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# Multiplication with Area Models

Teach your students to use an area model to solve multiplication problems with a two-digit factor.

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Students will be able to use an area model to solve multiplication problems with a two-digit factor.

(10 minutes)
• Explain to the class, "Today we are going to practice multiplying larger numbers."
• Remind students that one way to think about multiplication is through the context of area.
• Review concept of area (area= length x width).
• Provide students with an example of area by drawing a rectangle on the board and multiplying to find the area (i.e. 3 x 2 = 6)
• Remind students that another way to multiply is to break numbers into smaller parts, or decompose numbers (see resources for additional information about decomposing numbers).
• Review the concept of decomposing numbers by place value (i.e. 12 = 10 + 2 or 36 = 30 + 6).
• Ask students to decompose a few numbers with a partner and call on students to share answers (i.e. decompose: 82, 17, 24).
• Explain to the class, "We are going to use what we know about area and decomposing numbers to multiply two-digit numbers."
(10 minutes)
• Write a two-digit times one-digit problem on board (i.e. 5 x 16).
• Explain to your students, "There are many strategies that can be used to solve multiplication problems. The one we will be practicing today is called area model. When using an area model, each factor in the multiplication problem is used as a dimension of a rectangle. The area of the rectangle is the product, or answer, of the multiplication problem."
• Draw a rectangle on the board and explain that in this problem, the factors 5 and 16 are the length and width of the rectangle.
• Label the short side of the rectangle with 5.
• Then, tell students that since 16 is a two-digit number, it can be decomposed by place value (i.e. 10 + 6) so that it is easier to multiply.
• Draw a line to divide the long side of the rectangle into two parts. Write 10 and 6 over the two divided parts so that you have a rectangle that has an area of 10 x 5 and one with an area of 6 x 5.
• Multiply to find the area of each portion of the divided rectangle and write the product inside the corresponding piece of rectangle (i.e. 50 and 30).
• Add the two partial products (parts of the total answer) to get the area of the entire rectangle.
• Explain to your students, "The answer to our multiplication problem, 16 x 5 is 80. We used the concept of area to help us find the product, but since this was not an area problem to begin with, we do not need to add any units of measurement to our answer."
• Write 16 x 5 = 80 below the area model.
(15 minutes)
• Guide students through another example (i.e. 24 x 7).
• Give students a problem to try with a partner (i.e. 12 x 6).
• Give students a ‘try it’ problem to solve independently (i.e.13 x 9). Circulate and offer support as needed. Then go over the problem as a class.
(15 minutes)
• Hand out the Area Models with Bicycles worksheet and instruct students to complete it independently.
• Circulate and offer support as needed.

Support:

• Provide additional examples before assigning independent work.
• For independent work, assign problems with smaller two-digit factors in place of the worksheet.

Enrichment:

• Assign challenge problems with two two-digit factors (i.e. 12 x 15).
(5 minutes)
• Hand out a piece of scratch paper to each student.
• Write a multiplication problem on the board (i.e. 15 x 8).
• Have students create an area model to solve.
• Collect student work as an exit ticket and check for understanding.
(5 minutes)
• Show students the Area Model song.
• Start a discussion by asking, "How can the area model help us solve multiplication problems more easily in our head?"