Monthly Archives: April 2021

Fraction Discovery for First Graders

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First graders are a goldmine of discovery and excitement. Here’s a lesson idea that will turn fraction time into an epic adventure. Tap into your first graders’ capacity for wonder and innate knack for unlocking underlying patterns.

The idea

Do you know what you get if you compute 3/33? Try it on a calculator! How about 5/55? Hmmm, wow! Did you feel that spark of wonder? You might already know that these are both equal to 1/11 and that’s why they both produce the super cool repeating decimal result. But your first grader (or young math learner in that ball park) doesn’t know the punch line! It’s a mystery, and mysteries are the lifeblood of mathematical curiosity. This activity lets learners play with a few mysteries of division and fractions and encourages them to notice fascinating patterns.

Materials

Each learner or group of learners will need:

  • Calculator
  • 3 circles, one with 0.0909090909… filled in
  • Mystery fraction cards

Plan

Set the scene by passing out calculators and encouraging learners to play around for a few minutes. As I pass out the calculators I might say things like, “Does anyone like making long numbers on calculators?” “Oh, that’s a cool number! How did you make that one?” “Can you make a big number without pressing a lot of buttons?” Kids love calculators so you shouldn’t have too much trouble getting them to play around with them!

Grab everyone’s attention and let learners share with the group some of their favorite things they found while playing. Then ask, “Did anyone try 9 divided by 99?”. Write it on the board (as a fraction and with the divided by sign to show the equivalence) and give the learners a chance to spontaneously try it out. Notice and reflect the excitement at the super cool repeating decimal! “Wow! How neat is that?!”

Curiosity and playfulness are both in place – time for some structure! Pass out the circles and fraction cards, as shown in the image. Every group of learners should have all the fractions I suggested. The hope is that learners will relish the chance to try out these division problems on their calculators and sort them into the circles.

If they notice patterns, give praise and ask follow up questions. Most importantly, don’t forget to have fun. We are doing math, after all!

If you try this lesson please let me know how it went! Also, if you create some print-outs for this activity, please share them with the community and let me know!

Do most first graders hate math?

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I have a new student, let’s call him Sam. He is in first grade, he loves snakes and stories, but according to him, he doesn’t like numbers or challenges. He likes patterns a little bit. Sam doesn’t like it when his mom makes him do subtraction problems assigned by his teacher.

On our first lesson we read the first chapter of the book The Number Devil. It tells a story about a boy in whose dreams the number devil gives him a magical tour of number theory. We paused in our reading often for him to pull out his calculator and follow along with what the boy in the story was doing on his calculator. This frequently turned into Sam playfully experimenting with various operations on the calculator and discovering new patterns. In the beginning of our second lesson, my he asked eagerly, “But do you remember the Number Devil??” as if worried that I might forget about reading the second chapter.

Long story short, Sam clearly loves math. He is delighted by patterns, by making discoveries about numbers, and by big ideas like infinity and dividing by zero. Yet, a bit of first-grade level arithmetic in school had him convinced of the opposite. And that’s only in first grade. What would we expect to happen by middle school? By high school?

It is common knowledge that most people emerge from public school with a distaste for math. But what is less commonly recognized is that most first graders start out with the capacity to love math. All we have to do is allow them to play with it and encourage them to be imaginative about it. In fact, I think all we really have to do is refrain from forcing them to do repetitive and tedious arithmetic!