Ep 266: Solving Proportions - Within & Between

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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationWant more? Check out the archive of all of our #MathStratChat posts!

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 StringThinking about "between" and "within" relationships in a ratio tableSlope, rate of change, similar triangles, equivalence: all figure-out-ableRatios and proportional reasoning to functional reasoningSlope is a ratioCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC 

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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationWant more? Check out the archive of all of our #MathStratChat posts!

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 sophisticatedSeeking the "ooh" factor or the "aha" momentCompare strategies and make connectionsMaking choices based on numbers or the structureSeeking efficiency and making generalizationsStart with "What do I know?"Seek understanding and asking for moreThe importance of acknowledging mathematical behaviorsCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC 

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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationWant more? Check out the archive of all of our #MathStratChat posts!

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 studentsSometimes educators talk past each other, using words without examples to give meaningExperiencing mathing is different from helping students learn to do the mental actions of mathingIs there a continuum of how to teach?Examples of "direct" and "inquiry based" instructionShould we ever be explicit?Why is it so important to have a common experience?See the debate here: https://www.youtube.com/watch?v=CANtr9OHAvUCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC 

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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationWant more? Check out the archive of all of our #MathStratChat posts!

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 modelsAddition strategies modeled with equationsProporties that the addition strategies are based onWhen manipulatives are appropriateWhy teachers need to own the major strategies additionGet the free ebook of Major Strategies at: https://www.mathisfigureoutable.com/bigCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LL

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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationWant more? Check out the archive of all of our #MathStratChat posts!

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 equationsUsing models to visualize propertiesStrategies 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/bigCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting