00:00 -0500

The open number line is not just a powerful tool for computation, but it's an amazing model for developing all sorts of mathematical concepts! In this episode Pam and Kim discuss how to help students develop the open number line in a natural and meaningful way.
Talking Points:

What is an open number line vs a closed number line?
Are number lines, closed or open, discrete models and why does it matter?
Why shift to a measurement model vs a discrete model?
What are some common errors students make when we use the traditional way of teaching measurement?
We suggest a rich task by Cathy Fosnot to help students develop an understanding of the open number line through measurement
What can you model on an open number line? Elapsed time, addition and subtraction of whole numbers and integers and more
Is an open number line helpful for higher math concepts?

See episode 138 for more about subtraction pitfalls

Check out Cathy Fosnot's amazing rich task: https://www.heinemann.com/products/e01010.aspx

Ep 110: Thinking Through Decimal Multiplication

Tue, 26 Jul 2022 00:00:00 -0500

Multiplying decimals can be fun! In this episode Pam and Kim tackle several gnarly problems like 0.77 x 2.4, and have a blast doing it.
Talking Points:

Building reasoning allows students to be flexible and have fun with decimal multiplication
Kim uses percent and money to solve 0.77 x 2.4 with confidence (no need for a calculator)
Pam represents her thinking on a ratio table for 0.77 x 2.4
Different strategies for 0.77 x 0.24?
What about 7.7 x 0.24?
Why is thinking and reasoning so important?

Ep 109: Multiplying By One Tenth

Tue, 19 Jul 2022 00:00:00 -0500

Being able to scale comfortably is important for both whole and decimal numbers. And just as there are more sophisticated ways to handle scaling with whole numbers, we can also be more sophisticated scaling decimals! In this episode Pam and Kim describe how we can help students become comfortable with decimal multiplication using their understanding of whole number multiplication and then scaling.
Talking Points:

Reflecting on the more sophisticated strategy from Ep 106
Applying knowledge of whole number multiplication to decimals
It's more about reasoning than shifting the decimal
Reasoning in small steps builds understanding vs. just counting the decimals
Reasonableness comes from keeping kids in reasoning land
Language to focus on and language to avoid

Ep 108: Beginning Decimal Multiplication

Tue, 12 Jul 2022 00:00:00 -0500

How can we help students make sense of decimal multiplication? In this episode Pam and Kim run through two beginning Problem Strings that will get students feeling comfortable and understanding the world of multiplying decimals.
Talking Points:

Which models are helpful
Decimals and money
Students need to develop a few starting relationships before becoming more sophisticated
Smart Partial Products with decimals

Ep 107: All About Decimals

Tue, 05 Jul 2022 00:00:00 -0500

We've gotten a ton of questions about decimals. In this episode Pam and Kim discuss three different models and why they are great for questioning and building relationships, but may or may not be good for computation.
Talking Points:

Base Ten Materials
Exploding Dots by James Tanton
Money

Ep 106: Multiplying by 10

Tue, 28 Jun 2022 00:00:00 -0500

Most students can scale up by ten as they begin to multiply larger numbers and that is a great starting place for students. In this episode Pam and Kim discuss a more sophisticated way of scaling numbers in multiplication problems.
Talking Points:

How beginning learners will use multiplying by 10 in double digit multiplication problems.
How more sophisticated students deal with smaller numbers then scale up.
How this applies to middle school students.
How can Five is Half of 10 be used with more sophisticated thinking?

Ep 105: Let the Students Play

Tue, 21 Jun 2022 00:00:00 -0500

Often people misunderstand what this game we call mathematics is and feel they aren't good enough to play. In this episode Pam and Kim discuss how students need the opportunity to experience and play in the real game of mathematics.
Talking Points:

Mathematizing is not about speed
Pam, the basketball player
It's not about memorizing disconnected rules and procedures.
Kim, the teacher pleaser
Experience and opportunities are important so kids have choices
We need all students in the game of math
Is there such a thing as a "math gene" or natural talent?
All students have different talents to bring to the table
Take the Math Perspective Quiz to find more about your perspective of math class and instruction.
All students have talents to bring to the table

Ep 104: Things We Have Learned

Tue, 14 Jun 2022 00:00:00 -0500

It's our two year anniversary! We are so grateful you've spent this time with us. In this episode Pam and Kim discuss openly things they've learned and how they've grown during their journey as math teacher educators.
Talking Points:

It's not 'Pam Math', it's Real Math and developing mathematicians!
Coaching teachers is about mentoring, not just telling
The importance of a common vocabulary - Check out Episodes 58 and 101
Empowering teachers and leaders through Journey and Journey Leader
Deep dive online workshops for Kindergarten through middle school
Building Powerful Linear Functions for high school coming soon!

Ep 103: Rich Tasks, Investigations, 3-Act Tasks, Pt 2

Tue, 07 Jun 2022 00:00:00 -0500

What are some examples of rich tasks that are designed to intrigue and engage students? In this episode Pam and Kim give some specific examples and describe why they are so rich.
Talking Points:

Relatable to students not just real world
An eye towards equity
Lead to the mathematics
Packed with patterns
Natural extensions
Make the math realizable
Building Powerful Linear Functions coming Fall 2022

See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!

Ep 102: Rich Tasks, Investigations, 3-Act Tasks, Pt 1

Tue, 31 May 2022 00:00:00 -0500

Let's talk rich tasks! On Twitter we enjoyed a great conversation about what makes a rich task rich. We thought we'd comment on some great suggestions from Professor Tad Watanabe, inspired from his mentor Dr. Grayson Weatley.
Talking Points:

Invite students to make decisions
Replete with patterns
Promote discussion and communication
Tasks should lead somewhere
Be extendable
Have an Element of Surprise
And More!

Ep 101: Strategies!

Tue, 24 May 2022 00:00:00 -0500

What comes to mind when someone says the word "strategy"? There are at least four different meanings for the word "strategy" in mathematics teaching. In this episode Pam and Kim parse out the different meanings and discuss how those meanings shape the outcomes of our teaching.
Talking Points:

Numeracy Strategies
Problem Solving Strategies
Teaching Strategies
Strategies for Teaching
Why without one type of strategy, the other strategies will fall flat

Ep 100: Celebrating Place Value

Tue, 17 May 2022 00:00:00 -0500

We love that we've been able to make 100 episodes! We also love that 1 hundred is 10 tens, so let's talk place value! In this episode Pam and Kim discuss why students struggle with place value, and suggest some of their favorite place value activities.
Talking Points:

Why 'place labeling' is ok, but not enough
Count Arounds
Multiple Towers
Base 10 materials
Using correct place value language

Ep 99: If Not Algorithms, Then What? Finale!

Tue, 10 May 2022 00:00:00 -0500

In the last 5 episodes we've laid out the most important strategies for students to be able to solve for all four operations. So what? In this episode Pam and Kim solve a gnarly problem to demonstrate how mathematizing can empower you and your students, and open up to the world of Real Math.
Talking Points:

How to use the BIG downloadable e-book
A gnarly problem solved using Real Math
It's all about efficiency and developing more sophisticated reasoning
Partial strategies are a great starting point but not the ending place
Kudos to Pam's research and thoughtfulness
Why does Pam seem to focus on computation?
What believers are saying
Other ways to learn with Pam
We can make higher math more accessible
BONUS: Kim's failed attempt at the standard algorithm

Get the BIG download here! https://mathisfigureoutable.com/big

Ep 98: If Not the Division Algorithm, Then What?

Tue, 03 May 2022 00:00:00 -0500

Division is figure-out-able! In this episode Pam and Kim discuss the four main strategies students need to develop to solve any division problem that's reasonable to solve without a calculator.
Talking Points:

Pam's personal harmful experience from the long division algorithm
A precursor strategy: Partial Quotients
Smart Partial Quotients
Over-Under
5 is Half of 10
Equivalent Ratios
Combining strategies

Get the BIG download of all the major strategies for addition, subtraction, multiplication, and division here! https://mathisfigureoutable.com/big

Ep 97: If Not the Multiplication Algorithm, Then What?

Tue, 26 Apr 2022 00:00:00 -0500

What are the five major strategies for multiplication? In this episode Pam and Kim name and give examples of each of the five major multiplication strategies. If students own these strategies they should be able to solve any multiplication problem that is reasonable to solve without a calculator. They will be able to solve it as efficiently as a traditional algorithm and most of the time more efficiently than the traditional algorithm. But even more important than that, they will be developing Multiplicative Reasoning!
Talking Points:

Smart Partial Products
Over/Under
5 is Half of 10
How are these strategies related to the distributive property?
Doubling/Halving
How is this strategy related to the associative property?
Using Quarters & Scaling
Bonus! Flexible Factoring

Get a download of all the major strategies here: www.mathisfigureoutable.com/big

Ep 96: If Not the Subtraction Algorithm, Then What?

Tue, 19 Apr 2022 00:00:00 -0500

It's time for subtraction! In this episode Pam and Kim name and give examples of the four main subtraction strategies students need to own to solve any subtraction problem that is reasonable to solve without a calculator.
Talking Points:

Remove a Friendly Number
Remove a Friendly Number - Over
Remove to a Friendly Number
Constant Difference
How do students choose which one to use?

Get the download! www.mathisfigureoutable.com/big

Ep 95: If Not the Addition Algorithm, Then What?

Tue, 12 Apr 2022 00:00:00 -0500

What are the major strategies students need to know to solve any addition problem that is reasonable to solve without a calculator? In this episode Pam and Kim list them out, give examples, and some insights into how they choose which strategy to use for any given problem.
Talking Points:

Splitting by Place Value (a precursor strategy)
Add a Friendly Number
Add a Friendly Number - Over
Get to a Friendly Number
Give and Take
When do you use each strategy?

Get our download of all the major strategies here! mathisfigureoutable.com/big

Ep 94: If Not Algorithms, Then What?

Tue, 05 Apr 2022 00:00:00 -0500

We want students to be real problem solvers, and we know that means much more than helping them get correct answers. But we never want to put students in a position where they are disadvantaged because they don't know the traditional algorithms. We actually want them to have a much deeper and richer understanding of mathematical relationships. In this episode Pam and Kim begin a series exploring the major strategies for each operation that students need so that they can solve ANY problem that's reasonable to solve without a calculator.
Talking Points:

Pam's journey from learning only step by step procedures to mathematizing
How this series can take Pam's published books a step further
How Kim, and many other mathematicians approach problems
Ownership of the major relationships empowers students with choice
Honor students thinking, but don't leave students where they are

Get the download!: mathisfigureoutable.com/big

Ep 93: Partnering With Parents: Do Correct Answers Matter?

Mon, 28 Mar 2022 00:00:00 -0500

When we feel passionately about the way we teach, we can sometimes inadvertently miscommunicate when speaking with parents. In this episode, Pam and Kim discuss how to appropriately talk about getting correct answers and preparing for high stakes tests so that parents know their children are in good hands.
Talking Points:

Answers are important!
What we don't want to communicate to parents
Preparing students for high stakes tests is important!
Insight into a test writer's thinking when they write test items
Helping students mathematize will help them feel more confident and excel on high stakes tests

Ep 92: Partnering With Parents: Math Night!

Tue, 22 Mar 2022 00:00:00 -0500

Partnering with parents can be a blast! In this episode Pam and Kim describe how they organize and run math nights to help parents experience mathematizing and get excited about what their students will be learning.
Talking Points:

Typical parent math nights vs. our parent math nights
Opportunity to share grade level or school wide expectations
Importance of a Q & A for parents
Help parents experience math the way their students do
Mathematizing for parents at the "sweet spot" level of math
Suggestions for finding Problem Strings to use at math nights
Logistics tips for parent math night
Advantages of a series of parent nights

Ep 91: Partnering With Parents: Over Communicate

Tue, 15 Mar 2022 00:00:00 -0500

How can we proactively partner with and support parents? In this episode Pam and Kim discuss ways they over communicate to parents to keep parents involved and not confused.
Talking Points:

Newsletters: What is helpful information and tips for parents I can share?
Parent-teacher conferences: What can I share with parents about math other than just grades?
Homework assignments: I don't like drill and kill. What kinds of homework are helpful for students and parents?

Ep 90: Partnering With Parents: Listening

Tue, 08 Mar 2022 00:00:00 -0600

Parents are so important, and sometimes they get concerned when their child isn't being taught math they way they were expecting. In this episode Pam and Kim discuss hearing parents' concerns and helping them feel heard and then helping them understand the math. We appreciate parents and we are better with them!
Talking Points:

We want invested parents
Parents need to be heard, and then they need to understand
The importance of listening to understand

Ep 89: Playing With Fraction Multiplication

Tue, 01 Mar 2022 00:00:00 -0600

Kim has a story to tell that Pam hasn't heard yet! Listen in to get a feel of how math can be when students understand that Math is Figure-Out-Able.
Talking Points:

Pajama Math and exploring relationships in multiplying fractions
Can you really just multiply straight across with fractions?
Two ways to reason about 3/5 times 3/9
Pam and Kim reason multiple ways about 3/4 times 2/5
Join us in #MathStratChat!

Ep 88: Getting Correct Answers or Building Relationships?

Tue, 22 Feb 2022 00:00:00 -0600

Most of us are probably teaching the way we were taught, to get correct answers to problems. But we aren't actually helping students understand and reason about the math. Which is more important? In this episode Pam and Kim discuss answer getting versus relationship building.
Talking Points:

Phil Daro's research on patterns of math instruction from across the world
Student success from answer getting instruction vs instruction that focuses on outcomes from reasoning
The real purpose of math class
Now that I know different, how can I do different and help kids reason?

Resources:
Phil Daro video: https://vimeo.com/79916037

Ep 87: But I'm Required to Teach Algorithms

Tue, 15 Feb 2022 00:00:00 -0600

Do your standards require you to teach algorithms? What then? In this episode Pam and Kim discuss how they prepare their students for success on high stakes tests without ever teaching a step by step algorithm or process.
Talking Points:

All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems.
Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year.
Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and become good mathematicians.
Introduce the algorithm as a study of why the algorithm works for the very end of the year. Introducing the algorithm too early in the year risks giving students the option to turn their brains off.

Ep 86: Are Algorithms Necessary?

Tue, 08 Feb 2022 00:00:00 -0600

What purpose has and should algorithms have in mathematics education? Are step by step What purpose has and should algorithms have in mathematics education? Are step by step procedures even to be taught at all? In this episode Pam and Kim talk about our role as teachers and what students need to think like mathematicians.
Talking Points:

One student's perspective
What are algorithms?
Why have we taught algorithms in the past?
Where are algorithms helpful in today's world?
Do algorithms help students learn to mathematize?
From another student's perspective
Learn more in the online workshops

Ep 85: Single Digit Addition Facts Finale

Tue, 01 Feb 2022 00:00:00 -0600

Aren't addition facts cool?! By this point you've learned some amazing relationships and strategies to help your students make real sense of and automatize the single digit addition facts. But sometimes learning and applying are two different things. In this episode Pam and Kim detail how to help your students get out of counting mode and actually apply the relationships they've learned to become fluent with single digit addition facts.
Talking Points:

Why do some kids keep counting after they've learned these relationships?
How to help kids break the counting habit and why that is important
It's not about speed or only the answers, it's about developing more sophisticated thinkers and reasoners
Deep dive online workshops for teachers

Ep 84: Single Addition Facts, Part 4

Tue, 25 Jan 2022 00:00:00 -0600

It's time for you to learn about the most important relationship your students need to know to automatize their addition facts: partners of ten. Partners of ten influence strategies for adding bigger numbers as well as strategies for other operations. In this episode Pam and Kim will discuss some of those influences and some games and routines specifically made to provide experience and build partner of ten relationships for all levels and all ages.
Talking Points:

What are partners of ten?
Do older students need partners of ten?
Rich Tasks with 10
Collect Ten
I Have, You Need
Establish partners of ten early in the school year
Workshop registration is open until Feb 4!

Links:
bit.ly/partnersoftensgames
mathisfigureoutable.com/youneed
mathisfigureoutable.com/workshops

Ep 83: Single Digit Addition Facts Pt 3

Tue, 18 Jan 2022 00:00:00 -0600

We build addition facts through relationships and fluency through experience. So what important patterns and relationships can help students master or reason with their single digit addition facts rather than rote memorize? How can we teach those patterns and what experiences can help students automatize and become more fluent with addition facts? In this episode Pam and Kim dig deeper into single addition facts and how we as teachers can can empower students to reason like mathematicians.
Talking Points:

It's not about speed
Doubles are important
The Shoe Game
The Doubles Game (Cathy Fosnot)
Near doubles
Ten-and or The teens

Check out the patterns we talked about here:
mathisfigureoutable.com/addrelationships

And don't miss registration for one our deep dive workshops! https://www.mathisfigureoutable.com/workshops

Ep 82: Single Digit Addition Facts, Pt 2

Tue, 11 Jan 2022 00:00:00 -0600

Addition is figure-out-able! In this episode Pam and Kim describe some of the fundamental patterns students should learn as they get familiar and automatize with their single -addition facts. We want students at all levels to have access to their facts so they don't bog down every time they encounter them.
Talking Points

Connecting the concrete and pictorial experiences to symbolic representation.
Tips for using flash cards and addition table.
Noticing patterns can reduce the number of addition facts a student needs to fuss with.
The role the commutative property plays learning addition facts.
When is counting ok.
Learning to trust the commutative property.
Students need experience, lots of it.

Register for the You Can Change Math Class Challenge here: https://www.mathisfigureoutable.com/change
You can also register for a deep dive workshop today! Go to https://www.mathisfigureoutable.com/workshops to learn more.

Ep 81: Single Digit Addition Facts Pt 1

Tue, 04 Jan 2022 00:00:00 -0600

So many people get left behind when it comes to higher math, because they never learned mathematize or to think more sophisticatedly and build complex relationships and simultaneity in lower math. Teachers often share that their students lack numbers sense or fluency, specifically lack of memorized basic math facts. That's why in this episode Pam and Kim start a new series on single digit addition fact fluency. Are the facts important? You bet! But how they are taught is even more important to be accessible and equitable for all students.
Talking Points:

This series is for all grade level teachers!
Is speed or quick recall important?
Our goal: rote memorization or number relationships?

Learn more at bit.ly/pharrisinfo.
Don't forget to just the You Can Change Math Class Challenge at https://www.mathisfigureoutable.com/change!

Ep 80: Resolutions Anyone?

Tue, 28 Dec 2021 00:00:00 -0600

We've come to the end of another year, and we'd thought we'd leave you with some suggestions on goals you can set for your teaching. In this episode Pam and Kim highlight some transformative goals that you probably haven't considered before. How could your math class look next year or next semester?
Talking Points:

Learners setting goals around mathematical behaviors or practice standards.
Teacher goals centered around the NCTM mathematics teaching practices.
Teacher goal to elicit and use evidence of student thinking.
SMART goals.
Hey Australia! We appreciate you!

Ep 79: Talking Math With Your Kids For The Holidays

Tue, 21 Dec 2021 00:00:00 -0600

Don't you love the holidays? We sure do! It's such a great excuse to talk math with your family! In this episode Pam and Kim describe some ways (and activities they do) to involve math in their festivities, from formal games like I Have, You Need, Guess My Number, MathStratChat, to simply noticing and wondering.
Talking Points:

Cooking and Baking
Spending Holiday Money
Dinner Games
Daily Tasks
Walks
Car Games
Notice and Wonder

Ep 78: Gift Giving Ideas - Mathy Games for All Ages

Tue, 14 Dec 2021 00:00:00 -0600

As we approach Christmas and the holidays, we thought we'd talk about some of our favorite games that we love to gift others! In this episode Pam and Kim share what makes a great mathy game and list a few of their favorites that not only have numbers, but include some with strategy and logic. Also, don't forget to check out some of our Math is Figure-Out-Able merch for your own gift list!
Favorite Games:

Splendor
Multi (by joyfulmathematics.com)
Prime Climb (by mathforlove.com)
Tiny Polka Dot (by mathforlove.com)
Qwixx
Set
Proof
Mastermind
Sequence
Rack-O
High Ho Cherry-O

Ep 77: The 'Relational Thinking' Instructional Routine

Tue, 07 Dec 2021 00:00:00 -0600

We've got another one of our favorite routines for you today! In this episode Pam and Kim demonstrate the Relational Thinking routine, a routine that helps students understand equivalence and become more comfortable with relational strategies. Thanks to the Cognitively Guided Instruction group for introducing us to this routine!
Talking Points:

Examples of the routine for all four operations
What does the equal sign really mean?
Strategies based on equivalence: Give and Take, Constant Difference, Doubling and Halving, Equivalent Ratio

Resources:

Find examples of Relational Thinking problems here: https://www.mathisfigureoutable.com/relational-thinking
Find our Developing Mathematical Reasoning info graphics here: https://www.mathisfigureoutable.com/blog/development-4

Ep 76: The 'As Close As It Gets' Instructional Routine

Tue, 30 Nov 2021 00:00:00 -0600

There are a lot of great instructional routines out there, and today we want to highlight As Close as it Gets. In this episode Pam and Kim discuss how to use this instructional routine in your classroom and how it can help your students get mathematizing with estimation!
Talking Points:

A routine to help students learn what Real Math estimation is through reasoning.
Examples
Teacher moves to introduce the routine and common pitfalls
Why do we use the routine?
Where to find help for your classroom

Learn more about this powerful routine here: https://www.mathisfigureoutable.com/instructionalroutines

Ep 75: Stop Labeling Students

Tue, 23 Nov 2021 00:00:00 -0600

Are your students dumb or smart? Fast or slow? Under achiever or advance achiever? Or are they just your students with varying experiences? In this episode, Pam and Kim discuss labels, and the effect they have on you as teachers and your students. They propose a different way to look at your students so that you can provide opportunities and experiences for all students so that they continue to learn and love math.
Talking Points:

The problem with labels.
What do we believe about learning?
Focus on providing experience rather than natural talent or ability.

Ep 74: Know Your Content, Know Your Kids

Tue, 16 Nov 2021 00:00:00 -0600

How can we take what students already know and leverage that to make other mathematical connections? You've probably heard us mention that you should know your content and know your kids, but there's a lot of meaning behind that. In this episode Pam and Kim go in deep on how knowing your content and your kids support effective teaching practices and maximize learning for students.
Talking Points:

We need to know beyond our standards.
Why we need to look vertically and horizontally at our standard's landscape?
How knowing our students can help target their individual zone of proximal development.

Ep 73: Some Favorite Numbers - Milestones for Math is Figure-Out-Able

Tue, 09 Nov 2021 00:00:00 -0600

We did it! We made it to episode 73! Why is that an important milestone? Just cause it's Kim's favorite number :-). In this episode Pam and Kim take the opportunity to highlight some important milestones in the Math is Figure-Out-Able movement. We're so grateful you're a part of it!
Talking Points:

Pam and Kim's favorite numbers
Twitter followers and MathStratChat
You Can Change Math Class Challenge
Pam and Kim as colleagues
Podcast
Online Workshops
What's coming up next?

Ep 72: The Do's and Dont's of Problem Strings

Tue, 02 Nov 2021 00:00:00 -0500

Facilitating a Problem String is tricky business, so Pam and Kim take the time in this episode to provide some do's and don'ts that anyone can learn from.
Talking Points:

What is a Problem String?
How long should a Problem String last?
Can Problem Strings be given in a worksheet or as a bell ringer?
Does everyone share during the Problem String?
How do I know which students should share and in what order?
What if all of my students aren't using the strategy?
What if I don't understand a student's strategy?
How do I write Problem Strings?

If you want to hear more about Problem Strings, check out Episode 163.

Ep 71: What are Problem Strings Anyways?

Tue, 26 Oct 2021 00:00:00 -0500

What makes Problem Strings different from other sequences of problems? In this episode Pam and Kim get into the nitty gritty on how Problem Strings work and what sets them apart.
Talking Points:

Defining Problem Strings
The "Why or Purpose" - What sets a Problem String apart from just a list of problems?
The "How" - How are Problem Strings facilitated differently from a textbook lesson or rich task?
An example

If you want to hear more about Problem Strings, check out Episode 163.

Find examples of Problem Strings (including video!) at https://www.mathisfigureoutable.com/ps

Ep 70: Equations of Lines Pt 2

Tue, 19 Oct 2021 00:00:00 -0500

Problem Strings are meant to build off each other so that the math is always moving forward. That's why we've decided to build off the last episode with another Problem String! In this episode Pam and Kim find the equation of some lines using relationships and develop powerful strategies for more sophisticated thinking.
Talking Points:

You don't have to have lots of recent experience to notice the patterns.
Problem Strings to notice patterns and relationships between the x values and the y values.
How the relationships between the x values and the y values help you think and reason about slope and y intercept.
Algebra is Figure-Out-Able!!

Ep 69: Equations of Lines Pt 1

Tue, 12 Oct 2021 00:00:00 -0500

We've talked a lot about the types of reasoning we need to help students develop, but a lot of teachers believe that there comes a point in higher math where reasoning just won't cut it. In this episode Pam and Kim tackle functional reasoning, and demonstrate that algebra can be so much more than memorized steps.
Talking Points:

Is using the procedure of finding slope, plugging into a formula, etc the most efficient?
The importance of working with intuition
Examples of using patterns that you notice to find the equation of a line without formulas
Intuitively finding the equation of a line in standard form

Ep 68: Revisiting the Development of Mathematical Reasoning Pt 2

Tue, 05 Oct 2021 00:00:00 -0500

In Episode 67 revisited the Development of Mathematical Reasoning (DMR) and we described how students can solve addition problems with Counting Strategies. What about the addition algorithm and multiplication and division problems? In this episode Pam and Kim explore the Development of Mathematical Reasoning even further, and discuss how important it is that we help students become more sophisticated. It's more than just answer getting. And stay tuned to the end for a freebie!

Examples of solving addition problems with bigger numbers using Additive Reasoning.
Examples of solving multiplication problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.
Examples of solving division problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.
Brand new free infographics of the Development of Mathematical Reasoning.
Videos of students solving problems using the different types of reasoning to help you use the DMR in your classroom to identify where your students are in their reasoning.

Find the infographics here: https://www.mathisfigureoutable.com/blog/development-4

Ep 67: Revisiting the Development of Mathematical Reasoning

Tue, 28 Sep 2021 00:00:00 -0500

It's been over a year since Pam and Kim first introduced the DMR (Development of Mathematical Reasoning) and in that time they've refined their ideas even further. In this episode Pam and Kim dive deeper into the development and why it's so important.
Talking Points:

It's not about answer getting, or students doing it 'their way'.
Our goal is more sophisticated thinking and reasoning
Added Statistical Reasoning to DMR
Where do subtraction and division live on the DMR graphic?
We don't leave a level of reasoning behind
Examples of Counting, Additive and Multiplicative Reasoning
How can you build your own mathematical reasoning?
Free DMR workshop for anyone at anytime!

Ep 66: Shout Out to Leaders!

Tue, 21 Sep 2021 00:00:00 -0500

Math conferences are powerful ways to improve your teaching. But it's also really easy to go to a conference and accidently miss all the good sessions. In this episode Pam talks about a few powerful leaders in the math education community that she will always go see no matter what they're talking about.
Talking Points:

Karim Ani
Peter Liljedahl
Deborah Ball
Zaretta Hammond
Jenny Bay Williams and John SanGiovanni
Elham Kazeimi
Cathy Fosnot
Juli K. Dixon
Sarah Vanderwerf
Instructional Routines to find at MathisFigureOutAble.com

JourneyLEADER (learn more at https://www.mathisfigureoutable.com/leader)

Other people to follow: @JBayWilliams, @JohnSanGiovanni,
@ddmeyer, @joboaler, @ekazemi, @ctfosnot, @thestrokeofluck, @saravdwerf

Ep 65: Collaborative Coaching through Shared Experiences

Tue, 14 Sep 2021 00:00:00 -0500

How can we best grow as teachers? Together of course! In this episode Pam and Kim discuss the power of teachers honing their craft through collaborative experiences and conversations. Administrators, leaders and coaches will find this episode particularly helpful.
Talking Points:

Shared experiences help to communicate and reflect about critical moments and expert teacher moves.
How coaches, teachers and peers can benefit from coversations about shared experiences to implement action in the classroom.
How to create shared experiences.
Introducing JourneyLEADER

You can learn more about our exciting new experience for leaders at mathisfigureoutable.com/leader

Ep 64: Fun with Division: The Equivalent Ratios Strategy

Tue, 07 Sep 2021 00:00:00 -0500

Fun with Division: An Important Strategy

There is so much to division! Pam and Kim go through a quick Problem String that builds a less known, but super powerful, division strategy.
Talking Points:

Reasoning about division with scaling
Thinking partitively vs quotitively to solve gnarly division problems with whole numbers, fractions, decimals and even polynomials.

See Ep 132 and 176 for more on equivalent ratios!

Learn more about the Building Powerful Division workshop

See Episode 142 for further discussion of quotitive thinking when dividing with fractions
See Ep 132 and 176 for more on equivalent ratios!
See Ep 243 for more information on Integer Division

Ep 63: Counting is More Than A, B, C

Tue, 31 Aug 2021 00:00:00 -0500

Counting strategies can often go overlooked. Learning to count in a way that prepares students for Additive Reasoning is complex. But just how hard can counting be? Wait until you listen to this episode! Pam and Kim discuss how to help young learners increase in their sophistication as they count to add numbers.
Talking Points:

Counting is more than singing the song.
Addition requires a strong foundation of Counting Strategies.
C + M = ?
Double/triple counting, counting on, Commutative Property for addition.
Teacher moves to help students become more sophisticated counters.

Ep 62: Models That Aren't Our Fav

Tue, 24 Aug 2021 00:00:00 -0500

In this episode Pam and Kim show how three popular models - 100 charts, base ten blocks, and algebra tiles - while powerful for developing reasoning, can limit students' development of more sophisticated thinking as tools for computation.
Talking Points:

CRA vs tools for thinking
What are 100 charts, base 10 blocks and algebra tiles?
3 limitations for some manipulatives that prevent kids from doing Real Math
How each not-fav model have the 3 limitations for computing
Mimicking or Mathematizing?

Ep 61: Ten Frames

Tue, 17 Aug 2021 00:00:00 -0500

Continuing their series on models and modeling, Pam and Kim discuss the advantages and pitfalls of Ten Frames. They emphasize the power of models that can become tools for thinking and reasoning. Ten Frames can be an excellent tool for helping kids see the structure of 5 and 10 when counting. But what happens when students need to compute and build Additive Reasoning?
Talking Points:

What are Ten Frames?
The 3 limitations to Ten Frames
It's not just the model, it's how you use the model
Our 3 preferred models for transitioning from counting to Additive Reasoning

See Episode 5:How Do You Reason to learn more about the Development of Mathematical Reasoning, and how it transforms our understanding of what it means to learn and teach mathematics.

Ep 60: Number Bonds and Tape Diagrams

Tue, 10 Aug 2021 00:00:00 -0500

Let's keep talking about modeling! A lot of you may be familiar with Number Bonds and Tape Diagrams and may be wondering about how they fit in with our modeling framework. In this episode Pam and Kim discuss these models and some of the confusion and misunderstanding surrounding them. They offer suggestions to help teachers advance students from "modeling of the situation" to "modeling to make their thinking visible".
Talking Points:

What are Number Bonds and Tape Diagrams?
CGI and direct modeling confusion
Example of using Number Bonds and Tape Diagrams vs an Open Number Line
Models that can be tools for thinking for addition, subtraction, multiplication, and division

Ep 59: Why Not Manipulatives?

Tue, 03 Aug 2021 00:00:00 -0500

Are manipulatives sometimes overemphasized? When are they useful, and when can they actually get in the way of the mathematics? What role do they play in our discussion about the modeling framework? Pam and Kim discuss these tricky questions, and discuss the power of contexts and developing models as tools for reasoning.
Talking Points:

An important modeling framework
What are manipulatives?
Gail Burrill - Where's the Math?
Cathy Fosnot - Do manipulatives embody mathematics?
Are manipulatives bad?

Ep 58: Introducing the Modeling Framework

Tue, 27 Jul 2021 00:00:00 -0500

It's time to talk about one of our foundational ideas for facilitating Real Math! In this episode Pam and Kim detail a modeling framework that helps students to learn to model their own thinking, and then to use models as tools for, or in order to think about, computation. The goal of the framework is for students to be able to reason and solve complex problems on their own with confidence.
Talking Points:

Model vs. Strategies
The different meanings for "model"
In important modeling framework
An example with sticks of gum and a ratio table
How students learn to verbalize and model their own thinking
How this framework differs from CRA

Ep 57: For Parents: How Can I Help My Kid?

Tue, 20 Jul 2021 00:00:00 -0500

If my experiences as a student are different than my child's experience at school, how can I help them succeed? In this episode for parents, we provide two clear ways you can support your child to be the best math student they can be. Be sure to listen to episodes 55 and 56 for the rest our series for parents.
Talking Points:

We can all be mathy people
Parents' attitudes towards math affects your child's attitude towards math
Importance of student think time
Importance of parent involvement in math education

See Episodes 34-38 to learn more about best teaching practices for multiplication facts.

Ep 56: For Parents: Why Does "New Math" Look Different?

Tue, 13 Jul 2021 00:00:00 -0500

Hey parents! Thank you so much for listening to part two of our series for parents. It can be really frustrating to not understand what it is your kid is doing on their homework. What is up with all of the drawing? Where are the algorithms and simple steps? In this episode we'll explain the purpose and goal of why the math on your kid's paper looks different.
Talking Points:
Reasoning about math vs performing memorized steps

We want our students to be reasoners, not calculators
Representing students' thinking and reasoning on paper can look messy
As we understand the possibilities with Real Math, we can encourage and refine teaching so more students are more successful

Ep 55: For Parents: Why All the "New Math"?

Tue, 06 Jul 2021 00:00:00 -0500

This episode is for all the parents out there who are invested in helping their children! It can be frustrating to see how math class looks different than it did when we were students. Why is it different anyways? Why would math class have to change? We are so grateful you're taking the time to ask. We'll do our best to provide some answers.
Talking Points:

Why did the math we were taught in school look the way it did?
Why do generations of technology dependent students need a different way to learn math?
Why do students need to understand Real Math for our future?

Ep 54: Q&A Part 2, Data Analytics and Advice for First Year Teachers

Tue, 29 Jun 2021 00:00:00 -0500

We love answering your questions! In this episode Pam and Kim answer a question submitted from Rachel Adler. Pam shares her experiences familiarizing her students with data representations, and then Pam and Kim discuss their best advice for first year teachers.

Talking Points:

Jo Boaler's Data Talks: https://www.youcubed.org/resource/data-talks/
Integrating data analytics into what you are already teaching
Solidifying your teaching philosophy and belief system. See episode 12
The importance of good teacher partners and getting outside of your own classroom
The importance of good student-teacher relationships
Starting off the year by setting clear expectations to set the year up for success
Figure out how you fit as an adult with all students

Ep 53: Q&A Part 1, Do Strategies Change Over Time?

Tue, 22 Jun 2021 00:00:00 -0500

We loved getting all of your questions! Because there's so many questions, Pam and Kim will have to spend the next couple episodes answering them. In this episode they discuss a question about the relevancy of money strategies, and whether strategies will change over time.
Talking Points:

Why experience with coins and their relationships is important
Distinction between teaching strategies and mathematical strategies
Technology in classrooms as a teaching strategy

Extra resources: Which One Doesn't Belong (https://wodb.ca)

Ep 52: One Year Anniversary Highlight Reel

Tue, 15 Jun 2021 00:00:00 -0500

We are so grateful to be celebrating our one year anniversary of the podcast! It's been wonderful to hear all the feedback you've given us as you transform your classrooms. Here's to another year of mathematizing!
Highlights:

Ep 2: Pam's stance on algorithms
Ep 9: Defining models and strategies
Ep 34: Memorizing multiplication facts is not the answer
Ep 27: The students who need to know why

Ep 51: Fractions, a Clock Model Pt 2

Tue, 08 Jun 2021 00:00:00 -0500

We've had so much fun talking about fractions! In this episode Pam and Kim do another Problem String to demonstrate the effective use of a clock model.
Talking Points:

What denominators work well for a clock model?
Example Problem String with non-unit fractions and mixed numbers
Should we insist on the most simplified fraction answer?
Problems that work with both money and a clock model
Today's students need the experience from learning with a clock model

Ep 50: Fractions, A Clock Model

Tue, 01 Jun 2021 00:00:00 -0500

How important is fractional equivalence? Important enough for another model! These models are fantastic for helping students develop a natural understanding of equivalent fractions. Listen in as Kim and Pam discuss how to use a clock model for denominators uncommon to the money model.
Talking Points:

Use adding and subtracting fractions to help think and reason about fraction equivalence
Using the word "over" for fractions is NOT helpful
Equivalent fraction examples on a clock model
A real student's math journey

Jordan Using the Clock Model

Ep 49: Fractions, A Money Model Pt 2

Tue, 25 May 2021 00:00:00 -0500

In this episode Pam and Kim finish up their money Problem String from the last episode. But first, Pam wanted to reflect a little on how she was less than helpful when Kim was struggling to think about nickels. We all learn and grow, and self-reflection is super important!
Talking Points:

Do you need time, or do you need help? (see episode 40)
Once kids have an answer, do we force them to find another way?
For which denominators is thinking about money helpful?
Ways to think about 2 2/5 minus 9/20
The reciprocal relationships between fractions and coins can be confusing
Fractional equivalence is the goal by asking students to add and subtract fractions

Ep 48: Fractions, A Money Model

Tue, 18 May 2021 00:00:00 -0500

It's time to talk about everyone's two favorite things: fractions and money! Fraction equivalence is a super important concept in mathematics, and it is best developed naturally in a familiar context. In this episode Pam and Kim model using coin denominations to reason about fractional equivalence.

Talking Points:

If you understand fractional equivalence, you don't have to memorize any rules for operators of fractions
Examples of using the money model to think about fraction equivalence, and bonus, fraction operations as well:
Using decimals and fraction notation interchangeably
Kim's uncomfortable relationship with nickels

Ep 47: Fractions as Fair Sharing

Tue, 11 May 2021 00:00:00 -0500

Let's keep talking fractions! In this episode Pam and Kim discuss an interesting rich task from Cathy Fosnot to help students reason about fractions within the context of sharing fairly. Listen in to learn about the outcomes teachers should look for when teaching fractional sense in a rich contextual problem.
Talking Points:

Splitting the wholes into unit fractions
Splitting the leftovers into smaller unit fractions and re-unitizing
Patterns when comparing same-denominator fractions vs same-numerator fractions

See Ep 103 for more discussion on Rich Tasks

Additional Sources: Field Trips and Fund-Raisers

Ep 46: Fractions for Young Learners

Tue, 04 May 2021 00:00:00 -0500

How young can young learners begin to experience fractions? Younger than you think! In this episode Pam and Kim describe simple ways we can help young students begin to develop fractional understanding. Pay attention to how natural it can be for young learners to learn math!
Talking Points

Struggles that young learners may experience with "half"
Simple classroom activities to have students fair shares in early grades as they practice counting
Experiences and conversations in halving even and odd amounts
Standards and fractions of an object vs fraction of a set
Important unit fractions and resources
Doubling and halving simultaneously
Simple experiences parents can use to help their kids develop fractional understanding

Additional sources:

Ep 45: 5 Interpretations of Rational Numbers

Tue, 27 Apr 2021 00:00:00 -0500

Time to get into fractions! There is so much to learn about teaching fractions and in this episode we wanted to lay some important ground work. All too often we limit students by giving them experience with only one or two of the important ways fractions can be interpreted. When we help students fully understand fractions by using all of the interpretations, their ability to think proportionally skyrockets!
Talking Points

What is a rational number?
The 5 Interpretations of Rational Numbers (Credit to Susan Lamon)
Solving fractions with reasoning!
Shifting between the 5 interpretations as we solve
Applying all 5 interpretations to one problem

Ep 44: Is it About Personality?

Tue, 20 Apr 2021 00:00:00 -0500

Though some people think Kim and Pam's voices are hard to tell apart, teaching Real Math has nothing to do with a particular style or even personality type. We believe in seeing the humanity in students and empowering them with mathematical confidence!
Talking Points:

Pam and Kim's results on the Enneagram Test.
2 important things -
1. Teaching Real Math is more about beliefs about students and mathematics than personality
2. Leverage your beliefs to get support in teaching Real Math.

Ep 43: Standardized Tests

Tue, 13 Apr 2021 00:00:00 -0500

If there's one thing that often comes up in teachers' conversations, it's standardized tests. And Pam and Kim are not afraid to tackle the tough conversations! In this episode Pam asks Kim about her experience with standardized tests, and how teaching Real Math helped Kim's students to succeed. Also don't forget to send in questions for our special 50th episode! We're so excited!
Talking Points:

Can students succeed on tests if all they know is Real Math?
Everyone, in every demographic, can learn more Real Math than fake math.
How much time do students need to prepare for tests?
Suggestions for test prep.
How teachers view the test and their actions speak loudly
It's all about "know your content, know your kids".

Learn about numberless word problems here: https://bstockus.wordpress.com/numberless-word-problems/

Ep 42: Homework Pt 3

Tue, 06 Apr 2021 00:00:00 -0500

In this final episode in our series on homework, Pam and Kim discuss what types of homework teachers should send out, as well as some important pitfalls to avoid.
Talking Points:
Pen and paper homework

Games as homework and things to consider
Computer activities as homework and things to consider
Communication is critical to honor family time when assigning homework
Using homework as a teaching tool, not for the sake of work
Be sure you are sending the right message about mathematics when looking at returned homework.
How the goal of Real Math helps teachers make decisions about homework

Ep 41: Homework Pt 2

Tue, 30 Mar 2021 00:00:00 -0500

It's part two of our series on homework! Last time we heard Kim's perspective on when and what kinds of homework to give. Now it's Pam's turn. As a teacher for both high school and university classes, Pam gives an insightful look into when homework is necessary, and how we can always allow the humanity of our students to have precedence.
Talking points:

What does the research say about homework? How does it vary by grade level?
What is the purpose of homework?
How much homework should students have?
What topics should homework cover?
The role of students' humanity in grades and homework.

Ep 40: Homework Pt 1

Tue, 23 Mar 2021 00:00:00 -0500

Welcome to our first off the cuff episode! Pam and Kim have no notes this time and are happy to tackle the topic of homework. Turns out, they have enough to say that this will be part one of a new series! Listen in as Kim makes a confession, and Pam rats out her kids.
Talking points:

Some general thoughts about homework.
When is a topic appropriate to send home for homework?
Some suggestions for the kinds of homework we should send home
Parent's role in homework and how can homework be helpful?

Ep 39: Everybody Learns, Everybody Grows

Tue, 16 Mar 2021 00:00:00 -0500

In this episode Pam and Kim discuss why a traditional teaching approach is not effective and propose an alternate way of teaching to help every student learn and grow. It's one of their guiding principles, and they can't believe they're only just now sharing it! All students struggle at some point and all students need a challenge, so this is a great listen for everyone!
Talking points:

What is the traditional way of teaching?
The outcomes of the traditional approach of teaching to mastery
How to help all students grow from wherever they are
What are open tasks?
The outcomes of an open task
Rethinking the question: What if students aren't getting "it"?

Ep 38: Multiplication Facts: The Good, the Bad, and the Ugly Pt 5

Tue, 09 Mar 2021 12:00:00 -0600

We made it to our final episode in our multiplication facts series! In this episode Pam and Kim share ideas about helping kids narrow in on facts they struggle with after many opportunities and experiences with multiplication. This final episode exemplifies why we believe that taking the long view and building relationships and Multiplicative Reasoning all year can help students' fact fluency with just a little nudge.
Talking Points:

What it means to take the long view in multiplication facts
When it is appropriate for some work to "dial in" on most missed facts
Clue Cards: What do they look like? Who makes them? How do you use them?
The importance of really knowing your students and how do you get to know them?
Final thoughts on fact fluency and recommended additional optional resources:
Berkeley Everett's Math Flips
Stick and Split app

Show links:

Find the transcript here: https://podcast.mathisfigureoutable.com/1062400/8040345-ep-38-multiplication-facts-the-good-the-bad-and-the-ugly-pt-5

See episodes 55-56 on helping parents understand your math classroom.

Ep 37: Multiplication Facts: The Good, the Bad, and the Ugly Pt 4

Tue, 02 Mar 2021 00:00:00 -0600

It's time for what you've all been waiting for. GAMES! Sure we don't want kids memorizing songs or rhymes to build their facts, but in this episode Pam and Kim bring the fun into multiplication. What games are out there that can help students build their facts and Multiplicative Reasoning at the same time? We're glad you asked :-)
Talking Points:

Teacher and parent attitude is important
Students' job is to figure out the math facts not rote memorize or skip count or sing a song
Students need think time
When to use games
What are the best games today to help students own multiplication facts?
What makes a good math game?
What makes a poor math game?

Links

Live Problem Strings on Facebook Live
The Product Game (Link includes games for other grade levels as well!)

See episodes 55-56 on helping parents understand your math classroom.

Ep 36: Multiplication Facts: The Good, the Bad, and the Ugly Pt 3

Tue, 23 Feb 2021 00:00:00 -0600

Last episode Pam and Kim discussed how not to teach multiplication facts. So how should we teach them? This episode we look at multiplication facts through the lens of mathematizing using Problem Strings!
Talking Points:

The order that we teach math content matters to give students the best experience with multiplication throughout the year
The sequence we teach the multiplication facts matters
Example Problem Strings to build multiplicative relationships
The key relationships students need to own in order to recall multiplication facts that they don't remember
How parents can help their kids own their facts

See episodes 55-56 on helping parents understand your math classroom.

Free Problem String Download: mathisfigureoutable.com/factsps

Ep 35: Multiplication Facts: The Good, the Bad, and the Ugly Pt 2

Tue, 16 Feb 2021 00:00:00 -0600

When choosing tasks to teach multiplication facts, what are the pitfalls to avoid? In this episode Pam and Kim discuss ways teachers may inadvertently 1) overemphasize speed, 2) introduce shame into their classrooms, and 3) focus on learning facts in isolation. We've all made mistakes, and this episode is about learning and growing for our students.
Talking Points:

What the research says about the negative effects of timed activities such as multiplication fact tests
Shame is not a motivator to learn facts (harder then you think!)
Why learning facts as isolated ideas is not helpful

See episodes 55-56 on helping parents understand your math classroom.

Ep 34: Multiplication Facts: The Good, the Bad, and the Ugly Pt 1

Tue, 09 Feb 2021 00:00:00 -0600

In this episode Pam and Kim begin the first of another series: Multiplication Facts! What role can mathematizing and Real Math play in helping kids master their multiplication facts? Listen in as Pam and Kim outline the differences between 'knowing' and 'rote memorizing' multiplication facts.
Talking Points:

Multiplication facts are important
The problem is not the facts but the stress from rote memorizing facts
The difference between knowing and rote memorizing facts
What the standards say about mulitplication facts
Automaticity and Fluency
Cathy Fosnot on suggests that facts should be learned by developing relationships
How higher level mathematicians think about facts
Is your goal to get through memorizing the facts, or to develop Multiplicative Reasoning?
Pam's goal is mathematizing not rote memorizing

We recommend brushing up on episodes 5 & 6 in preparation for this series. Understanding what it means to develop multiplicative reasoning is so important!
See also episodes 55-56 on helping parents understand your math classroom.

Ep 33: Problem Strings vs Problem Talks

Tue, 02 Feb 2021 00:00:00 -0600

In the last two episodes, Pam and Kim did some really cool Problem Strings, but what do they think about Number Talks? Listen in as Pam explains how Number Talks and Problem Strings can go hand in hand for powerful results.
Talking Points:

Why call 'Number Talks' 'Problem Talks'?
Short term goals for Problem Talks
The major purpose of Problem Talks
MathStratChat as a Problem Talk
The purpose of Problem Strings
What is a Problem String?
When to do a Problem Talk or a Problem String
How much time to spend on Problem Talks vs. Problem Strings

Want to learn more about this powerful combination?
Head to: mathisfigureoutable.com/stringsvtalks

Ep 32: Another Cool Multiplication Strategy

Tue, 26 Jan 2021 00:00:00 -0600

It's time for another Problem String! In this episode Pam and Kim highlight one of their favorite multiplication strategies. It's so slick! In doing so they continue the conversation about the importance of letting students discover and develop relationships, as opposed to teaching strategies step by step.
Talking Points:

A Problem String for the ____ strategy
Modeling the strategy on an area model
Can you also triple, quadruple, etc.?
Bonus! A problem with decimals
Really cool decimal relationships
A common question about this strategy: How do we 'teach' kids the appropriate 'steps' of this strategy?
What to avoid when facilitating a Problem String for this strategy or any Problem String
Tweet at us your favorite name for this strategy!

Ep: 31: A Cool Multiplication Strategy

Tue, 19 Jan 2021 00:00:00 -0600

In this episode Pam and Kim want to help you develop a cool multiplication strategy. Which multiplication strategy? We aren't going to tell you until the end of the episode : -). We believe in developing strategies as natural outcomes, and then giving it a name. How do we do it? With Problem Strings! Listen in as Pam and Kim go through a Problem String to develop this super efficient multiplication strategy.
Talking points:

What does it mean to do mental math?
We can purposefully help people reason and mathematize mentally.
How mathematicians solve computational problems, Ann Dowker's research
What is a Problem String?
A multiplication Problem String example
Another multiplication Problem String example with decimals!
The big reveal: The _____ strategy

Ep 30: Ten Minute Math

Tue, 12 Jan 2021 00:00:00 -0600

Don't you just love taking a break to play with numbers? In this week's episode, Pam and Kim share some of the ways that they engage with kids of all ages outside of school to get them mathematizing. Parents, ever wondered what can you do for just ten minutes to help your kids build relationships? This episode is perfect for you. Together we can all learn to make math fun!
Talking points:

Finger Flash game
I Have, You Need routine
Alligator Song and counting backwards
Age games
MathStratChat
Which One Doesn't Belong
Adding 10 and 9; 100 and 99; 1,000 and 999 to anything
Listening and engaging with students is so important

Additional resources: https://talkingmathwithkids.com, https://mathbeforebed.com

Ep 29: Ratio Tables!

Tue, 05 Jan 2021 00:00:00 -0600

In this episode Pam and Kim dive deep into their favorite model for multiplication, division, and solving proportions: ratio tables! They'll discuss 3 ways ratio tables can be a powerful tool to help students mathematize from 3rd grade to high school.
Talking Points:

What are ratio tables?
How to, and not to, use ratio tables in the classroom
Three ways 3-5 grade can use a ratio table:
-to organize data
-to model multiplicative thinking
-for multiplication and division computation
But do 3-5 grade solve unit rate problems?
Where do non-unit rates show up?
Examples of using a ratio table to solve multiplication and division problems

Use this PDF to follow along with Pam and Kim's thinking!

Ep 28: Why Doesn't Everyone Teach Math This Way?

Tue, 29 Dec 2020 00:00:00 -0600

This week Pam and Kim wrap up their discussion on the Perspectives that Impact Math Pedagogy. Understanding the X, Y, and Z perspectives not only helps us understand one another better, but empowers us to choose to take on the Real Mathematics perspective. Listen in as Pam and Kim discuss the need for mathematics to be experienced, and the power in developing mathematical reasoning.
Talking Points:

Your perspective may not be the same for everyone around you
The ultimate goal is Real Math- all people can do more Real Math than fake math
Real Math offers something for all perspectives
Where to start teaching Real Math
What do you do with students that all have different perspectives
How to lean into the frustrations of students for each perspective
How leaders can work with teachers with the different perspectives
How can we all communicate better?

Take the XYZ quiz here! mathisfigureoutable.com/XYZ

Ep 27: Need to Know Why (The Y Perspective)

Tue, 22 Dec 2020 00:00:00 -0600

We've made it to our last (and maybe favorite) perspective that impacts pedagogy. The Y perspective describes those who struggle with fake math because they deeply desire to know "why". Pam and Kim describe people in their lives who grew up with the Y perspective and discuss their great value to the mathematics community.
Talking Points:

What describes the Y perspective?
Pam and Kim's personal experiences with the Y perspective
How adults and learners with the Y perspective feel about mathematics
Two things that people with the Y perspective need to understand
Why teaching Real Math is so important

Take the XYZ quiz here! mathisfigureoutable.com/XYZ

Ep 26: Math is Mimicking (The Z Perspective)

Tue, 15 Dec 2020 00:00:00 -0600

This episode is all about the Z perspective. Listen in to hear about the perspective that This episode is all about the Z perspective. Listen in to hear about the perspective that Pam estimates influences the majority of math educators. It was Pam's perspective too! Pam and Kim parse out the characteristics of the Z perspective and the huge impact it has on teaching today.
Talking Points:

Pam forgot how to subtract
What is the Z perspective?
How do Z-perspective students think?
Pam's first experience with Math Club
What people with the Z perspective need to understand
How can understanding the Z perspective empower teachers?
Take the new XYZ Quiz!

Ep 25: Making Sense of the Math (The X Perspective)

Tue, 08 Dec 2020 00:00:00 -0600

Continuing in the Perspectives Impacting Pedagogy Series, Pam and Kim discuss the X perspective. Did you play with numbers as a kid? Did math make natural sense to you, regardless of how your teacher taught it? You might relate to the X perspective. Listen in to learn how the X perspective influences teachers and students in mathematics.
Talking Points:

What is the X perspective?
Why X-perspective teachers teach with algorithms
Kim's experience growing up with the X perspective
Pam's experiences with her son and collegues with the X perspective
The 'math-gene' myth held by the X perspective
3 things teachers and students with the X perspective need to understand.
Take the new XYZ Quiz!

Ep 24: Perspectives Impacting Pedagogy: How Did You View Math?

Tue, 01 Dec 2020 00:00:00 -0600

This episode is part one to a new five part series! Pam and Kim introduce the three main perspectives that influence the way we teach math. Understanding these perspectives helps teachers analyze their past perspective so they can make choices and have productive conversations regarding changing and improving math education for all students.
Talking Points:

The three perspectives impacting our pedagogy
Is there one perspective that is the best?
How our perspective affects conversations about math teaching
Take the new XYZ QUIZ!

Ep 23: The Commutative Property

Tue, 24 Nov 2020 00:00:00 -0600

How can we help students feel comfortable with using the commutative property? In this episode Pam and Kim go through some addition and multiplication problems to demonstrate how they think and reason using the the commutative property.
Talking Points:

The commutative property when a student is counting on to add
The commutative property in addition of larger numbers
Using models to represent the commutative property
Using the commutative property for percentages
It's not just about naming the property

Ep 22: The Swapping Strategy

Tue, 17 Nov 2020 00:00:00 -0600

Pam went most of her life not knowing about this really cool thing! Listen in as Kim relates a great math experience she had with her son, Luke, while they were messing around with addition. Pam and Kim discuss the importance and kinds of place value experiences we provide for students as we mentor them as mathematicians.
Talking Points:

Introducing the Swapping strategy
What problems fit nicely with the Swapping strategy?
Place labeling vs. Place value
Necessary but not sufficient
Tweet us (@pwharris, @kimmontague) your slick swapping strategy solutions to gnarly looking problems!

Ep 21: Playing with Percents Pt 2

Tue, 10 Nov 2020 00:00:00 -0600

Are percents truly figure-out-able? You bet! Grab a pen and paper for this one as Pam and Kim discuss the 3 types of percent problems and how they solve them using relations, not with algorithms.
Talking Points:

What Journey members are emailing about
The three types of percent problems
Pam and Kim share their thinking as they solve all three types of percent problems
Two traditional ways of teaching percents and how they rob students of resoning fluently
Math is fun when it's figure-out-able!

Ep 20: Playing with Percents Pt 1

Tue, 03 Nov 2020 00:00:00 -0600

So are percents really figure-out-able too? In this episode Pam and Kim do a Problem String and share their strategies to solve some percent problems. Listen in as they play with percents!
Talking Points:

Can we make math fun?
Benchmarks that kids need to know around percents
Percent Problem String

Ep 19: Fractions, Decimals, Percents

Tue, 27 Oct 2020 00:00:00 -0500

Pam and Kim explore what it means to be flexible with fractions, decimals, and percents. They discuss how we can become more flexible as we deal with rational numbers to help us be more judicious problem solvers.
Talking Points:

Why kids of today are more familiar with percentages
Using benchmark fractions, decimals and percentages
How students might mess with gnarly fractions, decimals and percents
Why flexibility matters
How to become more flexible using different representations of rational numbers

Ep 18: This, Not That

Tue, 20 Oct 2020 00:00:00 -0500

You might want your magnifying glass for this one, because in this episode we're getting a little nitpicky. Pam and Kim discuss common and often traditional nomenclature/math-slang that can take the reasoning out of mathematics. They offer useful alternatives and illustrate the importance of using clear mathematical language so students have less opportunites for misunderstaning the mathematics.
Talking Points:

Adding a zero
No 'Butt-Cheeks' in math
'Canceling' can means many different things
Will reducing 6/8ths to 3/4s give me more pie...?
Three-point-two or three and 2 tentsh or $3 and 20 cents?
'Over' is a positional word, not a mathematical relationship
'And' in bigger numbers

See Episode 140 for further discussion of more unhelpful words we use in math class.

Ep 17: Social vs Logical Knowledge

Tue, 13 Oct 2020 00:00:00 -0500

Math is Figure-Out-Able, but surely there are some parts that are only memorizable, right? In this episode Pam and Kim parse out the difference between social knowledge and logical mathematical knowledge. They explain how knowing the difference can help determine how we teach the content.
Talking Points:

What is the difference between social and logical knowledge?
What are some examples for elementary and higher math?
How should we teach social knowledge?
How should we teach logical knowledge?
Is there an occasion where wait time is not helpful?

Ep 16: The Language of Counting

Tue, 06 Oct 2020 00:00:00 -0500

This week's episode is for all you parents and teachers of young children. Pam and Kim discuss ways to make counting Figure-Out-Able! How can we help kids make sense of our counting system and master the meaning behind the words we give to numbers? No matter what grade you teach, you're sure to learn something this episode.
Talking Points:

How different languages name numbers
How to support young learners to make sense of teens and multi-digit numbers
Give kids multiple representations of single-digits numbers
Finger Flash game - Pam even plays it at the grocery store!

Ep. 15: Problem Solving with a Twist

Tue, 29 Sep 2020 00:00:00 -0500

Have you tried teaching your students "the steps" to approaching word problems, but your students still struggled? Pam and Kim discuss a better way to help kids tackle math problems. They explain why the acronyms and problem annotation methods of the past simply won't cut it. They suggest to help your students live the problem solving process, and not just memorize it.
Talking Points:

The dangers of teaching and asking kids to memorize "Problem Solving Methods"
Engage students in Real Math so that problem solving is a natural outcome
Numberless word problems can be helpful

Resources: Brain Bushart's Numberless Word Problems

Ep 14: Guess My Number

Tue, 22 Sep 2020 00:00:00 -0500

Pam and Kim have some fun in this episode as they read out a submission from Aaron Houston about his mathy dad and having mathy fun at a restaurant. They talk about the kinds of things parents can do with their kids to have fun mathematizing!
Talking Points:

I Have, You Need
Kids Menus vs Adult Menus
Guess my Number game
How do you think about finding Prime Numbers?
Math can be fun!

Ep 13: Mathematics for Teaching

Tue, 15 Sep 2020 00:00:00 -0500

There are so many aspects to teaching, and it gets more complex when we want to discuss teaching math. Pam and Kim define the 5 layers for mathematics teaching. What do math teachers, who want to help their students mathematize, need to focus on?
Talking Points:

Building your own numeracy
Know the major strategies and models for your content
Modeling student thinking to make it visible and take-up-able
High leverage teacher moves
Advancing the mathematics by sequencing tasks
These stages repeat with new content
Need support with these stages? Check out Journey

Resources: Journey

Ep 12: Top 3 Things to Start the Year: Know Your Beliefs

Tue, 08 Sep 2020 00:00:00 -0500

As Pam and Kim wrap up their series on how to start the school year right, they discuss the importance of having your beliefs about teaching and learning solidified, so that everything that you do fits when making decisions in your classroom. They discuss how they approach analyzing and implementing other's ideas into their teaching practice, without giving up on their integrity.
Talking Points:

How did Pam get to a point where she know about who she wanted to be as a math teacher?
Knowing what you believe about teaching and learning can help you make choices.
It's more about a common belief system that personality with co-teachers
Intentional use of worksheets & resources can be determined by your teaching beliefs
Determine your system of beliefs so that everything you do fits and works together for students

Check out Episodes 114 of this podcast for more ideas about starting your school

Ep 11: Top 3 Things to Start the Year: Building Culture Remotely

Tue, 01 Sep 2020 00:00:00 -0500

Join Pam and Kim in part two of their Top 3 Things to Start the Year series. This week its all about building a classroom culture where students and students' thinking is valued. They'll talk about how to implement and facilitate familiar tasks and routines remotely and throw out some great advise that build a community of learners. You won't want to miss it!
Talking Points:

Building classroom culture is no less important in remote settings
Keeping the Math Practice Standards in mind as remote learning occurs
Designing interactive remote learning tips and ideas
How to facilitate Problem Strings remotely
How to facilitate Rich Tasks remotely

Check out Episodes 114 of this podcast for more ideas about starting your school

Resources:
How Pam uses her iPad to facilitate Problem Strings remotely: https://www.mathisfigureoutable.com/how

Ep 10: Top 3 Things to Start the Year: Student Names

Tue, 25 Aug 2020 00:00:00 -0500

As the world prepares for one of the most interesting beginnings to the school year, Pam and Kim are here to help us get it right. They start off this 3 part series by dialing in on the importance of using students' names to help them feel seen, acknowledged, and valued.
Talking Points:

Pam's maternal mathy person
How Pam learns students' names
Tips for learning students' names
Useful tools and tips for using students' names in a remote setting
How to help students use each others names

Check out Episodes 114 of this podcast for more ideas about starting your school

Resources: Name Tents from Sarah Van Der Werf: https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/

Ep 9: Strategies and Models

Tue, 18 Aug 2020 00:00:00 -0500

What is the difference between a strategy and a model? Listen as Pam and Kim define strategies and models and explain the difference. They also give examples from both elementary and high school content to demonstrate the importance of developing strategies and using models to communicate those strategies.
Talking Points:

Shoutout to Clay! Clay uses powerful additive reasoning when he uses his understanding of place value to add large numbers. Let us know about someone mathy in your life!
New Problem String videos!
What is a strategy? What is a model?
Examples of strategies and related models
Which is more important, models or strategies?
Why are models so important to help students build relationships?
Helping students understand strategy vs. models

Additional Resources
Strategies vs Models Article
Strategy vs Models Card Sorts

Ep 8: More Cool Things Mathy People Do

Tue, 11 Aug 2020 00:00:00 -0500

After last weeks discussion on partners of 10, 100, and 1000, Pam and Kim thought of more habits "mathy people" have in common. Listen in as they discuss three fun things mathematicians do.
Talking Points:

Mathematicians "Notice and Wonder"
Mathematicians double and halve numbers
Creating habits of thinking (as opposed to grabbing for a calculator)
Check out MathStratChat on Wednesday evenings.

Ep 7: I Have, You Need

Tue, 04 Aug 2020 00:00:00 -0500

In this episode Pam and Kim share one of their favorite instructional routines: I Have, You Need. They discuss some of the most common patterns that mathematicians play with, partners of 10, 100, and 1000. These "partners of ___ " patterns pop up everywhere! You'll never guess where they pop up daily for Pam (hint: its when she's the most worked up).

Try out I Have, You Need with your friends, colleagues, and students! A quick way to build anyone's reasoning abilities and to help us all become better mathematicians.
Download the guide to playing I Have, You Need HERE

Talking Points:

We can all be "mathy people"
What Kim thinks when she hears the number 36
The most important routine in Pam's university class
Pam and Kim play I Have, You Need
Taking ownership of your students' learning
Tips for playing I Have, You Need
I Have, You Need resolves the subtracting across zero horror
How I Have, You Need applies to middle and high school students

Check out Episodes 121 and 260 of this podcast for more about using I Have, You Need to develop the major strategies.

See also Episode 164 for more information about I Have, You Need.

Ep 6: The Development of Mathematical Reasoning Pt 2: Functional Reasoning

Tue, 28 Jul 2020 00:00:00 -0500

Reasoning and numeracy doesn't come to an end in highschool! Can we mathematize algebraic concepts? What is Functional Reasoning? Listen as Pam explains how Functional Reasoning builds off of Proportional Reasoning and empowers students to analyze and understand patterns of related value sets. Sounds complicated? Don't worry, Kim does her best to keep Pam on track and grounded.
Talking Points:

What is Proportional Reasoning: unit rates and non-unit rates
How Functional Reasoning builds on Proportional Reasoning: slope, transformations, rational functions
It's not about being able to visualize a static graph, it's understanding the relationship between the variables
How to tell if someone is using Functional Reasoning

Ep 5: The Development of Mathematical Reasoning

Tue, 21 Jul 2020 00:00:00 -0500

This episode is so important! Pam and Kim describe the Development of Mathematical Reasoning, and how it transforms our understanding of what it means to learn and teach mathematics. They discuss how freeing it feels to know that everyone can develop their reasoning, and how the Development of Mathematical Reasoning empowers teachers to know how best to help their students. Stay tuned to the end for the big announcement!
Talking Points:

What is The Development of Mathematical Reasoning and the different kinds of reasoning?
We don't need calculators, we need reasoners
Are we stuck where we are or can we develop more sophisticated reasoning?
Use the free download How Do You Reason guide to know how you, your friends, and students are reasoning.
Announcing the new Development of Mathematical Reasoning Workshop!

See episode 61 for more about tools to help students develop reasoning

Click here: A new free online workshop. So exciting! Be sure to tell all your colleagues about this amazing opportunity to learn how to help anyone develop reasoning.

Ep 4: Top Ten Influencers

Tue, 14 Jul 2020 00:00:00 -0500

Who's shaping math education today? Does Pam come up with it all herself? Far from it! In her fourth episode Pam wanted to pay homage to her top 10 influencers as well as share with you all some of her favorite resources for teaching Real Math. Join Pam and Kim as they share stories ranging from the excitement of the first graphing calculators to the embarrassment of mispronouncing their hero's name. It's sure to be a good time.
Talking Points:

Who were Pam's early influencers?
(Janie Schielack, Marilyn Burns, Investigations in Data, Number and Space, Cathy Fosnot and Martin Dolk, Pam Giles, TCubed, Jerry Murdoch)
Who is shaping Pam's math journey today?
(Cathy Fosnot, Desmos, MTBOS, Peter Liljedahl, Jo Boaler, university students and teachers)
Desmos' card sorts and polygraphs: excellent tools for remote teaching.

Ep 3: Mentoring Mathematicians

Tue, 07 Jul 2020 00:00:00 -0500

When we read, we are reading. When we write, we are writing. What is the verb for doing math? Pam and Kim continue from Episode 2 to discuss what it means to do and teach Real Mathematics. Listen in as they discuss what mathematicians really do, and how teachers can mentor students as mathematicians.
Talking Points:

What does "Math is Figure-Out-Able" mean?
What are Real Math and fake math?
What do real mathematicians do?
What is mathematizing?
What does it mean to mentor students as mathematicians?

Ep 2: Math Does Not Equal Algorithms!

Tue, 30 Jun 2020 00:00:00 -0500

What is 99 plus anything? What is 99 times anything? How can you use relationships to solve those problems? In this episode, Pam and Kim talk about how Real Math is not about mimicking an algorithm, but rather about letting the numbers and the structure dictate the strategy. Teaching Real Math is about listening to students - that you must know your content, and know your kids.
Talking Points:

What are Algorithms?
Do mathematicians typically use algorithms?
What does Pam mean when she says it's not about the algorithm?
You have to know your content, know your kids
If not algorithms, what is Pam's goal?
Kim's Over strategy for addition and multiplication
What is 99 + anything?

Ep 1: Math is Figureoutable

Tue, 16 Jun 2020 00:00:00 -0500

In this debut podcast, mathematics teacher educator Pam Harris talks with her cohost, Kim Montague, about how they met and the work that they do together now. They set the stage that in this podcast they will talk about Real Mathematics and about how to teach mathematics. They answer the question, "If not algorithms, then what?"