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# Modeling Multiplication Word Problems

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Students will be able to use a part-part-whole model to organize and solve multiplication word problems.

(1 minute)
• Tell students, "Today we are going learn a strategy that will help us solve word problems."
(10 minutes)
• Show students an example of a part-part-whole model for multiplication. Draw two rectangles stacked on top of each other and divide the bottom rectangle into two parts with a vertical line. Write two factors in the bottom parts and the product in the larger top rectangle (i.e. 5 x 4 = 20; see resources for an example).
• Point out the fact family contained in the model (i.e. 5 x 4 = 20, 20 ÷ 4 = 5).
• Explain that part-part-whole models can help us visualize a multiplication (or division) problem because it helps us see which numbers are the smaller parts, or factors, and which part is the product.
• Tell students that sometimes when we read a word problem, it can be hard to figure out how to start the problem. But drawing a model can help organize the information from the word problem and make it easier to solve.
• Write a simple word problem on the board (i.e. Hannah runs three miles every day. How many miles will she run in nine days?)
• Draw a model showing the two factors, 3 and 9, in the smaller sections and a question mark (or variable) in the larger section.
• Explain that when we draw the model we can organize the information from the word problem and use it to write an equation.
• Write an equation and solve (i.e. 3 x 9 = 27 miles).
(15 minutes)
• Guide students through another example (i.e. Jordan made a batch of 24 cupcakes for his mom’s birthday. He put four candles in each cupcake before singing happy birthday. How many candles did Jordan’s mom blow out?).
• Give students a problem to try with a partner (see resources for example word problems).
• Give students a "try it" problem to solve independently. Circulate and offer support as needed. Then go over the problem as a class.
(15 minutes)
• Write (or make copies of) three word problems (see resources).
• Hand out scratch paper or have students use math notebooks for their work.
• Instruct students to solve the word problems independently, using part-part-whole models.
• Circulate as students work and offer support as needed.
• Go over the problems as a class.

Support:

• Provide additional examples before assigning independent work.

Enrichment:

• Have students apply the modeling strategy to solve division words problems.
• Have students write their own word problems. Then have students exchange word problems with a peer and solve with a part-part-whole model.
(5 minutes)
• Hand out a piece of scratch paper to each student.
• Write a multiplication word problem on the board (see resources).
• Have students create a part-part-whole model to solve.
• Collect student work as an exit ticket and check for understanding.
(4 minutes)
• Ask and discuss, "How does the part-part-whole method compare to the other strategies you’ve learned?"

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