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 generaliza...
Dec 06, 2022•29 min•Ep. 129
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.
Dec 01, 2022•5 min
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...
Nov 29, 2022•26 min•Ep. 128
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.
Nov 24, 2022•6 min
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...
Nov 22, 2022•24 min•Ep. 127
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.
Nov 17, 2022•5 min
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://...
Nov 15, 2022•26 min•Ep. 126
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.
Nov 10, 2022•5 min
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 ...
Nov 08, 2022•24 min•Ep. 125
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.
Nov 03, 2022•8 min
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 ...
Nov 01, 2022•21 min•Ep. 124
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.
Oct 27, 2022•6 min
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 ...
Oct 25, 2022•26 min•Ep. 123
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.
Oct 20, 2022•6 min
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 prob...
Oct 18, 2022•20 min•Ep. 122
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.
Oct 13, 2022•5 min
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,...
Oct 11, 2022•28 min•Ep. 121
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. Student...
Oct 04, 2022•20 min•Ep. 120
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
Sep 27, 2022•21 min•Ep. 119
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
Sep 20, 2022•19 min•Ep. 118
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! G...
Sep 13, 2022•21 min•Ep. 117
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 - function...
Sep 06, 2022•36 min•Ep. 116
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...
Aug 30, 2022•20 min•Ep. 115
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 re...
Aug 23, 2022•27 min•Ep. 114
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, Math...
Aug 16, 2022•23 min•Ep. 113
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 doub...
Aug 09, 2022•31 min•Ep. 112
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...
Aug 02, 2022•26 min•Ep. 111
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?...
Jul 26, 2022•16 min•Ep. 110
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 who...
Jul 19, 2022•18 min•Ep. 109
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
Jul 12, 2022•25 min•Ep. 108
