Shows
Math is Figure-Out-Able!Ep 289: Pedagogical Moves vs PersonalityAll teachers are different, but we should all teach intentionally. In this episode, Kim surprises Pam with a collection of favorite "Pam-isms" and asks Pam to elaborate on whether each one is an intentional teacher move and why it is important, or if it is just her personality.Talking PointsNinety-niiiiiiiiine...Is that legal?Isn't it nice, when the answer is the question?Sit up tall, you just mathed!Math is Figure-Out-Able!Bam!Could I invite you to consider...I know you didn't, but could you?Tell us more about that.Who wants their brain to...
2025-12-3023 minMath is Figure-Out-Able!Ep 282: Playing With MathUnderstanding math is important, and fun. In this episode, Pam and Kim discuss the necessity of play in mathematics education and share when, where, and why they each play differently with math.Talking Points:Dr. Brad Ballinger's view that algorithms are...playful??The fun and educational value of simply playing with mathmatics How Pam and Kim differ in their purposes and preferences when playing with mathHow #MathStratChat can help you! Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Co...
2025-11-1120 minMath is Figure-Out-Able!Ep 276: Facilitating Pam's Favorite Problem StringFacilitating a Problem String is much more than providing a list of problems. In this episode Pam shares the moment to moment decisions she makes when facilitating a "Sticks of Gum" proportional realtionship building Problem String.Talking Points: Setting the stageHow to pull out thinking Using this string to math with teachers in professional developmentReinforcing mathematical behaviorsStrategically determining wait timeUsing potential misunderstandings as learning opportunities Applying models to student thinkingDeciding the order of strategies to elicitChoosing the numbers in the Problem StringCheck out the Sticks of Gum Problem String here:https://www.mathisfigureoutable.com...
2025-09-3039 minMath is Figure-Out-Able!Ep 253: Choosing a Problem StringWhich Problem Strings are appropriate for your students? In this episode Pam and Kim discuss what they consider when choosing a Problem String for a classroom.Talking Points:A fraction addition example stringThings to consider when choosing a Problem String:Prewritten vs write your ownTime of yearStrategies students already ownBuilding a model vs building a strategyOrder of sophistication of strategiesBuilding a model vs strategyNew content versus review/reteachSee episodes 33, 71, 72, 163, 226, 241 for more on Problem Strings!Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author...
2025-04-2229 minMath is Figure-Out-Able!Ep 252: Foundations for Multi-Digit Multiplication & Division StrategiesWhat kinds of tasks help students build multi-digit multiplication and division strategies? In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for multi-digit multiplication and division: Scaling, Over and Adjust, Partial Products, FactoringTalking Points:Benefits of using diverse task typesSample of three "messy" tasks to develop:Ratio tablesArea model2 different kinds of divisionRelationship between multiplication and divisionPractice ideasGet your kit from Hand2mind here: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-multiplication-division-small-group-kitCheck out our social mediaTwitter: @PWHarrisInstagram: Pam...
2025-04-1529 minMath is Figure-Out-Able!Ep 251: Foundations for Multi-Digit Addition & Subtraction StrategiesWhat kinds of tasks help students build multi-digit addition and subtraction strategies? In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for multi-digit addition and subtraction: Friendly numbers, place value, adjusting, the commutative property, decomposingTalking Points:Sequencing tasks is more than just moving from one page to the next in the teacher guideSample of three "messy" tasks to:develop number linesmake connections between addition and subtractionanalyze strategiessolidify a strategyFor more sequences, check out the Foundations for Strategies from Hand2mind!: https://www.hand2mind...
2025-04-0832 minMath is Figure-Out-Able!Ep 250: Foundations for Single Digit Multiplication & Division StrategiesMath class is richer and more fun when the goal is more than answer-getting!In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for single digit multiplication and division: doubling, making use of ten, and partial products/quotients.Talking Points:Three sample sequence of tasks that use:A product approachStudent exploration of patternsJust in time vocabularyDifferentiation Foundations of multiplicative reasoning, area, geometryContexts to develop 3 major modelsUseful fact practiceAnchoring the learningFor more sequences, check out the Foundations for Strategies from Hand2mind!: https://w...
2025-04-0129 minMath is Figure-Out-Able!Ep 249: Foundations for Single Digit Addition & Subtraction StrategiesWhat should the bulk of math class look like? In this episode Pam and Kim discuss sequencing tasks to build foundational relationships that develop into major strategies.Talking PointsMajor relationships that build the major strategiesProblem Strings are one kind of taskFoundational Relationships for young learnersRich tasks that get kids messing with relationshipsWhat does practice look like? (See Episode 38 for more information on Hint Cards)Check out pre planned sequence of tasks in the Foundation for Strategies small group kit Order information for Foundation for Strategies here: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit
2025-03-2526 minMath is Figure-Out-Able!Ep 248: Avoid the I'm Not A Math Person TrapWhy do students give up on learning math? In this episode Pam and Kim discuss how using algorithms as teaching tools is distorting students' perception of what the definition of math is, which results in a poor mathematical identity. Talking Points:A mysterious five pound bagA proportional reasoning Problem StringTrap #1 and #2 (see Ep 246 and 247 for more details)Trap #3 a false definition of math that leads to Identity Definition of Math TrapRead Pam's new book for more information: Developing Mathematical Reasoning: Avoiding the Trap of AlgorithmsPurchase Book here: http://www.mathisfigureoutable.com/avoidthetrapsC...
2025-03-1819 minMath is Figure-Out-Able!Ep 247: Avoid the Digit TrapWhy do students not realize their incorrect answers are completely unreasonable? In this episode Pam and Kim discuss another trap students fall into when taught to mimic algorithms as 'the way' to solve problems.Talking Points:The patterns in Remove a Friendly Number Over strategyImportant place value conversationsHow students can be stuck dealing with only digits rather than magnitudeReasonableness, or "Ish", numbersParsing out polynomials into too many piecesCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2025-03-1122 minMath is Figure-Out-Able!Ep 246: Avoid the Trap of Using Less Sophisticated ReasoningIf a student can perform an algorithm, have they developed the mathematical reasoning that operation calls for? Or are they answer-getting? In this episode Pam and Kim discuss a major trap students fall into when we teach mathematics as a series of steps to rotely memorize. Talking Points:A closer look at the multiplication algorithm and a major trap.Problem String that helps give students a high does of patterns for a multiplicative strategy.Algorithms disregard reasonableness.Memorizing an algorithm is forgetable but every strategy learned helps build mental maps to the make subsequent strategies easier t...
2025-03-0422 minMath is Figure-Out-Able!Ep 245: Three Distortions that Ruin Math TeachingIf math is figure-out-able why does the world not always teach it that way? In this episode Pam and Kim discuss the three major distortions holding back math education today.Autostereograms as a metaphorHow the distortions are learnedHow the distortions create frustrationHow classrooms transform without distortionsWe want all kids to "see the shark"!Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2025-02-2527 minMath is Figure-Out-Able!Ep 244: Opportunities for Awareness of Current Math Teaching TopicsThere are so many way to participate in math professional learning! In this episode Pam and Kim discuss some benefits of choosing your own learning and engaging in free opportunities. Talking Points:Traditional forms of professional developmentBenefits of multi-day online summits/conferencesThe value of a shared experience Join in on these great math summits from other fantastic educators!Bulid Math Minds Free Virtual Math Summit, sponsored by Christina Tondevold: https://virtualmathsummit.com/Make Math Moments FREE Virtual Summit sponsored by Jon Orr and Kyle Pearse: https://m...
2025-02-1817 minMath is Figure-Out-Able!Ep 243: Integer DivisionIn this episode Pam and Kim use what students know about integer multiplication to tackle integer division (without mismatching rules or randomly switching signs).Talking Points:Reasoning about integer multiplication is ground work for integer divisionAn integer division Problem StringTeacher move: time to pause and considerUsing the quotative meaning of divisionThinking about opposites and reflectionUsing the partitive meaningSee episode 64 for the equivalent ratio strategyCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2025-02-1122 minMath is Figure-Out-Able!Ep 242: Integer MultiplicationOne of our most requested topics! In this episode Pam and Kim discuss integer multiplication without mismatching rules or randomly switching signs. Talking Points:Whole number multiplication strategies + meaning of integers leads to integer multiplication.The meaning of integers (See episodes 169, 181, 182, 183, 186)An integer multiplication Problem String and how to model Important noticings about modeling and contextThe importance of distance, reflection and oppositesThe importance of equivalence and commutative propertyFree downloads!https://www.mathisfigureoutable.com/factsps https://www.mathisfigureoutable.com/big Check out our social mediaTwitter: @PWHarrisInstagram: Pam...
2025-02-0428 minMath is Figure-Out-Able!Ep 241: Algorithm vs Problem Talk vs Problem StringIs mathing just about allowing students to solve problems their way? Aren't Probem Strings and Problem Talks really just the same routine? In this episode Pam and Kim discuss how Problem Strings move beyond Problem Talks to develop student's mathematical reasoning at a more sophisticated level.Talking Points:Example of a Problem TalkWhat do we gain from Problem Talks?Example of a Problem StringProblem Strings are more focused conversations Problems Strings allow for constant feedback, a high dose of patterningCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam H...
2025-01-2822 minMath is Figure-Out-Able!Ep 240: Real Math, Fake Math?Math may be figureoutable, but communication can be tricky! In this episode Pam and Kim discuss things to consider in order to be clear in the message we send when we speak about mathematics education.Talking Points:Duking it out!Are algorithms fake math?A better word than mathing?What do mathematicians think about algorithms?Do the math in mathematics education discussions so we have a common experience.Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2025-01-2123 minMath is Figure-Out-Able!Ep 239: Counted OutPeople across the world are changing math education. In this episode Pam and Kim discuss the documentary Counted Out that they were fortunate to see. They spotlight some of the thoughts of a few of the great researchers and add their thoughts about affecting change.Talking Points:Spoilers! The effects of algorithms today What needs to change?How do we contribute to change?Math is everywhereGiving students choiceJo Boaler will be on the January 2025 Math is Figureoutable Challenge! Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, aut...
2025-01-1426 minMath is Figure-Out-Able!Ep 239: Counted Out (SPOILER FREE)People across the world are changing math education. In this episode Pam and Kim discuss the documentary Counted Out that they were fortunate to see. They spotlight some of the thoughts of a few of the great researchers and add their thoughts about affecting change.Talking Points:Spoilers! The effects of algorithms today What needs to change?How do we contribute to change?Math is everywhereGiving students choiceJo Boaler will be on the January 2025 Math is Figureoutable Challenge! Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, aut...
2025-01-1323 minMath is Figure-Out-Able!Ep 238: Inverse Variation Pt 2Are inverse functions figureoutable? In this episode Pam and Kim go more into the nuance of when and how we want students to tackle inverse relationships.Talking Points:When to introduce inverse proportions Experience versus instructionAllowing students to grapple to in order to experience those aha momentsProblem String designCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2025-01-0725 minMath is Figure-Out-Able!Ep 237: Inverse Variation Pt 1What does it mean for something to be an inverse, or to be inversely proportional? In this episode Pam and Kim look at a specific kind of proportional reasoning.Talking Points:It's worth thinking before doingInversely proportional vs direct variation with non-unit scalingCommon misunderstandingsCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-12-3121 minMath is Figure-Out-Able!Ep 236: Exponent Relationships Pt 5Did you know that students can understand negative exponents without being told what they mean? In this episode Pam and Kim wrap up their series on exponent relationships.Talking Points:New listeners, where to start? Episode 156 Start HereDiscovering Negative ExponentsGive students experiences first and let them make sense of itUsing equivalent expressions to help students visualize and make generalizationsWhat grade levels are these strings for?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-12-2424 minMath is Figure-Out-Able!Ep 235: Exponent Relationships Pt 4What if students actually understood using common factors to simplify complex division expressions? In this episode Pam and Kim divide exponents without reciting a rule.Talking Points:Thinking versus reasoningProblem String Dividing Exponents"Canceling" vs "Dividing out to equal 1"Focus on left over factors vs mimicking a ruleWhy start with smaller bases?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-12-1722 minMath is Figure-Out-Able!Ep 234: Exponent Relationships Pt 3When variables and exponents start mixing, we need to memorize the rules, right? In this episode Pam and Kim develop exponential relationships, not rules.Talking Points:How "Kim's Notes" became "Half Sheets"Problem String to explore multiplicative relationships when working with exponents.Generalizing multiplication of exponentsCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-12-1022 minMath is Figure-Out-Able!Ep 233: Exponent Relationships Pt 2Would you believe I'm more comfortable dealing with exponents because I haven't memorized the rules? In this episode Pam and Kim continue building exponentiation with a great problem stringTalking Points:Problem string to help build exponentiationWhen and how to introduce vocabularyTeacher move: Choosing who shares, and in what orderMore confident reasoning without the rulesTeacher Move: GeneralizingCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-12-0322 minMath is Figure-Out-Able!Ep 232: Exponent Relationships Pt 1Can we prepare students for really hairy exponent problems without resorting to memorized rules? In this first episode of a series, Pam and Kim share a task that could get kids and teachers thinking more and more multiplicatively and understandably about exponents.Talking Points:Can a task have too many layers for students to be successful?Can we sequence a task that works for 3rd grade to Algebra?Problem String to connect prime factorization to exponents.Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education
2024-11-2625 minMath is Figure-Out-Able!Ep 231: Systems of Equations with SubstitutionShould high school mathematicians be given choice of which strategy to use? In this episode Pam and Kim wrap up their exploration of systems of equations.Talking Points:What is needed to understand 3x?Where students mess up using substitution How do different systems lend themselves to different strategies?Ketchup problemsNext step Problem Strings and comparing strategiesGiving students choiceCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-11-1920 minMath is Figure-Out-Able!Ep 230: Systems of Equations with Elimination (with sandwiches and cookies)Don't you think math needs more cookies in it? In this episode Pam and Kim use Desmos graphing calculator to go through a routine to make sense of systems of equations before doing any elimination or substitution.Talking Points:Kim going to a Cafe for sandwiches and cookiesGraphing on Desmos graphing calculatorUnderstanding x and y interceptsUnderstanding where the lines intersect Relating systems of equations to each otherLink to Desmos Graphing Calculator: https://www.desmos.com/calculator/qq59ey0bub Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFa...
2024-11-1223 minMath is Figure-Out-Able!Ep 229: Solving InequalitiesDo we flip the sign when its negative? Or is it we keep the sign and flip the minus? I'm confused! In this episode Pam and Kim avoid all that confusion and make solving inequalities figureoutable!Talking Points:Open Number Lines for InequalitiesUsing "Reflecting the inequality" vs "flipping the sign"Reasoning about balancing the equationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-11-0522 minMath is Figure-Out-Able!Ep 228: Solving Equations Pt 2Solving equations is figureoutable! In this episode Pam and Kim do a follow up string to last week's episode to further develop algebraic reasoning.Talking PointsUsing a double open number line to build proportional reasoningUsing what you know to find x and explore multiple relationshipsUnderstanding equations vs mimicking stepsSimultaneity can be trickyAdditive vs Multiplicative thinking showing upOperator meaning of fractions comes into playCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-10-2925 minMath is Figure-Out-Able!Ep 227: Solving Equations Pt 1Do we need to memorize a bunch of rules to solve linear equations or can we reason about them? In this episode Pam and Kim use a model to make thinking visible and keep students reasoning! Talking Points: Modeling on a double open number lineFinding where x lies on a double open number line.Grappling with the opposite of x Building integer sense as well as building equation solving senseReasoning about an equation versus balancing an equationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mat...
2024-10-2228 minMath is Figure-Out-Able!Ep 226: Choosing Problem StringsHow can we help students who have always mimicked learn to reason through the content we need to teach? In this episode Pam and Kim lay out their approach to getting students up to speed while preparing them for the content of the day.Talking Points:How to avoid students feeling belittled Using a 1/3, 2/3 mindest to planning Planning with the entire year in mindLayering in complexity to build a single strategyOnly change one thing at a timeIt may take longer in the beginning or when you switch a strategyCheck out our social mediaTwitter: @PW...
2024-10-1522 minMath is Figure-Out-Able!Ep 225: Place Value TasksDo your students struggle with place value? In this episode Pam and Kim discuss great tasks to build real place value understanding for students of all ages.Talking Points:"Adding a zero" vs shifting place valuePlace Value versus Place LabelingAvoiding rules that expireBuild a Number activityPlace Value Mini-Workshop!Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-10-0820 minMath is Figure-Out-Able!Ep 224: NCTM NCSM TakeawaysWe love the math teaching community! In this episode Pam and Kim are live from NCTM and discuss the many things they are learning from other math teaching educators at NCSM and NCTM in Chicago.Talking Points:Too many great sessions to list! But here are a few.Announcing: Developing Mathematical Reasoning: Avoiding the Trap of AlgorithmsAnnounced: Foundations for Strategies Small Group LessonsPre order Developing Mathematical Reasoning: Avoiding the Trap of Algorithms here: https://us.corwin.com/books/dmr-289132?srsltid=AfmBOor-iPP6FJaP0vQS7MWXGMzv6U6psI-ZbqBwxYbE_y4rGgPHU4fU Pre order Foundations for S...
2024-10-0126 minMath is Figure-Out-Able!Ep 223: Foundations for StrategiesHow do you plan for the content you teach? In this episode Pam and Kim discuss task sequencing and a new resource for every classroom.Talking Points: Determining the big ideas, strategies, modelsAlternating between instructional routinesLeading into and getting out of a rich taskIntroducing Foundations For Strategies Small Group Lessons a collaboration with hand2mind! Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-09-2420 minMath is Figure-Out-Able!Ep 222: Love Maths GamesYou all know we love playing games in the classroom. In this episode Pam and Kim discuss the advantages of playing games to change students attitudes and beliefs about math, and just have some fun.Talking Points:The benefits of gamesThey don't even have to be math gamesMultiple Machine by Michael MinasCheck out more of Michael Minas' games at Love Maths: https://www.lovemaths.me/games Other Games: Cubit, Balance Beans, Quarto, Dimension, BlockusCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, a...
2024-09-1717 minMath is Figure-Out-Able!Ep 221: Geometry RiddlesIn this episode Pam and Kim discuss a fun way for students to practice their geometry vocabulary and relationships.Talking Points:Geometry riddlesHierarchies of polygonsPractice vocabulary in a meaningful way, in contextCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-09-1017 minMath is Figure-Out-Able!Ep 220: The Important Teacher Move You Are Not Doing EnoughHow can you intentionally build a Math is FigureOutAble culture in your classroom? In this episode Pam and Kim discuss Pam's recent month long trip to Australia and the important teacher moves she showcased in the lab lessons while she was there. Talking Points:Pam's time Down UnderWait timePrivate SignalFocus on thinking verses focus on the answerA challenge for some students: What hint could you give?Teacher engaged with students the entire timeDoes every kid need to finish the problem?Do you need more time or help?Check out our social mediaTwitter: @PWHarrisI...
2024-09-0327 minMath is Figure-Out-Able!Ep 219: Find the Mean, Median, ModeStatistics Problem Strings? Yes Please! In this episode Pam and Kim demonstrate a Problem String that helps students develop intuition for the meanings of mean, median, and mode.Talking Points:Names are social knowledge, but the feel for what they mean in the data is logical mathematical knowledgeExperience with data helps students develop real understanding of mean, median, mode Changing the data values and comparing how that affects the measures of central tendency deepen understandingCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education
2024-08-2729 minMath is Figure-Out-Able!Ep 218: Finding the MeanIs statistics figureoutable? In this episode Pam and Kim explore a Problem String to build logical mathematical sense for the meaning of mean.Talking Points:What is the mean?Just in time vocabularySocial vs Logical Mathematical knowledgeUnderstanding mean/average is much more than performing an averaging procedureCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-08-2019 minMath is Figure-Out-Able!Ep 217: Slow Reveal GraphsWe were joined by Jenna Laib at our last challenge where she facilitated an amazing routine called Slow Reveal Graphs. In this episode Pam and Kim share that same Slow Reveal Graph and explain along the way why it makes for such an impactful tool to teach data analysis and interpretation for students K-12.Talking Points:Shout out to Jenna Laib for currating the Slow Reveal Graphs websiteQuestions that focus on Strategy vs AnswersHigh level of engagementNatural extensions built into the routineBuilding thinking to analyze data representations and notice critical information or bias of the creatorThe advantages...
2024-08-1322 minMath is Figure-Out-Able!Ep 216: Assembling Great Resources With SemblHave you ever discoverd a super task or routine online only not be able to find it again when you really need it? In this episode Pam and Kim share Sembl, a curation of free, online math resources for your classroom that are filtered for quaility and organized for ease of use. Resources ready for you to integrate into your own curriculum!Talking Points:An amazing tool for finding and organizing tasks and other math contentGreat to find new math education creatorsApp is able to organize and share in and between schoolsWe probably should mention we don't...
2024-08-0618 minMath is Figure-Out-Able!Ep 215: Making Progress - Advancing The MathIt is helpful to find the particular lens to focus your own learning, in order to make real progress. In this episode Pam and Kim discuss planning and sequencing to keep the math moving forward in your classroom.Talking PointsThe stages help teachers focus their energyWriting an 'Echo' Problem StringWrite an 'Up the Ante' Problem StringSequencing StringsSequencing different routines within a taskSequencing TasksUnderstand the progression of modelsUnderstand the connections between strategiesExplore the different structures of Problem StringsDeveloping Mathematical Reasoning Free workshop: http://mathisfigureoutable.com/freeworkshop Check out our social mediaTwitter: @P...
2024-07-3020 minMath is Figure-Out-Able!Ep 214: Making Progress - Your Teacher MovesYou've worked hard to build your numeracy and already own the strategies and models for your operation that you're working on. What's next? In this episode Pam and Kim discuss Teacher Moves, the fourth stage on the Success Map.Talking Points:Differentiate for teachers' needs like they differentiate for studentsGreat teacher moves are only helpful when there's great math conversations happeningModel teacher moves in professional developmentUsing a private signal Using a neutral responseUsing focusing patterns for questions vs funneling patternsUsing partner talk appropriately Using teacher moves appropriatelyCheck out our social mediaTwi...
2024-07-2318 minMath is Figure-Out-Able!Ep 213: Making Progress - Representing Your Students' ThinkingReady to chat about the next layer of the Success Map? In this episode Pam and Kim discuss using your understanding of the relationships to represent student thinking.Talking Points:The stages layer and build on each other Different stages for different areas of math you are working onUse your own understanding of relationships to choose the best model to represent relationshipsProblem String vs Problem Talk, with purposeLearn to listen to, elicit, and represent thinking at every opportunityShare your experiences in the Math is Figureoutable Facebook group!The How Do You Reason? fr...
2024-07-1616 minMath is Figure-Out-Able!Ep 212: Making Progress - Modeling Your StrategiesWhat's next on the landscape for teachers after they've built their own math understanding in a particular area? In this episode Pam and Kim discuss math for teaching, the next layer on the Success Map that teachers should consider as they are learning how to make math more figure-out-able for themselves and their students.Talking Points:Math for teaching is different body of math than the math anyone doesUnderstanding and naming the major strategies and models for each operationJudiciously using the major strategies and modelsCrafting rich problemsBuild understanding in this stage alongside your studentsRegister...
2024-07-0919 minMath is Figure-Out-Able!Ep 211: Making Progress - Building Your NumeracyWhat does a landscape look like for teachers trying to develop their skills to facilitate real math? In this episode Pam and Kim discuss one stage of the Success Map. Talking Points: Teachers, like students, are in different places in their journey in teaching real math.Designing the Success Map was not trivialBuilding your own Numeracy - a starting pointThe Success Map journey is cyclicalWhat are the major milestones in develping numeracy?Solving problems using relationshipsUnderstanding models versus strategiesOwning partners of 10, 100, 1000, and 1Describing mathematical relationships correctlyDeveloping Mathematical Reasoning free online workshop is a great place to begin...
2024-07-0220 minMath is Figure-Out-Able!Ep 210: Number HiveHow can students gain fact fluency in a productive, fun way? In this episode Pam and Kim discuss Number Hive, a game that builds students multiplication fact fluency.Talking Points:Product Game is great, but Number Hive is even betterHow to play Number HiveWho will win? Kim or Pam?A product approach to multiplication by considering factor pairsOpportunities for great classroom discussionLow cost of failureNumber Hive is flexible with lots of variety and levelsCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin...
2024-06-2520 minMath is Figure-Out-Able!Ep 209: Stick and SplitDeveloping multiplicative reasoning, let alone learning multiplication facts, has never been more fun. In this episode Pam and Kim discuss Stick and Split, a simple digital game your students or own kids can explore to learn multiplication in a whole new way.Talking Points:We don't recommend products lightly - Stick and Split is amazing!Taking the product approach - How is that different?Noticing the commutative propertyUsing common factors as toolsWhat do the levels look like?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics...
2024-06-1830 minMath is Figure-Out-Able!Ep 208: Fraction Multiplication Part 3What does it look like when students confidently and efficiently reason through fraction multiplication problems? In this episode Pam and Kim discuss more sophisticated and efficient strategies for solving fraction multiplication problems.Talking Points:How to model the commutative property in fraction multiplication.How to reasoning through "slash and burn".In a classroom, we would expect for students to have a variety of strategies to solve a rich problem.It's not about multiple representations but about connections between multiple representations so that kids have a series of connections in their head. Check out our social mediaTwi...
2024-06-1124 minMath is Figure-Out-Able!Ep 207: Fraction Multiplication Part 2Can students reason through fraction multiplication beyond unit fractions? In this episode Pam and Kim finish out last week's Problem String and build on those relationships to reason through more complex fraction multiplication problems.Talking Points:Can building Additive and Multiplicative reasoning with whole numbers help with fraction multiplication?Does the area model just explain a procedure or can you actually reason with it?How does building reasoning about multiplying fractions using scaling impact future learning (like slope)?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author...
2024-06-0421 minMath is Figure-Out-Able!Ep 206: Fraction Multiplication Part 1This week we're kicking off our series on fraction multiplication! In this episode Pam and Kim describe a classroom's experience discovering unit fraction multiplication.Talking Points:We sometimes have to hear something multiple times for it to "click"What is 1/4 of 1/5?Suggestions for modeling fractions and whyLayers of ReunitizingHow memorized procedures can work against studentsExplicit teaching the use of a model is actually teaching a procedureCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-05-2836 minMath is Figure-Out-Able!Ep 205: Beat the CalculatorWhen should students use calculators? In this episode Pam and Kim discuss how to help students determine when and for what reasons to turn to technology.Talking PointsHelp students learn judicious use of technologyGreat game: Beat the CalculatorDo you know enough to put that in your calculator?What about competition?What about speed?An easy extension for Beat the CalculatorCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-05-2125 minMath is Figure-Out-Able!Ep 204: Building a CommunityIs your classroom a place where students' thinking is valued? In this episode Pam and Kim discuss building a healthy classroom culture.Talking Points:Know your content, but also know your kidsMe versus us statements Walking the line of planning for the community and being part of the communityA great place to start is recognizing 'hidden' studentsNames are important, learn them, use themCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-05-1429 minMath is Figure-Out-Able!Ep 203: Instructional RoutinesWhat kind of instructional routines should you use in your classroom? In this episode Pam and Kim describe why instructional routines are useful and what makes some of their favorites shine.Talking Points:Unlocking creativity and reasoning with routineContent flexibility within routinesThe downside to one and done routinesHow to decide which routines are worth establishingWhat makes Problem Strings a great routineAre games routines?Each of our 3 favorite routinesCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-05-0722 minMath is Figure-Out-Able!Ep 202: You Could Have Understood Trigonometry (Radian Measure)All students can learn more math when it is taught as figure-out-able! In this episode Pam and Kim wade into trigonometry and make sense of it as they go.Talking Points:Making sense of Pi and angle measure of a circleDefining radiansUnderstanding the unit circleA Problem String using a unit circleThe importance of modelingI Have, You Need with angles Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-04-3032 minMath is Figure-Out-Able!Ep 201: Clearing Up MisconceptionsGot questions about the Math Is Figureoutable movement? In this lightning round episode, Pam and Kim answer questions and address misconceptions they've heard people have.Talking Points:Is it only about Problem Strings?Does math-ing have be done in all in your head?Is "one and done" desirable?Are we doing "Pam Harris Math"?Are algorithms bad?Is Math is Figuroutable appropriate for all grades K-12?Is Math is Figuroutable only numeracy?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam...
2024-04-2329 minMath is Figure-Out-Able!Ep 200: Mathematicians or Math-ers?We're so excited to celebrate our 200th episode with you! In this episode Pam and Kim change up their intro and discuss how the things they've learned continue to shape how they spread the Math is FigureOutAble movement today.Talking Points:200 Episodes!!!Is the math mathing?Pam, a former mimickerPerspectives versus distortionsKim, a reasoner who can now share her thinkingAlgorithms are amazing historical feats, but not good teaching tools!The reason for math classCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education...
2024-04-1624 minMath is Figure-Out-Able!Ep 199: NumberblocksReal math is never fun and cute, or is it? In this episode Pam and Kim discuss a cartoon they've fallen in love with that builds number sense intuitively and entertainingly.Talking Points:What is Numberblocks? What makes it stand our?Different representations of numbersSquaresDoublingMath symbolsOdd and evenWho is Numberblocks for?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-04-0928 minMath is Figure-Out-Able!Ep 198: Look Fors for School Wide Vision What can schools use to create a shared vision for math instruction? In this episode Pam and Kim discuss the New York Department of Education's Look Fors for School-Wide Mathematics Teaching and Learning.Talking PointsWho is this Look For for?Specifics for equity around scheduling teachers with an eye on content knowledge and pedagogyMaking space for observing, sharing, and discussing teaching practices that engage students with challenging mathematicsShare the school's vision throughout all parent communication and eventsThe importance of shared vision about pathways for students to have access to high quality mathFind the Look F...
2024-04-0221 minMath is Figure-Out-Able!Ep 197: Look Fors for TeachersWhat conversations can teachers and coaches have about improving instruction in the classroom? In this episode Pam and Kim discuss the Look Fors for Teachers provided by the New York Department of Education.Talking Points:Coaching requires more than observation or modeling a lessonAvoid analysis paralysis Coaching through conversationHow to inform your in-the-moment decisionsMaintain students' opportunities to develop their own ideas and understandingsCreating a shared visionFind the Look Fors here:For Students: https://drive.google.com/file/d/1spWxDFP_FRVGFkNmWAjGxKnDscGSctYD/view For Teachers: https://drive.google.com/drive/u/0/folders/1zZI4Y1M...
2024-03-2625 minMath is Figure-Out-Able!Ep 196: Look Fors for StudentsWhat goals do you have for your classroom? How do you measure your success? How to plan to achieve those goals? In this episode Pam and Kim discuss New York City's Look Fors for Students and how they can help us focus on the changes we want to see in our classrooms.Talking Points:Kim and Pam have different styles and personalities as the approach planning a lesson or sessionTaking time to think deeply about a lessonNew York City's Look ForsKim and Pam highlight a Look ForTo avoid burnout, innovate in burstsFind the Look...
2024-03-1927 minMath is Figure-Out-Able!Ep 195: Early Addition Important RelationshipsWhen should you start developing which relationships? In this episode Pam and Kim discuss the important addition relationships for first grade and how to develop them throughout the year.Talking Points:When do I teach what?Download The Most Important Numeracy Strategies Free Ebook!We want students to understand relationships so that strategies are natural outcomes, not memorized procedures.Partners of TenDoublesPlus tenModeling is super importantCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-03-1226 minMath is Figure-Out-Able!Ep 194: Quarter Strategy for MultiplicationCan we really be efficient in solving multiplication problems without algorithms? What about the really cranky ones? In this episode Pam and Kim discuss the quarter strategy- a clean, efficient, figureoutable way of solving traditionally difficult multiplication problems.Talking Points:Baby strategies! What?!A problem string for the Quarter StrategyCOMING SOON! Problem String books: A shared vision for how we could develop the major relationships for each operation, with strings for ALL yearClick here for more information on "Using Quarters" https://www.mathisfigureoutable.com/quarters Check out our social mediaTwitter: @P...
2024-03-0522 minMath is Figure-Out-Able!Ep 193: Compliance TooWhat message do we want to send to students about compliance? In this episode Pam and Kim talk about the importance of respecting student dignity and separating math from punishment.Talking Points:Senario of compliance Reasons we seek compliance from studentsMath is not a punishment or taking it away, a rewardPam and Kim reflect on some of their early experiencesIs it about the math or about the compliance?Do your grades reflect compliance?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam H...
2024-02-2725 minMath is Figure-Out-Able!Ep 192: Compliance - What do you require in a math class?A huge part of any teacher's life is classroom management, setting expectations, and compliance. In this episode Pam and Kim consider when compliance might or might not be helpful in a math classroom.Talking Points:Sucked down the Math Is Figureoutable vortexWould you rather have compliant students? Or have students who question?There are times when compliance is importantKim and Pam's early experiences with complianceNegative consequences for non-compliance aren't always helpfulCreating a learning atmosphereModel your expectationsTime for reflection not finger waggingCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook...
2024-02-2023 minMath is Figure-Out-Able!Ep 191: PEMDAS Is FigureoutableThinking and reasoning is always more powerful than rotely memorizing steps. In this episode Pam and Kim demonstrate how to help students reason about Order of Operations.Talking Points:Nat Banting's "Oops, I Meant"Representing a context using the grouping symbols to communicate Demonstrate how mathematicians communicate with symbols earlUsing the equals sign correctly to mean "equal" vs "Do it"" No more unnecessarily difficult practiceCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-02-1322 minMath is Figure-Out-Able!Ep 190: The Problem With PEMDASOrder of operations seems more rote memorizable than figure-out-able, or is it? In this episode Pam and Kim discuss the pitfalls of teaching order of operations as an acronym to memorize, and offer a better alternative.Talking Points:It's about communication rather than a thing to memorize.The notation is social knowledge.The order is logical mathematical knowledge and therefore figure-out-able!Open-middle problems for meaningful practice.Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-02-0630 minMath is Figure-Out-Able!Ep 189: The Operator Meaning of FractionsFinding a fraction of something can be a tricky concept. In this episode Pam and Kim run through two strings that help reason about using fractions as operators.Talking Points:How are unit fractions related like halves, fourth and eighths? Scaling and Over Strategy with unit fractionsFractions as operatorsWhy is scaling a unit fractions critical? Knowing that three fourths is the same as three 1/4s? Knowing non-unit fractions from fractions is a precursor.Thinking of fractions only as part-whole is not sufficient. A different problem string using the operator meaning of fractions.Check out our social med...
2024-01-3022 minMath is Figure-Out-Able!Ep 188: The Whole MattersDoes it really matter what we call the whole? In this episode Pam and Kim take a closer look at fraction problems where the unit matters.Talking Points:Kim and the beachHow can there be 2 possible answers to the question "What is 1/2?"Focusing on the unitNaming the unitWhat happens when the unit changes? Help students focus on the unit, changing the unit, and finding a fractional amount of that new unitEven test writers struggle with fractionsRe-unitizing will support students to reason through fraction multiplicationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Ha...
2024-01-2332 minMath is Figure-Out-Able!Ep 187: Getting Answers to Fraction Problems is Not EnoughHow many people do you know that shy away from fractions? In this episode Pam and Kim discuss why teaching students to use step by step procedures to solve fraction problems actually leaves them not able to think about fractions at all.Talking Points:We love hearing your stories!What kind of reasoning do fractions engage?What happens when students learn to mimic steps rather than reason about fractions?What does reasoning about fractions look like?Are least common denominators really that important?See Episode 5, 67, 68 for more about Development of Mathematical ReasoningCheck out...
2024-01-1627 minMath is Figure-Out-Able!Ep 186: Subtracting Integers - Add The OppositeMinus-minus, plus-plus, or is integer subtraction actually figureoutable? In this episode Pam and Kim use a Problem String to build real understanding of integer subtraction.Talking Points:The importance of having multiple contextsSeeing the negative symbol as "opposite of"Using distanceUnderstanding takes time, but is so worth it!See Episodes 181-183 for more about Integer operations.See Ep 242 for more information on Integer MultiplicationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2024-01-0931 minMath is Figure-Out-Able!Ep 185: TrackingTracking students and sorting them into 'higher'/'lower' tracks is a topic that we have really, really firm feelings about. In this episode Pam and Kim discuss the unintended consequences of tracking students and offer some ideas to consider.Talking PointsWho does tracking benefit, who does it hurt?Distaste for the vocabulary used to describe tracks of kidsEveryone can do more real math than fake mathFrom our experience as a teacherFrom our experience as a parentFrom a student's perspectiveCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook...
2024-01-0236 minMath is Figure-Out-Able!Ep 184: Revisiting - But I'm Required To Teach AlgorithmsHappy holidays! Pam and Kim invite you to revisit Ep 87, it's super important! How do you navigate teaching math that is figure-out-able if your standards include the teaching of algorithms?Talking Points: All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems. Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year. Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and...
2023-12-2624 minMath is Figure-Out-Able!Ep 183: Integer SubtractionCan integer subtraction feel intuitive without rote memory? In this episode Pam and Kim delve into a Problem String and explore integer subtraction relationships.Talking Points:Integer chips?Students reason about subtracting integersDistance versus removal Problem String subtracting integers in contextWhen context is less helpfulDon't go to rules, stay in reasoningSee Episodes 149 and150 for more about distance vs removal See Ep 242 for more information on Integer MultiplicationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LL...
2023-12-1928 minMath is Figure-Out-Able!Ep 182: Integer AdditionMimicking rules for integer operations does not help students become doers of Real Math, and frankly doesn't often stick in their long term memory. In this episode Pam and Kim walk through a Problem String that helps students develop an intuitive understanding of integer addition!Talking Points:Exploring the beach as a contextEquations and number lines in contextCarefully chosen numbers to avoid distracting cognitive load Subtraction symbol or adding a negative? Parentheses or not? Let students grapple, then support and help make sense of ambiguitySee Ep 242 for more information on Integer MultiplicationCheck ou...
2023-12-1225 minMath is Figure-Out-Able!Ep 181: IntegersHow can we help students reason about integers? In this episode Pam and Kim discuss fun and natural ways to explore and understand both positive and negative integers.Talking Points:The Pen/Pencil argument continues5th graders can reason about integersGames do develp understanding of integersClothes line math with integersExploring four useful contexts for integersSee Ep 242 for more information on Integer MultiplicationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2023-12-0533 minMath is Figure-Out-Able!Ep 180: Revisit With a Twist - An Important Subtraction PitfallHow do you label fractions on an open number line? How do you label a fraction of a candy bar? How many cuts do you make to cut a candy bar into fourths? Pam and Kim invite you to revisit episode 138, this time with an ear towards fractions. Do your students ever get confused about counting obects vs counting distance? In this episode 138 Pam and Kim use a Problem String to help build intuition about everyday subtraction problems.Talking Points:Experience a Problem String to build relationshipsFencepost Problems are all over the placeStudents can't just p...
2023-11-2825 minMath is Figure-Out-Able!Ep 179: Fake Math, Not Fake PeopleWhat does it mean when we say 'fake math' or 'less sophisticated'? Pam and Kim discuss how learning Real Math is empowering and opens a whole new world of understanding.Talking Points:Are squared numbers an important thing to own?The MatrixIt takes experience to understand perspectivesMartiansDoing 'fake math' or using a 'less sophisticated' way of thinking does not make the person fake or unsophisticatedReal math is empowering and can open up a new reality!Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education...
2023-11-2130 minMath is Figure-Out-Able!Ep 178: Talking Math With Your Kids: Division With DecimalsWe can be our own kids' best teachers, even when it comes to gnarly division problems. In this episode Pam and Kim relay their experiences exploring decimal division with their own kids. Talking Points:A tool for holding your thinking - a ratio tableIt's not about how much you can hold in your headHelp them start with what they knowProblem Strings are not about answering just the last problemIt isn't about being able to solve every problem It's about owning the major relationships in order to think like a mathematicianCheck out our social mediaTw...
2023-11-1428 minMath is Figure-Out-Able!Ep 177: NCTM Conference ReflectionsRecorded live from NCTM! Pam and Kim discuss some of their experiences and takeaways from the 2023 National Council of Teachers of Mathematics conference.Talking Points:Travel storiesAs kids grow, teachers grow as wellKnow your content know your kids to choose Problem Strings for your studentsTools that focus on answer getting stifle students reasoningUsing a neutral response to keep students and adults continue their thinkingWe all need to understand the content - teachers and learning Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: P...
2023-11-0731 minMath is Figure-Out-Able!Ep 176: Place Value and Exploding DotsPlace value is so much more than labeling digits. In this episode Pam and Kim dive into place value and common teaching practices that are necessary, but not enough.Talking Points:A fascination with the macabreTypical place value labeling and additional things you can think about to develop place valuePrecise questioning yields deeper place value thinkingWhat are Exploding Dots?More about our place value systemPracticing expanded notation is not enoughYou can register for the Place Value Mini-Workshop now! Don't miss your opportunity to transform your math teaching: https://www.mathisfigureoutable.com/mini Check o...
2023-10-3126 minMath is Figure-Out-Able!Ep 175: The Most Sophisticated Division StrategyDivision is figure-out-able! In this episode Pam and Kim discuss the most sophisticated strategy for division and precursors that students can begin developing in the fourth grade!Talking Points:An Equivalent Ratios Problem StringPrecursor relationshipsScaling up or Scaling downWhat makes Equivalent Ratios the most sophisticated strategy for division4th grade can begin to reason about division using the "bigger, smaller thing" to reason about division5th grade can begin to reason about equivalence Relational thinkingSee Ep 64 and 132 for more on equivalent ratios!Checkout mathisfigureoutable.com/relational-thinking for free exercises to develop the equivalent r...
2023-10-2427 minMath is Figure-Out-Able!Ep 174: The Most Sophisticated Multiplication StrategyOur students can learn to approach math problems like mathematicians! In this episode Pam and Kim look at one of the most sophisticated multiplication strategies that many mathematicians use. Talking Points:Creating an equivalent problem by Doubling and Halving.What makes a problem reasonable to solve without a calculator?Double/Halve; Triple/Find a Third; Quadruple/Find a fourthWhat makes Doubling and Halving one of the most sophisticated multiplication strategiesFlexible Factoring - for more information see Ep 153Pitfalls of direct teaching and strategyCheck out the Instructional Routine called Relational Thinking at: mathisfigureoutable.com/relational-thinking
2023-10-1732 minMath is Figure-Out-Able!Ep 173: The Most Sophisticated Subtraction StrategySome subtraction strategies can only get you so far, but with a little more sophistication complex problems become really nice to think and reason about! In this episode Pam and Kim build and discuss the Constant Difference strategy for subtraction and use it to solve a really gnarly problem.Talking Points:Equivalence strategies are more sophisticatedHallmarks of sophisticated stategiesModeling Constant DifferenceRelational Thinking RoutineCheck out the Instructional Routine called Relational Thinking at: mathisfigureoutable.com/relational-thinkingCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author...
2023-10-1037 minMath is Figure-Out-Able!Ep 171: Tips For Parents, Part 2Kids learn best with support from their parents, and helping with math has never been easier! In this episode, Pam and Kim are excited to share some tips about how to encourage your children as they grow in mathematical thinking and reasoning.Talking Points:Wait a little longer Resist the urge to tell the right answerAsk questions to cement the thinkingCounting on and back from numbers other than oneGuess my NumberDiscuss fractions by their unit fractionsCompare fractions using landmarksGet all these tips and more at https://www.mathisfigureoutable.com/parenttipsCheck out o...
2023-09-2623 minMath is Figure-Out-Able!Ep 170: Tips For Parents, Part 1This one's for all you, parents! How can you support your children in becoming mathematicians? In this episode Pam and Kim go over their favorite ways to explore math at home in fun game-like activities.Talking Points:Speak about math positivelyWonderingDoubling and HalvingUsing 10s to find 9s and using 10s to find 5sI Have, You NeedGet the free download: https://www.mathisfigureoutable.com/parenttipsCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2023-09-1929 minMath is Figure-Out-Able!Ep 169: Graphing, Integers, Quadrants, Oh My!Can you reason about what it means for a point to be within a given quadrant? Can your students? In this episode Pam and Kim discuss weather and geography to develop understanding of the quadrants in the cartesian coordinate system.Talking Points:Understanding points relative to their quadrants and the y = x lineKim's connection to AlaskaWhat makes Australia so uniqueGraphing inequalities is Figure-Out-Able! See Ep 242 for more information on Integer MultiplicationCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam H...
2023-09-1228 minMath is Figure-Out-Able!Ep 168: Guessing in Math ClassLet's do some guessing! In this episode Pam and Kim develop some functional reasoning by analyzing the relationships between their guesses and reality.Talking Points:Pam's guesses using her pop culture knowledgeHow would you know if you are a good guesser?Graphing guesses and actual age as an ordered pairUsing the data to discuss the meaning of y=x The parent function for building all functionsCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2023-09-0528 minMath is Figure-Out-Able!Ep 167: How, What, Why to Change Math ClassWhat does it mean for math to be figure-out-able? What will you teach? How? Why? In this episode Pam and Kim discuss their thoughts to changing the "how" and "what" of math education around the world and explore the "why".Talking Points:"What" math we teach should come first"How" the math should be embedded in the "what"What Pam and Kim think about "Why" make the change?Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2023-08-2924 minMath is Figure-Out-Able!Ep 166: Just In Time Vocabulary vs Key WordsWhat role does terminology have in math teaching? How do we want students to approach problems? In this episode Pam and Kim discuss when to teach vocabulary how we can prepare students to tackle problems with confidence.Talking Points:"Just In Case" vs "Just In Time" vocabularySocial Knowledge vs Logical Mathematical KnowledgeAnchor Charts to cinch learningRejecting key words for operationsWrong answers are opportunities for good teacher feedbackFor more about Anchor Charts check out Episode 123Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics...
2023-08-2222 minMath is Figure-Out-Able!Ep 165: Where Popular Things Go WrongThere is so much that is good happening in the math teaching community! In this episode Pam and Kim discuss how we can determine how much of which good things to put into our classrooms.Talking Points:Going beyond nixing tricksSocial versus logical knowledgeNixing the tricks is more than explaining the math betterThe dangers of going all in on any good teaching practiceNumber Talks Exploding DotsManipulativesKeep asking for clarification and refining your craft in order to create mathematicians in your classroomCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: P...
2023-08-1526 minMath is Figure-Out-Able!Ep 164: I Have, You Need With a TwistWho does not love a quick, easy routine that gives students useful problem solving relationships? In this episode Pam and Kim revisit I Have, You Need and apply it with different target numbers.Talking Points:Kim and Pam play I Have, You Need often with clocks and marathonsIt's not about speedGoal is reducing cognitive load in the midst of solving other problems Another goal is building fluency Other important target numbers for early elementary and even middle and high school studentsGet the free I Have, You Need...
2023-08-0820 minMath is Figure-Out-Able!Ep 163: A Problem String Is NOTWhat exactly is a Problem String? In this episode Pam and Kim dig into that question and give examples of what a problem string is and is not.Talking Points:Pam's conversation with Howie Hua - Problem Strings are not strategiesExample of a helper clunker structure Problem StringWhat is structure vs strategy? Example of an equivalent structred Problem StringThe power of owning multiple strategiesIf you want to hear more about Problem Strings, check out Episodes 71, 72 and 260. Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, au...
2023-08-0128 minMath is Figure-Out-Able!Ep 162: Comparing Fractions Pt 2What are some important relationships that students can use to do Real Math with fractions? In this episode Pam and Kim discuss some important relationships that can help develop deeper understanding about fractions for fractional equivalence and comparison.Talking Points:A listener's reviewUsing benchmark fractions to compareUsing a number line to compare fractionsHow does understanding unit fractions help compare ugly fractions?Why we use symbols to represent complex ideasCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2023-07-2517 minMath is Figure-Out-Able!Ep 161: Comparing Fractions Pt 1What if your students could think and reason about the relative sizes of fractions? In this episode Pam and Kim think about where fractions go on clotheslines to show how you can help your students compare fractions without a memorized procedure.Talking points:A podcast listener shares her perspective of mathematics as a studentClothesline Math examples using fractions and percentsConnecting fractions and percentsGeneralizing about comparing fractions using reasoningHelp students clarify the meaning of numerators and denominatorsTake our math perspectives quiz! http://bit.ly/xyzquizSee Episodes 24-27 for more about The...
2023-07-1823 minMath is Figure-Out-Able!Ep 159: Building Thinking Classrooms and Math is Figureoutable Pt 2We think Dr. Peter Liljedahl has some great ideas about how to keep students thinking and reasoning in math class. In this episode Pam and Kim continue to discuss some of his ideas and how they align with the Math is Figure-Out-Able mindset. Talking Points: Which questions to answer Get in, get outApproach groups with your own questionUsing neutral responsesCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC
2023-07-0426 minMath is Figure-Out-Able!Ep 158: Building Thinking Classrooms and Math Is FigureOutAble Pt 1We love it when students are thinking and reasoning, and it's important to know how best to build and experience sophisticated strategies. In this episode Pam and Kim continue discussing Dr. Peter Liljedahl's work and finetune where it's appropriate to use vertical nonpermanent surfaces, and what other kind of tasks we should be doing whole class with students.Talking Points:Randomized Groups at Vertical Non Permanent Surfaces in random groups are great for Rich Tasks that follow your curriculum Problem Strings are best used whole class to build specific strategies, models, and big ideasSee E...
2023-06-2717 minMath is Figure-Out-Able!Ep 157: Building Thinking ClassroomsWe want our students to be confident problem solvers who can think and reason through complex problems. In this episode, Pam and Kim highlight some of Dr. Peter Liljedahl's work on Building Thinking Classrooms to use student's natural inclinations to help them work better and more collaboratively. Talking Points:It's about thinking, not mimickingThinking Tasks not mimicking tasksVertical Non Permanent SurfacesVisibly random groupsIt takes time for kids to accept working in random groupsPulse of the room: Are student's opting out? What math are groups using?The "how " is important, but so is the "what"C...
2023-06-2015 minMath is Figure-Out-Able!Ep 156: Start HereWe've reached our third anniversary of the podcast! There's a lot that's been said, so we thought we'd highlight some of the quintessential Pam Harris topics from previous episodes that you need to transform your math classroom. In this episode Pam and Kim blitz through what makes the Math is Figure-out-able Movement so important and unique. They also list out which episodes you can listen to for more information about these key concepts.Talking Points:The Development of Mathematical Reasoning: Ep 5, 6, 67, 68Models vs Strategies: Ep 9Algorithms Are Not the Goal: Ep 2, 94-99Different Math Perspectives...
2023-06-1324 min