Math is Figure-Out-Able!

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

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 prepa...

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...

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 routin...

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 strate...

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 o...

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 numbe...

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 i...

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  Di...

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....

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 Product...

We've gotten a ton of questions about decimals. In this episode Pam and Kim discuss three different models and why they are great for questioning and building relationships, but may or may not be good for computation. Talking Points: Base Ten Materials  Exploding Dots by James Tanton Money 

Most students can scale up by ten as they begin to multiply larger numbers and that is a great starting place for students. In this episode Pam and Kim discuss a more sophisticated way of scaling numbers in multiplication problems.  Talking Points: How beginning learners will use multiplying by 10 in double digit multiplication problems. How more sophisticated students deal with smaller numbers th...

Often people misunderstand what this game we call mathematics is and feel they aren't good enough to play. In this episode Pam and Kim discuss how students need the opportunity to experience and play in the real game of mathematics. Talking Points: Mathematizing is not about speed Pam, the basketball player It's not about memorizing disconnected rules and procedures. Kim, the teacher ple...

It's our two year anniversary! We are so grateful you've spent this time with us. In this episode Pam and Kim discuss openly things they've learned and how they've grown during their journey as math teacher educators. Talking Points: It's not 'Pam Math', it's Real Math and developing mathematicians! Coaching teachers is about mentoring, not just telling The...

What are some examples of rich tasks that are designed to intrigue and engage students? In this episode Pam and Kim give some specific examples and describe why they are so rich. Talking Points: Relatable to students not just real world An eye towards equity Lead to the mathematics Packed with patterns Natural extensions Make the math realizable Building Powerful Linear Functions coming Fall 2022...

Let's talk rich tasks! On Twitter we enjoyed a great conversation about what makes a rich task rich. We thought we'd comment on some great suggestions from Professor Tad Watanabe, inspired from his mentor Dr. Grayson Weatley. Talking Points: Invite students to make decisions Replete with patterns Promote discussion and communication Tasks should lead somewhere Be extendable Have an Eleme...

What comes to mind when someone says the word "strategy"?  There are at least four different meanings for the word "strategy" in mathematics teaching. In this episode Pam and Kim parse out the different meanings and discuss how those meanings shape the outcomes of our teaching. Talking Points: Numeracy Strategies Problem Solving Strategies Teaching Strategies Strategies for Tea...

We love that we've been able to make 100 episodes! We also love that 1 hundred is 10 tens, so let's talk place value! In this episode Pam and Kim discuss why students struggle with place value, and suggest some of their favorite place value activities. Talking Points: Why 'place labeling' is ok, but not enough Count Arounds Multiple Towers Base 10 materials Using correct place...

In the last 5 episodes we've laid out the most important strategies for students to be able to solve for all four operations. So what? In this episode Pam and Kim solve a gnarly problem to demonstrate how mathematizing can empower you and your students, and open up to the world of Real Math. Talking Points: How to use the BIG downloadable e-book A gnarly problem solved using Real Math It&apos...

Division is figure-out-able! In this episode Pam and Kim discuss the four main strategies students need to develop to solve any division problem that's reasonable to solve without a calculator.  Talking Points: Pam's personal harmful experience from the long division algorithm A precursor strategy: Partial Quotients Smart Partial Quotients Over-Under 5 is Half of 10 Equivalent Ratios Com...

What are the five major strategies for multiplication? In this episode Pam and Kim name and give examples of each of the five major multiplication strategies. If students own these strategies they should be able to solve any multiplication problem that is reasonable to solve without a calculator. They will be able to solve it as efficiently as a traditional algorithm and most of the time more effi...

It's time for subtraction! In this episode Pam and Kim name and give examples of the four main subtraction strategies students need to own to solve any subtraction problem that is reasonable to solve without a calculator. Talking Points: Remove a Friendly Number Remove a Friendly Number - Over Remove to a Friendly Number Constant Difference How do students choose which one to use? Get the dow...

What are the major strategies students need to know to solve any addition problem that is reasonable to solve without a calculator? In this episode Pam and Kim list them out, give examples, and some insights into how they choose which strategy to use for any given problem.  Talking Points:  Splitting by Place Value (a precursor strategy) Add a Friendly Number  Add a Friendly Number - Over  Get to...

We want students to be real problem solvers, and we know that means much more than helping them get correct answers. But we never want to put students in a position where they are disadvantaged because they don't know the traditional algorithms. We actually want them to have a much deeper and richer understanding of mathematical relationships. In this episode Pam and Kim begin a series explor...