April 15, 2017
by Sarah Sumnicht

Lesson plan

Multiplication of Mixed Numbers with Area Models

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Students will be able to use an area model to solve multiplication problems with mixed numbers.

(10 minutes)
  • Review area models with whole numbers by showing students an example (see resources).
  • 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.
(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).
(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.
(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).
(5 minutes)
  • 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.
(5 minutes)
  • Ask and discuss, "How can this strategy help us understand fractions and multiplication?"

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