Ep 324: Solving Equations Using Equivalence

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 23, 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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education 

When do we allow students more freedom, and when do we need to be more explicit? In this episode, Pam and Kim analyze a Distance vs. Removal subtraction Problem String, identifying when they are explicit and when they are not.Talking Points:Intentional contexts, number choices, and problem orderChoosing which strategies to elicit and representPlanned board layouts Focusing the conversation Highlighting mathematical behaviorsLayering explicit content, behavior, and community goals around open-ended student reasoningLinks:1. Podcasts Episodes Distance vs. Removal: Ep96 and Ep149  2. Pam's BooksCheck out Pam's 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 September 16, 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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education 

Many aspects of teaching can be improved by being more explicit. In this episode, Pam and Kim identify specific categories where explicit teaching is necessary, borrowing Piaget's distinction between social-conventional and logical-mathematical knowledge.Talking Points:Being explicit about a goal doesn't mean teaching it as a step-by-step procedure.Good teaching requires explicit goals.Examples of Math Content Goals Examples of Math Behavior Goals Examples of Community Behavior Goals Links:Blog Post: Searching for a Better WayWhich Workshop to Take QUIZBuilding Powerful Mathematics RegistrationCheck out Pam's 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 September 9, 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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education 

Is the popular discussion around "explicit teaching" helpful? Do we all envision the same thing? In this episode, Pam and Kim discuss their thoughts about "explicit teaching", and which parts of mathematics require explicit teaching, and which do not. Talking Points:The difference between social-conventional knowledge and logical- mathematical knowledgeExamples of social knowledge and when students must be told something in mathematicsExamples of logical-mathematical knowledge and how it should be built through experiences, not rote rules.Most of mathematics is logical-mathematical and requires varied experiences.Links:Blog Post: Searching for a Better WayWhich Workshop to Take QUIZBuilding Powerful Mathematics RegistrationCheck out Pam's 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 September 2, 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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education 

What does reasoning about algebraic expressions look like? In this episode, Kim facilitates a Problem String that has Pam solving equations using equivalence.Talking Points:Using comparison to ignore commonalities on both sides of an equationEquivalence strategies are the most sophisticatedLearning to think relationally, rather than procedurallyRelational thinking builds mathematical identity and genuine engagementLinks:Blog Post: Searching for a Better WayWhich Workshop to Take QUIZBuilding Powerful Mathematics RegistrationCheck out Pam's 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 26, 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: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education 

With so much to teach every year, we know you're always looking for the biggest impact for long term success for your students. In this episode, Pam and Kim discuss models that grow with students as they learn more and more mathematics.Talking Points:Verticality in practice standards, content progressions, vocabulary, notation, and strategies How area models extend from elementary to high schoolOpen number lines mature into double number linesRatio tables can start as early as 3rd grade and scale to decimals, large numbers, proportional relationships.How models act as lasting mental anchors, not just "picture drawing" as a substitute for mathematical ability.LinksBlog:  Post: Searching for a Better Check out Pam's social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC