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

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:<ul><li>Which models are helpful </li><li>Decimals and money</li><li>Students need to develop a few starting relationships before becoming more sophisticated</li><li>Smart Partial Products with decimals</li></ul>

Ep 108: Beginning Decimal Multiplication

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 

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:<ul><li>Base Ten Materials </li><li>Exploding Dots by James Tanton</li><li>Money </li></ul>

Ep 107: All About Decimals

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?

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:<ul><li>How beginning learners will use multiplying by 10 in double digit multiplication problems.</li><li>How more sophisticated students deal with smaller numbers then scale up.</li><li>How this applies to middle school students.</li><li>How can Five is Half of 10 be used with more sophisticated thinking?</li></ul>

Ep 106: Multiplying by Ten

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

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:<ul><li>Mathematizing is not about speed</li><li>Pam, the basketball player</li><li>It's not about memorizing disconnected rules and procedures.</li><li>Kim, the teacher pleaser </li><li>Experience and opportunities are important so kids have choices</li><li>We need all students in the game of math</li><li>Is there such a thing as a "math gene" or natural talent?</li><li>All students have different talents to bring to the table</li><li>Take <a href="https://www.mathisfigureoutable.com/xyz" rel="nofollow" target="_blank">the Math Perspective Quiz</a> to find more about your perspective of math class and instruction.</li><li>All students have talents to bring to the table</li></ul>

Ep 105: Let the Students Play 

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!

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:<ul><li>It's not 'Pam Math', it's Real Math and developing mathematicians!</li><li>Coaching teachers is about mentoring, not just telling</li><li>The importance of a common vocabulary - Check out Episodes 58 and 101</li><li>Empowering teachers and leaders through Journey and Journey Leader</li><li>Deep dive online workshops for Kindergarten through middle school</li><li>Building Powerful Linear Functions for high school coming soon!</li></ul>

Ep 104: Things We Have Learned

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!

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:<ul><li>Relatable to students not just real world</li><li>An eye towards equity</li><li>Lead to the mathematics</li><li>Packed with patterns</li><li>Natural extensions</li><li>Make the math realizable</li><li>Building Powerful Linear Functions coming Fall 2022</li></ul>See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!

Ep 103: Rich Tasks, Investigations, 3-Act Tasks, Pt 2

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!

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:<ul><li>Invite students to make decisions</li><li>Replete with patterns</li><li>Promote discussion and communication</li><li>Tasks should lead somewhere</li><li>Be extendable</li><li>Have an Element of Surprise</li><li>And More!</li></ul>

Ep 102: Rich Tasks, Investigations, 3-Act Tasks, Pt 1

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

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:<ul><li>Numeracy Strategies</li><li>Problem Solving Strategies</li><li>Teaching Strategies</li><li>Strategies for Teaching</li><li>Why without one type of strategy, the other strategies will fall flat</li></ul>

Ep 101: Strategies!

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

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:<ul><li>Why 'place labeling' is ok, but not enough</li><li>Count Arounds</li><li>Multiple Towers</li><li>Base 10 materials</li><li>Using correct place value language</li></ul>

Ep 100: Celebrating Place Value

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! https://mathisfigureoutable.com/big

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:<ul><li>How to use the BIG downloadable e-book</li><li>A gnarly problem solved using Real Math</li><li>It's all about efficiency and developing more sophisticated reasoning</li><li>Partial strategies are a great starting point but not the ending place</li><li>Kudos to Pam's research and thoughtfulness</li><li>Why does Pam seem to focus on computation?</li><li>What believers are saying</li><li>Other ways to learn with Pam</li><li>We can make higher math more accessible</li><li>BONUS: Kim's failed attempt at the standard algorithm</li></ul>Get the BIG download here! <a href="https://mathisfigureoutable.com/big" rel="nofollow" target="_blank">https://mathisfigureoutable.com/big</a>

Ep 99: If Not Algorithms, Then What? Finale!

Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what?Join them for ~15 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able.

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 algorithmA precursor strategy: Partial QuotientsSmart Partial QuotientsOver-Under5 is Half of 10Equivalent RatiosCombining strategiesGet the BIG download of all the major strategies for addition, subtraction, multiplication, and division here! https://mathisfigureoutable.com/big

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:<ul><li>Pam's personal harmful experience from the long division algorithm</li><li>A precursor strategy: Partial Quotients</li><li>Smart Partial Quotients</li><li>Over-Under</li><li>5 is Half of 10</li><li>Equivalent Ratios</li><li>Combining strategies</li></ul>Get the BIG download of all the major strategies for addition, subtraction, multiplication, and division here! <a href="https://mathisfigureoutable.com/big" rel="nofollow" target="_blank">https://mathisfigureoutable.com/big</a>

Ep 98: If Not the Division Algorithm, Then What?

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 efficiently than the traditional algorithm. But even more important than that, they will be developing Multiplicative Reasoning! Talking Points:Smart Partial ProductsOver/Under5 is Half of 10How are these strategies related to the distributive property?Doubling/HalvingHow is this strategy related to the associative property?Using Quarters &amp; Scaling Bonus! Flexible FactoringGet a download of all the major strategies here: www.mathisfigureoutable.com/big

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 efficiently than the traditional algorithm. But even more important than that, they will be developing Multiplicative Reasoning!  Talking Points:<ul><li>Smart Partial Products</li><li>Over/Under</li><li>5 is Half of 10</li><li>How are these strategies related to the distributive property?</li><li>Doubling/Halving</li><li>How is this strategy related to the associative property?</li><li>Using Quarters &amp; Scaling </li><li>Bonus! Flexible Factoring</li></ul>Get a download of all the major strategies here: <a href="http://www.mathisfigureoutable.com/big" rel="nofollow" target="_blank">www.mathisfigureoutable.com/big</a>

Ep 97: If Not the Multiplication Algorithm, Then What?

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 NumberRemove a Friendly Number - OverRemove to a Friendly NumberConstant DifferenceHow do students choose which one to use?Get the download! www.mathisfigureoutable.com/big

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:<ul><li>Remove a Friendly Number</li><li>Remove a Friendly Number - Over</li><li>Remove to a Friendly Number</li><li>Constant Difference</li><li>How do students choose which one to use?</li></ul> Get the download! <a href="http://www.mathisfigureoutable.com/big" rel="nofollow" target="_blank">www.mathisfigureoutable.com/big</a>

Ep 96: If Not the Subtraction Algorithm, Then What?

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 a Friendly Number Give and Take When do you use each strategy?Get our download of all the major strategies here! mathisfigureoutable.com/big

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: <ul><li>Splitting by Place Value (a precursor strategy)</li><li>Add a Friendly Number </li><li>Add a Friendly Number - Over </li><li>Get to a Friendly Number </li><li>Give and Take </li><li>When do you use each strategy?</li></ul> Get our download of all the major strategies here! <a href="https://www.mathisfigureoutable.com/big" rel="nofollow" target="_blank">mathisfigureoutable.com/big</a>

Ep 95: If Not the Addition Algorithm, Then What?

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 exploring the major strategies for each operation that students need so that they can solve ANY problem that's reasonable to solve without a calculator. Talking Points:Pam's journey from learning only step by step procedures to mathematizingHow this series can take Pam's published books a step furtherHow Kim, and many other mathematicians approach problemsOwnership of the major relationships empowers students with choiceHonor students thinking, but don't leave students where they areGet the download!: mathisfigureoutable.com/big

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 exploring the major strategies for each operation that students need so that they can solve ANY problem that's reasonable to solve without a calculator.  Talking Points:<ul><li>Pam's journey from learning only step by step procedures to mathematizing</li><li>How this series can take Pam's published books a step further</li><li>How Kim, and many other mathematicians approach problems</li><li>Ownership of the major relationships empowers students with choice</li><li>Honor students thinking, but don't leave students where they are</li></ul> Get the download!: <a href="https://mathisfigureoutable.com/big" rel="nofollow" target="_blank">mathisfigureoutable.com/big</a>

Ep 94: If Not Algorithms, Then What?

When we feel passionately about the way we teach, we can sometimes inadvertently miscommunicate when speaking with parents. In this episode, Pam and Kim discuss how to appropriately talk about getting correct answers and preparing for high stakes tests so that parents know their children are in good hands.Talking Points:Answers are important!What we don't want to communicate to parentsPreparing students for high stakes tests is important!Insight into a test writer's thinking when they write test itemsHelping students mathematize will help them feel more confident and excel on high stakes tests

When we feel passionately about the way we teach, we can sometimes inadvertently miscommunicate when speaking with parents. In this episode, Pam and Kim discuss how to appropriately talk about getting correct answers and preparing for high stakes tests so that parents know their children are in good hands. Talking Points:<ul><li>Answers are important!</li><li>What we don't want to communicate to parents</li><li>Preparing students for high stakes tests is important!</li><li>Insight into a test writer's thinking when they write test items</li><li>Helping students mathematize will help them feel more confident and excel on high stakes tests</li></ul>

Ep 93: Partnering With Parents: Do Correct Answers Matter?

Partnering with parents can be a blast! In this episode Pam and Kim describe how they organize and run math nights to help parents experience mathematizing and get excited about what their students will be learning.Talking Points:Typical parent math nights vs. our parent math nightsOpportunity to share grade level or school wide expectationsImportance of a Q &amp; A for parentsHelp parents experience math the way their students doMathematizing for parents at the "sweet spot" level of mathSuggestions for finding Problem Strings to use at math nightsLogistics tips for parent math nightAdvantages of a series of parent nights

Partnering with parents can be a blast! In this episode Pam and Kim describe how they organize and run math nights to help parents experience mathematizing and get excited about what their students will be learning. Talking Points:<ul><li>Typical parent math nights vs. our parent math nights</li><li>Opportunity to share grade level or school wide expectations</li><li>Importance of a Q &amp; A for parents</li><li>Help parents experience math the way their students do</li><li>Mathematizing for parents at the "sweet spot" level of math</li><li>Suggestions for finding Problem Strings to use at math nights</li><li>Logistics tips for parent math night</li><li>Advantages of a series of parent nights</li></ul>

Ep 92: Partnering With Parents: Math Night!

How can we proactively partner with and support parents? In this episode Pam and Kim discuss ways they over communicate to parents to keep parents involved and not confused. Talking Points: Newsletters: What is helpful information and tips for parents I can share?Parent-teacher conferences: What can I share with parents about math other than just grades?Homework assignments: I don't like drill and kill. What kinds of homework are helpful for students and parents? 

How can we proactively partner with and support parents? In this episode Pam and Kim discuss ways they over communicate to parents to keep parents involved and not confused.  Talking Points: <ul><li>Newsletters: What is helpful information and tips for parents I can share?</li><li>Parent-teacher conferences: What can I share with parents about math other than just grades?</li><li>Homework assignments: I don't like drill and kill. What kinds of homework are helpful for students and parents? </li></ul>

Ep 91: Partnering With Parents: Over Communicate

Parents are so important, and sometimes they get concerned when their child isn't being taught math they way they were expecting. In this episode Pam and Kim discuss hearing parents' concerns and helping them feel heard and then helping them understand the math. We appreciate parents and we are better with them!Talking Points:We want invested parentsParents need to be heard, and then they need to understandThe importance of listening to understand

Parents are so important, and sometimes they get concerned when their child isn't being taught math they way they were expecting. In this episode Pam and Kim discuss hearing parents' concerns and helping them feel heard and then helping them understand the math. We appreciate parents and we are better with them! Talking Points:<ul><li>We want invested parents</li><li>Parents need to be heard, and then they need to understand</li><li>The importance of listening to understand</li></ul>

Ep 90: Partnering With Parents-Listening

Kim has a story to tell that Pam hasn't heard yet! Listen in to get a feel of how math can be when students understand that Math is Figure-Out-Able.Talking Points:Pajama Math and exploring relationships in multiplying fractionsCan you really just multiply straight across with fractions?Two ways to reason about 3/5 times 3/9Pam and Kim reason multiple ways about 3/4 times 2/5Join us in #MathStratChat!

Kim has a story to tell that Pam hasn't heard yet! Listen in to get a feel of how math can be when students understand that Math is Figure-Out-Able. Talking Points:<ul><li>Pajama Math and exploring relationships in multiplying fractions</li><li>Can you really just multiply straight across with fractions?</li><li>Two ways to reason about 3/5 times 3/9</li><li>Pam and Kim reason multiple ways about 3/4 times 2/5</li><li>Join us in #MathStratChat!</li></ul>

Ep 89: Playing With Fraction Multiplication

This was a great introduction. I can’t wait to listen to your next!  I would encourage any teacher, parent, and student to listen and open your minds to REAL math.

Very insightful

Math is Figure-Out-Able with Pam Harris

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