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 ...
Mar 21, 2023•25 min•Ep. 144
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...
Mar 16, 2023•8 min
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...
Mar 14, 2023•32 min•Ep. 143
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 ...
Mar 09, 2023•8 min
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 Pro...
Mar 07, 2023•25 min•Ep. 142
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 ...
Mar 02, 2023•6 min
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 kno...
Feb 28, 2023•33 min•Ep. 141
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...
Feb 23, 2023•9 min
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 way...
Feb 21, 2023•26 min•Ep. 140
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...
Feb 16, 2023•6 min
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.c om/big Check out our social media Twitter: @PWHarris Ins...
Feb 14, 2023•22 min•Ep. 139
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...
Feb 09, 2023•5 min
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 problem...
Feb 07, 2023•23 min•Ep. 138
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...
Feb 02, 2023•5 min
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 getti...
Jan 31, 2023•25 min•Ep. 137
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...
Jan 26, 2023•6 min
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 Registratio...
Jan 24, 2023•21 min•Ep. 136
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.
Jan 19, 2023•7 min
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 challe...
Jan 17, 2023•25 min•Ep. 135
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.
Jan 12, 2023•7 min
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 "pro...
Jan 10, 2023•28 min•Ep. 134
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.
Jan 05, 2023•6 min
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 re...
Jan 03, 2023•29 min•Ep. 133
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.
Dec 29, 2022•8 min
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 an...
Dec 27, 2022•31 min•Ep. 132
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.
Dec 22, 2022•5 min
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 ...
Dec 20, 2022•18 min•Ep. 131
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.
Dec 15, 2022•6 min
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 ...
Dec 13, 2022•26 min•Ep. 130
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.
Dec 08, 2022•6 min
