Finding equivalent fractions can be a
confusing concept for students. It’s
counter-intuitive to change both the numerator AND the denominator, especially
if students have been working on composing/ decomposing fractions or adding and
subtracting fractions.

When you count by, add, or subtract
fractions, the denominator stays the same:

one sixth, two sixths, three sixths…

3/8 + 2/8 = 5/8

7/10 – 3/10 = 4/10

But to find equivalent fractions (and
later, to reduce fractions), we need to change both the numerator and the
denominator, and that can be a source of confusion.

Helping students understand the
difference between adding and subtracting (or composing and decomposing) and
doubling or multiplying will make it easier for them to find equivalent
fractions. When we add or subtract, we
are changing the amount we have- increasing it when we add and decreasing it
when we subtract. When we are finding
equivalent fractions, we are keeping the exact same amount- and that’s why both
the numerator and the denominator need to change- to keep the same amount of
fraction.

This can be a really abstract concept for kids, but, fortunately, there are ways to make it much more tangible for them! Folding (or cutting) is one of the most concrete ways for students to visualize how equivalent fractions work. This helps them see that it’s still part of the same whole, and that we are not changing the amount of the fraction.

Here’s an example:

1. Take a piece of paper.

2. Fold it in half.

3. Color one half and leave the other
half blank.

4. Fold it back in half.

5. NOW, fold it AGAIN, to make fourths.

6. Open it up! Voila! Now it’s clear that the same ½ that
was colored is now actually 2 parts (because of the new fold). BUT, where there used to only be 2
total pieces, there are now FOUR.

This process makes it easier for kids
to see the doubling that is happening when we make equivalent fractions. The
numerator (shaded part) is being doubled by folding the paper in half. AND, the
denominator (totally pieces) is ALSO being doubled by folding the paper in
half. So ½ will
become 2/4 because both the top and bottom are doubled. And we didn’t change the are that was
shaded, so we know the two fractions are equivalent!

PRO tip: Have the students write an
equation to match each folding that they do. For the above example, one equation
could be: 1/2 x 2/2 = 2/4.

This exercise can be repeated over and
over until students start to see the how the equivalent fractions are related. They can even refold papers that
are already folded or fold papers in a sequence to make a string of equivalent
fractions. Start with
doubling (folding in half), then move on to tripling or quadrupling. Have different students work with
different sized papers to help them generalize their understandings for
different size wholes.

Once students
have a strong grasp of how equivalent fractions work, it will be much easier
for them to add and subtract fractions with unlike denominators, reduce
fractions, and convert between improper fractions and mixed numbers.

For ready-made, guided discovery
folding equivalent fractions lessons, check out my best-selling Third Grade Fraction unit.

Happy (equivalent fractions) Teaching!

Christine Cadalzo

Tell me what you think!

Click here to take a 2 minute survey and share your thoughts on teaching fractions.