Math Journals and Creative Reasoning

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically. To make sense of math concepts and persevere in figuring things out. To notice the numbers, shapes, and patterns all around. To wonder about big ideas.

Journaling is a great way to help children learn to see with mathematical eyes. Not just to remember what we tell them, but to create their own math.

Get started with creative math journaling today. Visit the Make 100 Math Rebels Kickstarter page to download the free “How To Be a Math Rebel” sampler pictured above, which contains one of my all-time favorite math prompts.

Make 100 Math Rebels

It doesn’t matter whether your students are homeschooled or in a classroom, distance learning or in person. Everyone can enjoy the experience of playing around with math.

Puzzle from the free Math Rebel Sampler.

Continue reading Math Journals and Creative Reasoning

What Is Multiplication, Anyway?

At some point during the process of teaching multiplication to our children, we really need to come to terms with this question:

What IS multiplication?

Did your device hide the video? Find it on YouTube here.

“What’s my answer? It’s not one that society’s going to like. Because society expects — demands, even — that mathematics be concrete, real-world, absolute, having definitive answers.

    I can’t give a definitive answer.

      Multiplication manifests itself in different ways. So maybe the word ‘is’ there is just too absolute. And it’s actually at odds with what mathematicians do.

        Mathematicians do attend to real-world, practical scenarios — by stepping away from them, looking at a bigger picture.”

        —James Tanton, What is Multiplication?

        For Further Study

        You may also enjoy these posts from my blog archive:

        Memorizing the Times Table: A Life Skills Approach

        Continuing on my theme of times table facts, here’s the inimitable James Tanton:

        Did your device hide the video? Find it on YouTube here.

        “If our task is to memorize this table, please make it about mathematics — about thinking your way through a challenge, and what can I do to make my life easier.”

        —James Tanton, Making Memorising Multiplication Facts (if one really must) a meaningful Life Skill Lesson

        For Further Study

        You may also enjoy my blog post series about working through the times tables, paying attention to mathematical relationships (and a bit of prealgebra) along the way.

        Times Tables Series

        Click the button to see the whole series. Scroll down to the first post to go through it in order.

        Only Three Facts to Memorize

        A comment from a friend got me playing around with multiplication. I found a few videos from some of my favorite math people, so I’ll be sharing over the next few days.

        Here’s one from Sonya Post of Learning Well at Home. Also, Sonya just hosted Playful Math Education Carnival #143, which is well worth your time to explore!

        Did your device hide the video? Find it on YouTube here.

        “When students have to drill multiplication facts, it’s frustrating, unproductive and it makes them hate math. A better way to master the multiplication table is work on the skills that allow students to multiply quickly and efficiently.”

        —Sonya Post, Why We Don’t Drill Multiplication Facts – What We Do Instead

        Doubling and Halving

        Making doubles and halves are a great foundation for all sorts of math.

        Do you ever play the doubling game with your children? One player picks a starting number, and then you take turns doubling it until your mental math skills run out. How far can you go?

        Or try the halving game: One player chooses a starting number, and you take turns cutting it in half. How tiny can you go?

        As Sonya demonstrated, these skills help your child master their multiplication facts. And they are fantastic preparation for exponents and logarithms, too!

        Make Sense of Math

        So, I decided to rewrite the Standards for Mathematical Practice into student-friendly language.

        Here’s the final installment…

        Math Tip #8: Make Sense of Math.

        • Use the patterns you discover to help you solve problems.
        • Don’t get lost in the details of a problem. Look for general truths.
        • Apply common sense to math situations.
        • Think about how different things are similar.
        • Think about how similar things are different.
        • Remember that your mind is your most important math tool.
        • Pay attention to your thinking process. What patterns do you find there?

        Continue reading Make Sense of Math

        Discern Patterns

        I’m almost done rewriting the Standards for Mathematical Practice into student-friendly language.

        They say mathematics is the science of patterns. So here’s…

        Math Tip #7: Discern Patterns.

        • Look for patterns in numbers, shapes, and algebra equations.
        • Notice how numbers can break apart to make a calculation easier.
        • Number patterns morph into algebra rules.
        • Adapt math situations to make the structure clear. (For example, by adding new lines to a geometry diagram.)
        • Step back from a situation to see it from a new perspective.
        • Try to find simpler patterns within complex equations or diagrams.
        • Not all patterns continue forever. Test your patterns. Can you trust them?

        Continue reading Discern Patterns

        Exciting New Homeschool Math Program

        Homeschooling friends, check out this new homeschool math program that’s fun, rigorous, and engaging — a delightful, hands-on course that helps parents (and their children) understand math.

        Introduction to Cuisenaire Rod Structures Course

        I had the privilege of previewing this class as Sonya and Lacy put it together. I highly recommend it to anyone who struggles with math, or who wants to take a non-traditional approach.

        By focusing on making sense of number relationships, and by teaching algebra before arithmetic, this course provides a stress-free path to rich mathematical mastery.

        And for all they provide, including weekly live workshops and a slew of printable math journal pages that prompt deep thinking, the price is a steal!

        Continue reading Exciting New Homeschool Math Program

        Say What You Mean

        Continuing my project of rewriting the Standards for Mathematical Practice into student-friendly language.

        Here’s my version of SMP6…

        Math Tip #6: Say What You Mean.

        • Words can be tricky, so watch your language.
        • Label drawings and graphs to make them clear.
        • If you use a variable, tell what it means.
        • Care about definitions and units.
        • Pay attention to rules (like the order of operations).
        • Use symbols properly (like the equal sign).
        • Understand precision. Never copy down all the digits on a calculator.

        Continue reading Say What You Mean

        Master Your Tools

        As I’ve mentioned before, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

        Here’s my version of SMP5…

        Math Tip #5: Master Your Tools.

        • Collect problem-solving tools.
        • Practice until you can use them with confidence.
        • Classic math tools: pencil and paper, ruler, protractor, compass.
        • Modern tools: calculator, spreadsheet, computer software, online resources.
        • Physical items: dice, counters, special math manipulatives.
        • Tools for organizing data: graphs, charts, lists, diagrams.
        • Your most important weapon is your own mind. Be eager to explore ideas that deepen your understanding of math concepts.

        Continue reading Master Your Tools

        Look Beneath the Surface

        So, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

        Here’s the fourth installment…

        Math Tip #4: Look Beneath the Surface.

        • Notice the math behind everyday life.
        • Examine a complex situation. Ignore the parts that aren’t relevant.
        • Pay attention to the big picture, but don’t lose track of the details.
        • Make assumptions that simplify the problem.
        • Express the essential truth using numbers, shapes, or equations.
        • Test how well your model reflects the real world.
        • Draw conclusions. Explain how your solution relates to the original situation.

        Continue reading Look Beneath the Surface