How to Teach Fraction Operations with Models - Make Sense of Math

# How to Teach Fraction Operations with Models

Ahh Fractions.

The key to teaching fraction operations: adding, subtracting, multiplying and dividing, is to FIRST teach your students conceptually. They need to make sense of the math behind the fractions. Once students feel comfortably conceptually, then help them recognize patterns in their work. Guide your middle school math students to discover the algorithms. Once they understand the algorithm, and the why of the algorithm, then they can practice fraction operations fluency.

Let's look at each of the fraction operations with bar models.

Adding & Subtracting Fractions

Model each fraction on a separate model. Draw the lines vertical on one model, and horizontal on the other model.

Then, copy the lines to the other model, this creates a common denominator.
The models can then be added or subtracted accordingly.

Multiplying Fractions
Thinking of multiplication as "groups of" helps make sense of multiplying fractions using models. 3/4 x 1/2 can be thought of as three-fourths a group of one-half.

Start be modeling 1/2 (yes, you can model 3/4 first, but when thinking of a "group of" then it might make more sense to do 1/2 first, since 1/2 is what you have, and 3/4 is the group.)
After modeling, then model 3/4 on top of the 1/2.
The overlapped portion will be the product, since you are taking 3/4 of 1/2.
Dividing Fractions
Let's first remember what does division mean. 8 divided 2 can mean two things. Partitive division means divide 8 into 2 groups. The quotient, 4, means how many is in one whole group.

Quotative division means 8 divided into groups of 2. The quotient, 4, means how many total groups there are.

So let's transfer this knowledge to dividing fractions 3/4 divided by 1/2.

Partitive. Divide 3/4 into 1/2 a group, the quotient is how many is one whole group.

Quotative. Divide 3/4 into groups of 1/2. How many total groups are there.

Anchor charts are a great visual reminder for your students. I had anchor charts with fraction operations displayed on my classroom walls all year long. Fractions are a constant in math, and many middle school math students are still working on solidfying their understanding of fraction operations.

If you don't want to make your own, you can grab these ones displayed below