Multiplication Models: Fractions and Whole Numbers

Explicit Instruction/Teacher modeling

• Using fraction strips or fraction bars, show students an example of a multiplication model with a fraction. Write the problem on the board (i.e., 3 x ⅕).
• Hold up one ⅕ bar and explain that 3 x ⅕ is three groups with ⅕ in each group.
• Draw three circles and place a ⅕ bar in each. Then write a repeated addition sentence to go with the drawing (i.e., ⅕ + ⅕ + ⅕).
• Ask, "How many fifths are there altogether?" The answer is three fifths. Take a student response and then explain that three times ⅕ is ⅗. (Write 3 x ⅕ = ⅗ on the board.)
• Show another example that does not use unit fractions, like 3 x ⅖. Demonstrate with fraction bars and write a repeated addition sentence to solve (i.e., ⅖ + ⅖ + ⅖).
• Ask, "How many fifths are there altogether?" The answer is six fifths. Take a student response and then explain that three times ⅖ is 6/5. (Write 3 x 2/5 = 6/5 on the board.)

Guided Practice

• Hand out a page of fraction strips and a sheet of construction paper to each student. (Note: in order to save time, have students cut only the fraction strips they need as they build models.)
• Write a problem on the board, like 4 x ⅙.
• Instruct students to work with a partner to build a model. Remind students to draw circles on their construction paper to show the number of groups and glue their fraction strips to illustrate the problem. (Note: have students fold their paper in half and use just one half for their first model.)
• Have students write a repeated addition sentence and multiplication sentence to go with their model.
• Write a second problem on the board, like 2 x ⅜, and instruct students to build a model independently on the other half of their construction paper. Remind students to write a repeated addition sentence and multiplication sentence to go with their model.
• Ask students to talk with a partner and come up with a rule to multiply a fraction times a whole number (i.e., multiply the whole number times the numerator—the denominator remains the same).
• Note: if students are unable to come up with the rule based on the first several examples, give a few more examples (i.e., 2 x ¼, 2 x ¾). Demonstrate with strips and guide students as needed to discover the algorithm.
• Show students an example using the algorithm (i.e., 4 x 2/10 = 8/10).

Independent working time

• Keep the examples from earlier in the lesson posted for student reference.
• Write four problems on the board and have students independently solve each, using the algorithm (i.e., 5 x 1/4, 4 x ⅔, 3 x 3/12, 6 x 5/8).
• Hand out scratch paper or have students use math notebooks to solve.
• Circulate as students work and offer support as needed.
• Go over the problems as a class.