Lesson 2

More Multiplication Stories

Est. Class Sessions: 2

Developing the Lesson

Part 3. Breaking Factors into Tens and Ones

Read Multiplication Stories. After discussing various ways to multiply, tell students that you would now like them to focus on a particular way to break products apart: partitioning factors into tens and ones. This is used in the paper- and-pencil multiplication algorithm and is helpful in doing mental calculations.

The More Multiplication Stories pages in the Student Guide continue with two stories, Julia's story for 72 × 3 and Luis's story for 63 × 4, which involve partitioning one factor into tens and ones. Discuss these stories with the class.

  • How did Julia break apart a number to solve the problem? (She wrote 72 = 70 + 2.)
  • How is Julia's second story different from her first story? (The first story says only that 72 children had their tricycles. The second story describes 70 children had tricycles and 2 more children got their tricycles later.)
  • How does her new story match the way she solved the problem? (The 70 × 3 in her solution is the number of wheels on the tricycles of the first 70 children. The 2 × 3 is the number of wheels on the new tricycles. When she adds them up, she gets the total number of wheels.)

Ask similar questions about Luis's stories for 63 × 4.

Write Multiplication Stories. Continue writing and illustrating stories for more two-digit by one-digit multiplication problems, first as a class and then individually when the students are ready.

The stories should have a common theme of splitting numbers into smaller groups of tens and ones. Drawing pictures should help students see why this particular way of solving multiplication problems—breaking apart products into tens and ones—makes sense. Making number sentences and pictures will help students connect the arithmetic process they use to standard symbols.

  • How can you break 53 into tens and ones? (50 + 3)
  • Write a number sentence that uses a break-apart method to solve 6 × 53. (6 × 50 + 6 × 3)
  • Explain how to solve 6 × 50 + 6 × 3 using a break-apart method. (Possible response: I think about money. Two 50s make 100, so six 50s are 300. I know 6 × 3 = 18. Then 300 + 18 = 318.)
  • Think of a story for 6 × 50 + 6 × 3. (See Figure 3 for a sample story and matching picture.)
  • How does your story match the way you solved the problem? (In the sample story, 6 buses with 50 passengers matches 6 × 50. Three new passengers on each of the 6 buses matches 6 × 3. Then 300 plus 18 equals 318 passengers altogether.)

Use Roberto's Chart to Solve Problems. Direct students' attention back to the More Multiplication Stories pages in the Student Guide. Read the Use Roberto's Chart to Solve Problems section. Students can organize their work the way Roberto does by showing the products to add, their calculations, the story, and a picture. Emphasize to students that they should draw simple pictures. Point out that instead of drawing 185 flies, Roberto uses base-ten shorthand to represent them in his picture. He draws 3 skinnies to show 30 flies in each lizard's lunch. Then he draws 7 bits by each lizard to show how many flies each lizard eats for a snack.

Display the blank Roberto's Chart Master. Pose the following problem and demonstrate how students can use Roberto's chart to organize their work. Record students' responses on the display. See Figure 4 for a sample problem and completed chart.

  • Let's solve 37 × 4. How can you break 37 into tens and ones? (3 tens and 7 ones, or 30 + 7)
  • What are the products that you need to calculate? (30 × 4 and 7 × 4)
  • Think of a story for 30 × 4 + 7 × 4. (Possible response: There are 30 trees with 4 red apples, and 7 trees with 4 green apples. How many apples are there altogether?)
  • Explain how to solve 30 × 4 + 7 × 4 using a break-apart method. (Possible response: 30 is 3 tens, so I thought about 4 groups of 3 skinnies. I counted by tens to 120. 7 × 4 = 28, so 120 + 28 = 148.)
  • How does your story match the way you solved the problem? (In the sample problem, 30 trees with 4 red apples each plus 7 more trees with 4 green apples each matches 30 × 4 = 120 plus 7 × 4 = 28, 120 + 28 = 148 apples altogether.)

Assign Questions 1–5 on the Roberto's Charts pages in the Student Activity Book. Students solve one-digit by two-digit multiplication problems by breaking the two-digit number into tens and ones and then multiplying. For each problem, they write a story and pictures to match the solution. They organize their work the way Roberto did by showing the products to add, their calculations, story, and picture. They should clearly indicate their answers on their work.

As students work, pay close attention to how they solve the problems. When they are done, you can selectively choose students to share different solution strategies. Look for one or two interesting strategies that students could use to solve another problem later.

Select one of the problems from the Roberto's Charts pages to discuss. Based on your monitoring of the students' problem solving, select several students to share their work so that you can discuss a variety of strategies. Allow students to display their charts.

  • How did you break your number apart to solve the problem?
  • What story and picture did you create to match your solution?
  • How do the parts of your solution match the parts of your story and picture?
  • Solve this problem another way to check it.
  • Use [student's name]'s method to solve this problem.
  • How is [student's name]'s method alike or different from [student's name]'s method?

Use Check-In: Question 5 on the Roberto's Charts pages with the Feedback Box in the Student Activity Book to assess students' progress toward the following Expectations:

  • Represent 2-digit by 1-digit multiplication problems using drawings, stories, and number sentences [E1].
  • Show connections between models and strategies for multiplication [E2].
  • Solve multidigit multiplication problems using mental math strategies (e.g., decomposing numbers and halving) [E3].
  • Multiply one-digit whole numbers by multiples of ten [E5].
  • Solve multiplication problems by breaking products into the sum of simpler products (applying the distributive property of multiplication over addition) [E7].

Use Check-In: Question 5 to also assess students' abilities to find an appropriate strategy [MPE2] and show their work [MPE5]. As you are evaluating student work look for:

  • a strategy that matches the story and the picture.
  • efficient ways to break apart the product (tens and ones or known facts).
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6 × 53 passengers
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Using Roberto's chart to solve 37 × 4
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