Saturday, December 13, 2014

Three Ways to Divide Fractions

Most students learn about fractions using the area model.  Understanding only this representation of fractions can pose a problem when students advance into the upper elementary grade levels as well as into middle school.  

The area model is usually represented with a circle that is divided into equal sections. Rectangles are also used for this model. When different word problems are posed, students often have difficulty with visualizing the meaning of fractions when only one representation is used.  This limited view of fractions becomes even more apparent as students move into ratios and rate.  Below is an example of a dividing fractions question. By reading it, it can be seen how challenging it would be to use the area model to visualize this problem.

Sample Problem

If 1/3 is 6 groups, how many are in one group?

Using multiple formats to represent fractions is an effective way to deepen understanding about fractions and help students understand what it means to divide fractions.  It also helps students gain context to better decipher word problems.  The Common Core Number and Operation-Fractions Standards as well as many state assessments urge students to be able to work with fractions in multiple contexts.

The chart shows three ways for students to represent and solve for 3/4 ÷ 2/3.  The following questions can be asked when teaching students about fractions:

Can you think of another way to solve this problem?

Can you draw a diagram that represents what you just did in the math algorithm?

How are each of your representations similar? How are they different?

Common Core Aligned Fraction Task Cards That Teach And Review Concepts
(Printable Storage Boxes Are Included)

1 comment:

  1. If you have never read the book, "Extending Children's Mathematics" by Susan B. Empson and Linda Levi, it is a great read before teaching students anything about fractions or decimals. It was an eye opener for me!