Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (71 page)

Students can model multiplication of fractions using rectangles. In the problem
, for example, students may begin by drawing 1 whole as shown below in Step 1. They would then divide the whole into 3 equal parts and shade 2 of these parts as shown in Step 2. Multiplying by
divides the whole into 2 equal parts as shown in Step 3. Since the numerator is 1, note that 1 of the 2 equal parts is shaded in Step 4 (the top three squares). The region that is shaded twice shows the product, which is
.

Activity 1: Modeling Multiplication of Fractions

Working in pairs or groups of three, students will receive a model of a multiplication problem. They are to write an equation, based on the model, and then write a story context for the problem.

Materials

One copy of reproducible, “Modeling Multiplication of Fractions.”

Preparation

After making a copy of the reproducible, cut out the 10 models, one for each pair or group of students. (
Note:
For large classes, more than one pair or group may work with the same model, in which case you will need two copies of the reproducible.)

Procedure

1.
Explain the model for the problem
to your students as shown in the Background. Suggest that students copy it so that they may refer to it later, if necessary.

2.
Hand out a model of a multiplication problem to each pair or group of students. Explain that the model is similar to the example you just discussed.

3.
Explain that students are to write an equation that represents their model. They are then to write a story context for the problem. They should then solve the problem.

Closure

Discuss the models, equations, and answers. Have each pair or group of students share their work and their story context with another pair or group. Instruct students to discuss if the story context matches the problem, and if the equation is an accurate representation of the model.

Answers

Story contexts will vary, but should represent the problem. Following are the equations that correspond to each model.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)