Multiplication Models: Fractions and Whole Numbers
Students will be able to multiply a fraction by a whole number.
- Show students an example of a multiplication model with two whole numbers, like 3 x 5.
- Write the problem on the board and draw three circles to represent the three groups. Draw five dots in each circle.
- Write a repeated addition sentence to go with the picture (i.e., 5 + 5 + 5 = 15).
- Explain, "Three groups of five is 15, so 3 x 5 is 15."
- Tell students that today they are going to learn how to multiply a fraction by a whole number by using equal groups.
Explicit Instruction/Teacher modeling(10 minutes)
- 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(15 minutes)
- 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(10 minutes)
- 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.
- Provide completed models and have students write a repeated addition sentence to go with the models.
- Have students change improper fractions to mixed numbers when applicable.
- Hand out a blank sticky note to each student.
- Write a problem on the board, like 4 x 2/9. Instruct students to solve on their sticky note.
- Collect the problem as an exit ticket and check for understanding.
Review and closing(10 minutes)
- Hand out one prepared sticky note to each student, with fractions written on each (e.g., eight students will have sticky notes that say ⅛, six students will have sticky notes that say ⅙, and so on so that every student has a sticky note).
- Instruct students to stick their fraction to their shirt and remain seated.
- Announce a multiplication problem, like 4 x 2/8, and have students (who are wearing the appropriate fraction) stand and group themselves together to make a human model.
- Repeat with other problems, like 2 x 3/6, so that everyone has a chance to create a human model.