There have been a lot of changes in Math objectives and instruction over the past few years. One change that I wasn’t so sure about at first was “decomposing fractions“. At the time I was teaching third grade and there were already so many fraction concepts to teach. But, let me tell you, after working with my students on decomposing fractions, I see that they understand fractions a lot better than when we just labeled the fractions. Composing and decomposing the fractions helps them to really see how the parts and wholes relate. Now that I am tutoring 4th, 5th and 6th graders, I see how decomposing fractions really helps them to understand the “bigger” things that they do.
Here is an example of how decomposing fractions helps with simplifying an improper fraction to a mixed number:
Works really well! Now, when I learned how to change an improper fraction into a mixed number we divided the numerator by the denominator and then used the remainder to write the fraction. That works too, but not for everyone. About 16 years ago I taught 5th grade and we used this traditional approach. We even had a cute rhyme … but some students just didn’t “get it”. They couldn’t remember the steps because they didn’t have that deeper understanding. Decomposing fractions helps the students to see why we have the whole number and the remainder as a fraction.
I think it is important as math teachers for us to build understanding that will carry our students through their academic careers, so I like presenting and practicing the solution both ways and then discussing with the student which way they understand the best.
If you are looking for some fun games to practice decomposing fractions I have two: They are both matching games. The first one is decomposing numbers less than 1 and the second is decomposing numbers greater than 1 (mixed numbers and improper fractions). They are available together in one download with a bonus sorting activity: