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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 timeNotice and tell what time it is a lot with kidsNotice 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 prepare students for linear functionsExample Problem StringsRegistration for workshops closes this Friday!Get a workshop while you can:
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 halving3rd Grade - concepts around 1005th Grade - multiplication and volume7th Grade - rates (see Episode 112 for Unit Rate Problem String)Algebra I - exponential functionsPre-Calculus - functionsOur workshops are open for registration! Take advantage now to change your math classroom!
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 ruleRich Tasks - see Episodes 102 and 103Test Prep?!Use instructional routines for spiral reviewTune in to the next episode for examplesRegistration for our workshops are open now! Sessions for everyone, K-12! Check them out!
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 studentsPartial strategies are a great starting place but we have to help students develop more sophisticated strategiesThe starting strategies for each major operationStudents need lots of experience developing relationships through Problem Strings and Rich Tasks for strategies to be natural outcomesCheck out our free eBook to learn more about these strategies: don't miss out on the You Can Change Math Class Challenge! out Episodes 10 and 12 of this podcast for more ideas about starting your school year.
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, MathStratChat and other instructional routines and gamesWhat you celebrate, answers or thinking, is what students will shareHow to transform your curriculum if you're super gung-ho Don't miss out on the You Can Change Math Class Challenge! Register today at more about I Have, You Need by listening to episode 7, or visit us at
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 lineWhen could an double open number line be helpful in middle school and high school?When is a ratio table more versatile than a double open number line?What other concepts can a double open number line be helpful for students?The percent bar is a double open number line?Check out our free download on Double Number Lines:
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 when we use the traditional way of teaching measurement?We suggest a rich task by Cathy Fosnot to help students develop an understanding of the open number line through measurementWhat can you model on an open number line? Elapsed time, addition and subtraction of whole numbers and integers and moreIs an open number line helpful for higher math concepts?Check out Cathy Fosnot's amazing rich task:
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?
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 106Applying knowledge of whole number multiplication to decimalsIt's more about reasoning than shifting the decimalReasoning in small steps builds understanding vs. just counting the decimalsReasonableness comes from keeping kids in reasoning landLanguage to focus on and language to avoid
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 moneyStudents need to develop a few starting relationships before becoming more sophisticatedSmart Partial Products with decimals
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 TantonMoney 
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 then scale up.How this applies to middle school students.How can Five is Half of 10 be used with more sophisticated thinking?
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 speedPam, the basketball playerIt's not about memorizing disconnected rules and procedures.Kim, the teacher pleaser Experience and opportunities are important so kids have choicesWe need all students in the game of mathIs there such a thing as a "math gene" or natural talent?All students have different talents to bring to the tableTake the Math Perspective Quiz to find more about your perspective of math class and instruction.All students have talents to bring to the table
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 tellingThe importance of a common vocabulary - Check out Episodes 58 and 101Empowering teachers and leaders through Journey and Journey LeaderDeep dive online workshops for Kindergarten through middle schoolBuilding Powerful Linear Functions for high school coming soon!
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 worldAn eye towards equityLead to the mathematicsPacked with patternsNatural extensionsMake the math realizableBuilding Powerful Linear Functions coming Fall 2022See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!
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 decisionsReplete with patternsPromote discussion and communicationTasks should lead somewhereBe extendableHave an Element of SurpriseAnd More!
Ep 101: Strategies!

Ep 101: Strategies!


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 StrategiesProblem Solving StrategiesTeaching StrategiesStrategies for TeachingWhy without one type of strategy, the other strategies will fall flat
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 enoughCount AroundsMultiple TowersBase 10 materialsUsing correct place value language
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-bookA gnarly problem solved using Real MathIt's all about efficiency and developing more sophisticated reasoningPartial strategies are a great starting point but not the ending placeKudos to Pam's research and thoughtfulnessWhy does Pam seem to focus on computation?What believers are sayingOther ways to learn with PamWe can make higher math more accessibleBONUS: Kim's failed attempt at the standard algorithmGet the BIG download here!
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