Rebecca Zook - Math Tutoring Online

Pizzas. They’re the best way to represent fractions, right? Everyone has seen a pizza. Everyone knows you can slice a pizza different ways. When you need to visually represent fractions, pizzas are the go-to metaphor, right?

Well, that’s what I thought until I tried using pizzas to teach equivalent fractions. Sure, it’s easy to use a pizza to represent quarters, sixths, eighths. Thirds aren’t even too bad.

But just try dividing a circle into five equal pieces. Or seven. Or ten. Even though I’m a grown-up and a professional math educator, it’s really hard for me to consistently do this.

And as for showing visually how two fifths equals four tenths? Unless I do an impossibly immaculate job of dividing those pizzas into pieces, forget about it.

Are they really the same?

Fortunately, I’ve found a much better way to represent fractions visually: the Math-U-See fraction overlays. If we’re going to use a food metaphor, they’re flat and square, like brownies from a square pan.

And like brownies, they are much easier to slice evenly than pizzas. In fact, because they’re reusable transparent overlays, you don’t even have to draw (or slice) anything. You just arrange them on top of each other.

Check it:

Awwww, yeah! Those fractions are DEFINITELY equivalent!

You can use the overlays to represent basic fractions with divisors from two through seven, or combine multiple overlays to build other denominators.

Not only do they make it really easy to see how equivalent fractions work, but using them is way easier than drawing pizzas and hoping the slices come out even.

The fraction overlays make the concepts extremely clear, and because they’re tactile, visual, and kinesthetic, they make fractions feel like a game instead of work. Whenever I’ve used them with my students, either in person or during online tutoring sessions with a webcam, they’ve react the same way: “This is fun!”

Now that’s how I want my students to feel about fractions!

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I stumbled across this curriculum while looking at a website of suggested resources for Visual-Spatial Learners. Math U See is designed to be a homeschool curriculum, but I’m wondering why more people don’t know about it and use it. I really wish I had learned about it a lot earlier—like when I was in middle school.

Some core principles set this curriculum apart. Students use blocks (aka “manipulatives”) to build all the numbers first. So for every problem they “build it, say it, AND write it”—thus appealing to many different learning styles—tactile, visual, verbal, etc. An integral goal of the curriculum is that students not only know how to do math operations, but also that they know when to do each one.

Also, teaching Math U See style involves four steps: preparing the lesson by watching a DVD of Math U See founder Steve Demme teaching the curriculum; presenting the lesson to the student; practicing in the workbook; and proceeding when the student can demonstrate mastery by teaching the material back to you.

I love the autonomy support aspect of this curriculum. Steve Demme explains that many people ask how long they should spend on a lesson, and he believes you should really take as much time as you need. I think it’s so cool that the student really sets the pace for when it’s time to move to the next new idea.