Using Scrap Paper to Solve Math Problems

Using Scratch Paper for Math

Happy Pi Day! For those who are rusty on geometry, pi (the Greek letter π) is the symbol for a number that represents the ratio of a circle’s circumference (distance around) to its diameter (distance from edge to edge, through the center). The cool thing about pi is that it’s a constant; for all circles of any size, pi will be the same. And while pi has been calculated to over a trillion digits beyond the decimal point, most non-mathematicians round pi to 3.14—which is why March 14 is known as Pi Day and celebrated by math teachers and students worldwide!

Why not celebrate Pi Day to spark your children’s interest in and use of math in everyday life? Make a Pi Day pie, reinforcing terms like radius, diameter, and circumference while you roll out the crust! Or plan a Pi Day math scavenger hunt, in which kids follow clues to locations where they find math problems to solve. Be sure to give prizes! Whatever you do, make it fun—and celebrate with Pi Day pie—even if it’s store-bought.

In honor of Pi Day, I’d like to share a tip for helping students solve math problems: using scrap paper. Picture this: it’s a hot summer day, and you want to fill the small pool in the backyard—but there’s no garden hose. You grab a bucket and fill it right to the brim, but by the time you walk to the pool, half the water has splashed out. Then you have an idea—next time you fill up, you place the bucket in a large baking pan to carry it across the yard. Any splashes of water land in the pan—so it all ends up in your pool!

Believe it or not, this is exactly how scrap paper works for you in math. Your brain is like the bucket. As you work on a math problem, you fill it with numbers, information, and calculations. But sometimes, when you begin to move toward finding a solution, your brain just can’t juggle all the data and it spills out! Unfortunately, remembering just one number incorrectly can ruin all of your hard work.
Instead of trying to remember it all, encourage your children to use scrap paper like the baking pan in the bucket story. Scrap paper can “catch” all the data to keep it handy while doing the problem solving—and accurate data will lead to success!

A student once told me that he didn’t need scrap paper. He said he could keep his data in his head because he is so good at remembering stories and details. If your children tell you this, remind them there’s a big difference between math and stories. Remembering a story like a chapter book or a novel is easier for the brain because you can use your imagination to visualize the action, characters, setting, etc. But when solving a math problem, your brain is doing a different, and often more complex, job.

I tell students that using scrap paper does not mean you cannot calculate in your head. Instead, using scrap paper means you are using a helpful tool to “catch the overflow” that your brain cannot handle alone. This makes using scrap paper a wise choice!

As kids grow up, their math becomes even more complicated, with multiple steps and calculations. At age nine, students might use a little bit of scrap paper, but when they become teenagers, they’ll need lots and lots of scrap paper! Whether you call it scrap paper or scratch paper, it can be colored paper, small paper, large paper—any kind of paper will do, as long as it’s there to help with brain overflow!

To summarize, remind your kids that to be sure their calculations are accurate, they should keep using scrap paper—and always double-check their work!

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