Math is Figure-Out-Able!

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 choiceRatio tables aren't a strategy, they're a model/representation of the strategy or strategies being usedIf you understand fractional equivalence, you don't need rules for fraction operationsHow to add 3/4 and 5/7 thinking and reasoning using a ratio tableDo 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 131See Ep 64 and 176 for more on equivalent ratios!Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education

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.

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 StringRatios must be equivalent in a ratio tableReasoning proportionally can be much cleaner than cross-multiply-and-divideModel building strings verses strategy building stringsStart with reasoning and representing thinking then dive deeper into propertiesWhat's next? A strategy building string using a ratio table as a modelDon't forget to post how you represented your ratio table on social media!

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.

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 MathStratChatDoes 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

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.

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 tableSome powerful generalizations from the problem string using a ratio table modelAre we done talking about ratio tables?Online workshop registration opens in January!

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.

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 doWe can do more than we can say and say more than we can representDo, Say, RepresentThe importance of knowing your content and knowing your studentsHelping 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

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.