How to Teach Fraction Operations Using Bar Models
The key to teaching fraction operations—adding, subtracting, multiplying, and dividing—is to teach conceptually first. Students need to make sense of the math behind fractions before learning shortcuts and algorithms.
Once students understand the models, help them recognize patterns, discover the algorithms, and develop fluency. Let's look at the four operations using fraction bar models.
Adding and Subtracting Fractions
Model each fraction separately. Draw vertical partitions on one model and horizontal partitions on the other.
Copy the partition lines onto both models to create equivalent fractions with a common denominator.
With equal-sized pieces, students can now add or subtract the fractions and explain why common denominators are needed.
Multiplying Fractions
Think of multiplication as taking a fraction of another quantity. For example, 3/4 × 1/2 means taking three-fourths of one-half.
Start by representing one-half.
Next, partition that half into four equal parts and represent three-fourths of it.
The overlapping region represents the product, three-eighths.
Dividing Fractions
Before introducing fraction division, revisit the two meanings of division: partitive and quotative.
Partitive division: Eight divided into two equal groups. The quotient of four tells how much is in each group.
Quotative division: Eight divided into groups of two. The quotient tells how many groups there are.
Now use these ideas for 3/4 ÷ 1/2. In a partitive interpretation, 3/4 is one-half of a group. How much makes a whole group?
For the quotative interpretation, ask how many groups of one-half fit into three-fourths. The result is one and a half groups.
Fraction Operations Anchor Charts
Anchor charts are helpful visual reminders. Fractions appear throughout middle school math, so I kept fraction operations models on my classroom walls. You can also use these Fraction Operations Anchor Charts.
Save These Fraction Models for Later
Save this post to your math teaching Pinterest board for ideas on teaching addition, subtraction, multiplication and division of fractions using visual models.
