Looking at Equivalent Fractions

Recently a teacher came to me and explained how her students were learning about equivalent fractions and some quickly picked up on the pattern. You know the one where you multiply the numerator and denominator by the same number to make an equivalent fraction?

Well, at this point in the learning process, students were encouraged to use math tools. Fraction strips, pattern blocks, fraction circles, number lines. Any tool that could help verify the equivalency of fractions. Students questioned, why do I have to show it if I already know it?

Good question. But what do the students already "know"? A quick pattern of computation? Or the true conceptual understanding of what it means for fractions to be equivalent? As teachers, we have to be careful not to have students jump right to the abstract. It is important to keep in mind the C-R-A sequence of instruction. That is to start with the concrete (use a math tool to verify reasoning), move to the representational (draw the model pictorially), then to the abstract (numbers and symbols: reducing, multiplying, etc.). Check out a previous blog post if you want to read more about C-R-A. Click here.

So, we decided to show students fractions where equivalency could not be simply determined by multiplying the numerator and the denominator by the same number. Students would have to reason and verify using the different math tools because the "rule" no longer worked. Check out the fractions below. Can you see how different thinking might be required using problems such as these? Click on the images if you would like to grab a freebie.

Clipart from Creative Clips and Graphics from the Pond.
 When students are working through these types of problems allow them to choose a math tool of choice. Have students see different ways to defend thinking and multiple ways to show the fractions using the different manipulatives.

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