Why do our students struggle to understand fractions? A big part of the problem is that fractions are incredibly abstract. If I were to ask you, Which is greater, 1/8 or 1/4? you would likely have an image in your head corresponding to those fractions. Unfortunately, many students see only symbols in their heads. Without the ability to visualize these unit fractions, there’s a good chance they’ll say 1/8 is greater than 1/4 because 8 is greater than 4. Not understanding what the denominators 8 and 4 actually represent, they are applying whole-number thinking to fractions.
So how do we put those images in their heads? The answer is actually amazingly simple—we provide them with lots of concrete and pictorial experiences so they can connect a visual to the abstract symbols. Too often we bypass the manipulatives, blaming lack of time or too much to “cover.” But when we don’t use manipulatives, we end up spending more time in the long run trying to fill the gaps that our students end up with.
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The foundations for fraction understanding begin in 3rd Grade, and there’s a LOT packed into the 3rd Grade fraction standards. Included is an introduction to unit fractions, which are the building blocks of all fractions. A unit fraction is any fraction with a numerator of 1. It’s basically one part of a whole divided into n parts. In 3rd grade, students learn that a fraction is the sum of unit fractions. For example, 3/4 = 1/4 + 1/4 + 1/4. In 4th grade, students extend that thinking to an understanding that fractions can be composed and decomposed in different ways. For example, 5/6 = 2/6 + 3/6 but also 5/6 = 4/6 + 1/6.
What better way to engage students in learning than with math games? Introduce this simple game called Cover Up at your small group table. You’ll need a set of fraction tiles for each player (yourself included), or students can make fraction strips. Students will love this game, and, with well-placed probing questions, you can generate some terrific mathematical discussions. Once students are familiar with the game from playing in a small group, move it to your workstations. If students play this game enough, I’d be hard-pressed to see how they could ever say that 1/8 is greater than 1/4! Or add together the denominators when adding fractions. Or NOT see that 2/4 is equivalent to 1/2. I think you get the idea. 🙂
Check out the video for how to play and questioning techniques you can use while playing. Then scroll down for the link to download two spinners for working with different sets of fractions.
You can grab the spinners for playing Cover Up here. Enjoy!