Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (78 page)

Activity: Dividing Unit Fractions

Working in pairs or groups of three, students will match word problem cards with cards containing the correct equation and solve each problem by modeling division.

Materials

1 set of Cuisenaire rods; rulers; scissors; glue sticks; crayons; colored pencils; 9-inch-by-12-inch unlined paper; graph paper; reproducibles, “Division—Unit Fraction Cards, I” and “Division—Unit Fraction Cards, II,” for each pair or group of students.

Procedure

1.
Work as a class and show your students how to model the examples in the Background using the Cuisenaire rods.

• In the first problem,
  , let the brown rod equal 1 whole, the purple rod equal
  , and the red rod equal
  . Tell your students to find two rods of the same color that, when put end to end, will equal the length of the red rod. They should find that two white rods equal the length of the red rod and this models
  . To find the quotient, determine what the white rod represents compared to 1 whole. The white rod is
  of the whole or, in this case, the brown rod.
  is the quotient.
  
• Explain that in the second problem,
  , students must find a rod that can be divided into thirds. This time let the dark green rod equal 1 whole. To model this problem, students need 2 dark green rods because they are dividing 2 wholes. Ask students to find the rod that represents
  of the dark green rod. It is the red rod. You may want to remind students that in the last problem the red rod was equal to
  . The red rod now represents a different fraction because a different color rod represents 1 whole. Instruct your students to find the number of red rods that when placed end to end will have the same length as the 2 dark green rods. Because 6 red rods equal the length of the 2 dark green rods, 6 is the quotient.
  

2.
Remind your students that they are not limited to only using single rods to equal 1 whole. They can create a “train” of rods, for example 1 orange and 1 dark green together may equal 1 whole.

3.
Hand out copies of the reproducibles. Explain that they contain 8 word problem cards and 8 equation cards, each of which represents one of the problems.

4.
Explain that students are to cut out the problem cards and the equation cards, and match each word problem with its correct equation. Once they have matched a word problem with its equation, they are to glue the problem card and equation card on their unlined paper. They must then create a model of the problem on graph paper, cut their model out, and glue it beneath the problem on the unlined paper. Note that they may use Cuisenaire rods to help them create their models. Finally, they are to solve the equations.

Closure

Check students' matched problems, equations, and models. Have students share their work and solutions with another pair or group. Discuss how models may vary and different models may represent the same problem.

Answers

Models will vary but should represent the following answers.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)