Math Prompt: True-False-True

Posted on by Denise Gaskins
girl writing in a notebook, sitting on couch with her corgi

Book, Charlotte Mason's Living MathOne of the stretch goals for my Charlotte Mason’s Living Math Kickstarter campaign is to add a math journaling prompt to the end of each chapter. So, I’ve been playing around with ideas to get readers writing.

Since the book’s all about how to build mathematical reasoning, I’m looking for ways to prompt creative thinking and flexibility in math calculations.

Check Out the Kickstarter

I found some fun ideas in Guy Gattegno and Martin Hoffman’s Handbook of Activities for the Teaching of Mathematics (which you can download here), including the following riff off a puzzle created by Lewis Carroll.

Continue reading Math Prompt: True-False-True

What Is Math Game Monday?

Posted on by Denise Gaskins
Learn a new math game every week, for free

There’s a new Math Game Monday this week.

Have your kids tried it yet?

This week’s game is one of my favorites for upper-elementary and middle school students, offering plenty of practice doing estimation and mental math with fractions. Or you might prefer last week’s game, featuring a classic two-player logic puzzle that develops strategic reasoning.

Or, if you’re reading this post later and missed those, there’s another great new game this week for you to play.

Check it out:

Visit Math Game Monday

Continue reading What Is Math Game Monday?

Musings: Math is Communication

Posted on by Denise Gaskins
Young boy writing math expressions

The question came up on a homeschool math forum:

“My first grader and I were playing with equivalent expressions. We were trying to see how many ways we could write the value ‘3.’

    “He wrote down 10 – 2 × 3 + 1.

      “When I tried to explain the problem with his calculation, he got frustrated and didn’t want to do math.

        “How can I help him understand order of operations?”

        [If you think this sounds like too complex of a math expression for a first grader, you may want to read my blog post about math manipulatives and big ideas.]

        Order of operations doesn’t matter in this instance. What matters is communication.

        The mother didn’t know how to read what her son wrote.

        He could help her understand by putting parentheses around the part he wanted her to read first.

        He doesn’t need to know abstract rules for arbitrary calculations, or all the different ways we might possibly misunderstand each other. He just needs to know how to say what is in his mind.

        Continue reading Musings: Math is Communication

        Mental Math: Advanced Subtraction

        Posted on by Denise Gaskins
        mother and daughter talking about math homework

        As our children grow and develop their math skills, the mental math strategies grow with them.

        The basics of mental math don’t change:

        • Use friendly numbers.
        • Estimate and adjust the answer.

        But we have new ways to help children do math in their heads as the numbers get bigger and the problems more challenging.

        For example, how might kids figure out a multi-digit subtraction like 67 − 38?

        First, we need to adjust our mindset…

        Continue reading Mental Math: Advanced Subtraction

        Mental Math: Advanced Addition

        Posted on by Denise Gaskins
        photo of kids having fun with math

        Mental math is doing calculations with our minds, and perhaps with the aid of scratch paper or a whiteboard to jot down notes along the way.

        But we cannot simply transfer the standard pencil-and-paper calculations to a mental chalkboard. That’s far too complicated.

        We still want to follow our basic strategies of using friendly numbers, estimating, and adjusting the answer. So how can we help children do math in their heads as the numbers get bigger and the problems more challenging?

        How might kids figure out a multi-digit addition like 87 + 39?

        Here are three useful strategies…

        Continue reading Mental Math: Advanced Addition

        Mental Math: Early Division

        Posted on by Denise Gaskins
        Boy doing mental math calculation

        Mental math is doing calculations with our minds, though we can use scratch paper or whiteboards to make notes as we work.

        Doing mental math, children use the basic principles of arithmetic to simplify problems so they can think about number relationships, mastering the basic structures of how numbers work, the same structures that underlie algebraic reasoning.

        As always, we rely on two key mental-math strategies.

        • Use friendly numbers.
        • Estimate, then adjust.

        Division is the mirror image of multiplication, the inverse operation that undoes multiplication, which means we are scaling numbers down into smaller parts. Important friendly numbers include halves, thirds, and tenths, plus the square numbers and any multiplication facts the student happens to remember.

        Continue reading Mental Math: Early Division

        Mental Math: Early Multiplication

        Posted on by Denise Gaskins
        mother and daughter talking math together

        Children learn best through interaction with others, and mental math prompts can lead to fascinating conversations, listening as our kids apply their creativity to the many ways numbers interact.

        With mental math, students master the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.

        And these 3Rs are the foundation of algebra, which explains why flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.

        Let’s Try an Example

        Multiplication involves scaling one number by another, making it grow twice as big, or three times as much, or eightfold the size. Multiplication by a fraction scales the opposite direction, shrinking to half or a third or five-ninths the original amount.

        The key friendly numbers for multiplication and division are the doubles and the square numbers. As with addition and subtraction, students can estimate the answer using any math facts they know and then adjust as needed.

        How many ways might children think their way through the most-missed multiplication fact, 8 × 7?

        Continue reading Mental Math: Early Multiplication

        FAQ: Can I Use Your Books as a Math Curriculum?

        Posted on by Denise Gaskins
        Father helping girl with math homework

        I recently listened to you on Cindy Rollins’ podcast, and I was captivated by your perspective on math. It was exciting, freeing, and wonder-filled. I would absolutely love to be able to teach in the ways you described.

          We use early-elementary Saxon Math right now, which is thorough, but has SO MUCH to do that I’ve always struggled to do it all. Then I feel like I’m missing things, and I never know quite what is important. And yet, the actual lessons move so slowly that my kids get bored with the repetition.

            I use a published curriculum because I have no idea of an appropriate scope and sequence, or similar flow of learning. With your playful approach to math, how do I know where to start, and what to do each day?

              Do you have a suggested order to approach your books to have a full math approach? A sort of curriculum, per se, using your books.

              [For those who missed my chat with Cindy Rollins about a Charlotte Mason approach to math, you can listen to it here.]

              Continue reading FAQ: Can I Use Your Books as a Math Curriculum?

              FAQ: Real Math for Early Learners

              Posted on by Denise Gaskins
              photo of family hiking a rocky trail

              “I love your image of math as a nature walk. My children are ready to start their homeschooling journey, and I want to put them on the right track from the beginning. How can I help them think about math and problem-solving without using a textbook?”

              The most difficult part of teaching our children real math is to change our own way of thinking about the subject you’ve already taken that step, so it looks like your family’s learning journey is off to a great start.

              [For readers who are wondering what I mean by math as a nature walk, check out this post. You may also enjoy my article on natural learning: Math with Young Children.]

              Continue reading FAQ: Real Math for Early Learners

              Get a Weekly Dose of Playful Math

              Posted on by Denise Gaskins

              Our leaves haven’t started to turn yet, but summer’s on the wane, farmers are busy with harvest, and the back-to-school rush has calmed down into a daily routine.

              But if you’re like me, you keep tweaking that routine, constantly looking for the perfect balance for your family or classroom. I especially love to discover easy ways to add more playful math to our schedule.

              So here’s a collection of sites that offer fresh math resources on a weekly or monthly basis throughout the school year.

              Which one will you try?

              KenKen Classroom

              Every week, they’ll email you a set of free KenKen arithmetic puzzles for all ages. As the challenge level subtly shifts week to week, students develop their math and logical thinking skills without even knowing it.

              Subscribe ❯

              #MathStratChat

              Pose an interesting math problem. How can you figure it out? What else could you do? How many different ways can you find? Which strategy do you like best for this problem?

              Follow Pam Harris on your favorite social media site to get a new problem every Wednesday.

              Choose a Problem ❯

              The Parallel Universe

              Dr Simon Singh, author of the No. 1 bestseller Fermat’s Last Theorem and The Simpsons and Their Mathematical Secrets has created a set of weekly maths challenges – just 15-30 minutes of interesting, fun and challenging tidbits of mystery and history, activities and oddities, puzzles and problems.

              Help students expand their mathematical horizons beyond the school curriculum and build strong mathematical thinking skills. Stretch your brain every week!

              Learn More ❯