The Fraction Orange is a sphere partitioned into two hemispheres; one hemisphere is further partitioned into fourths, eighths, and sixteenths of the whole; the other hemisphere is further partitioned into sixths and eighteenths.

Big Idea

The Fraction Orange manipulative is particularly useful tool for exploring the measurement meaning of division. It’s also useful for teaching fractions through multiple representations, like drawings of partitioned wholes and symbols of the form a/b.

Engaging students in ideas that are represented in multiple ways is fundamental to their deep learning of mathematics. As students coordinate and negotiate the meanings they make from each representation, they can develop more formal and sophisticated mathematical meanings.

Purpose

Students can use the Fraction Orange to make sense of the measurement meaning of fraction division (i.e., 1/2 ÷ 1/4 means “How many 1/4s are in 1/2?). They can use this understanding to find the quotient of two fractions and to solve problems involving fraction division.

Sample Tasks and Explorations

• Use the Orange to find equivalent fractions. For example, use the Orange to find 1/2 and then verify that 1/2 = 2/4 = 4/ 8 = 8/16. Then do the same for fractions equal to 1/3.
• First, use pen and paper to solve the problem 1/2 ÷ 1/4. Then, use the Orange to solve the problem. As you solve the problem using the manipulatives, can you find the Orange pieces that correspond to particular parts of the algorithm?
• Find 1/2 ÷ 1/3 using the Orange.
• You may have learned that 1 ÷ 1/3 = 1 x 3/1. Use the Orange to verify that this is true. Then do the same for another unit fraction (i.e., a fraction whose numerator is 1).