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Multiplication of Mixed Numbers with Area Models
Students will be able to use an area model to solve multiplication problems with mixed numbers.
- Review area models with whole numbers by showing students an example (see related media).
- Explain, "Today we are going to use area models to multiply a mixed number times a whole number."
- Remind students that a mixed number is a number that has a whole number and a fraction, like 5½.
Explicit Instruction/Teacher modeling(10 minutes)
- Write a mixed number multiplication problem on board (i.e., 3¼ x 2).
- Decompose the mixed number (3 + ¼).
- Draw a rectangle on the board. Label the short side with a 2.
- Draw a line to divide the long side of the rectangle into two parts. Write 3 and ¼ over the two divided parts so that you have a rectangle that has an area of 2 x 3 and one with an area of 2 x ¼.
- Multiply to find the area of each portion of the divided rectangle and write the product inside the corresponding piece of rectangle (i.e., 6 and 2/4).
- Add the two partial products (parts of the total answer) to get the answer.
- Simplify the fraction and rewrite the multiplication sentence with the answer (i.e., 3¼ x 2 = 6½).
Guided Practice(15 minutes)
- Guide students through another example (i.e., 15 x 4½) Remember to decompose two-digit whole numbers and draw additional sections in the area model as needed.
- Give students a problem to try with a partner (i.e., 13 x 5⅙).
- Give students a "try it" problem to solve independently (i.e., 1⅔ x 6). Circulate and offer support as needed. Then go over the problem as a class.
Independent working time(15 minutes)
- Hand out scratch paper or have students work in math notebooks.
- Write three mixed number times whole number problems on the board and instruct students to solve them independently, using area models (i.e., 7 x 2⅘, 6¾ x 19, 25 x 3⅛).
- Circulate and offer support as needed.
- Provide additional examples before assigning independent work.
- For independent work, assign problems with unit fractions or single digit whole numbers.
- Assign challenge problems with a fraction times a mixed number and have students try the same strategy to solve (i.e., 5¾ x ½).
- Hand out a piece of scratch paper to each student.
- Write a multiplication problem on the board (i.e., 3⅛ x 9).
- Have students solve using an area model.
- Collect student work as an exit ticket and check for understanding.
Review and closing(5 minutes)
- Ask and discuss, "How can this strategy help us understand fractions and multiplication?"