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Unit 6

Recording Partial Products: One-digit and Three- or Four-digit Factors

Lesson 9

Multiplying and Dividing Multi-digit Numbers

Expressions and Equations

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Let’s analyze and try an algorithm that uses partial products.

Unit 6 ● Lesson 9

Learning

Goal

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Expressions Galore

Unit 6 ● Lesson 9 ● Warm-up

Which one doesn’t belong?

  • 7 ✕ 50
  • (3 ✕ 50) + (4 ✕ 50)
  • (5 ✕ 10) ✕ 7
  • 50 + 50 + 50 + 50 + 50 + 50 + 50

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How are the expressions alike?

Were there expressions that you knew right away were equivalent? Which ones? How did you know?

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Which One Doesn’t Belong?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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An Algorithm for Noah

Unit 6 ● Lesson 9 ● Activity 1

What do you notice? What do you wonder?

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Launch

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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An Algorithm for Noah

Unit 6 ● Lesson 9 ● Activity 1

  • Noah drew a diagram and wrote expressions to show his thinking as he multiplied two numbers.

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How does each expression represent Noah’s diagram? Be prepared to share your thinking with a partner.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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An Algorithm for Noah

Unit 6 ● Lesson 9 ● Activity 1

  • Later, Noah learned another way to record the multiplication, as shown here.

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Make sense of each step of the calculations and record your thoughts. Be prepared to explain Noah’s steps to a partner.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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An Algorithm for Noah

Unit 6 ● Lesson 9 ● Activity 1

  • Complete the diagram to find the value of 217 ✕ 8. Use Noah’s recording method to check your work.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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An Algorithm for Noah

Unit 6 ● Lesson 9 ● Activity 1

Let’s share how you made sense of the steps in the second problem.

  • The recording strategy that Noah learned is an algorithm that uses partial products. We used an algorithm to add and subtract large numbers in our last unit.
  • How do we know if we have finished finding all the partial products?

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Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Try an Algorithm with Partial Products

Unit 6 ● Lesson 9 ● Activity 2

  • What strategy would you use to find the value of 8 ✕ 3,419?
  • Take a quiet moment to make sense of Noah and Mai’s work. How do you think they arrived at the last four numbers?

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  • Which representation is more like how you thought about it?

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Launch

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Try an Algorithm with Partial Products

Unit 6 ● Lesson 9 ● Activity 2

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Noah and Mai want to find the value of 8 ✕ 3,419. They recorded their steps in different ways, as shown.

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  • How are Mai’s and Noah’s notation alike? How are they different?
  • Use a diagram to show what each of the partial products 72, 80, 3,200 and 24,000 represent. Then, find the value of 8 ✕ 3,419.
  • Find the value of each expression. For at least one expression, use the algorithm that Noah used. Show your reasoning.
    • 4 ✕ 5,342
    • 7 ✕ 983

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Recording Partial Products: One-digit and Three- or Four-digit Factors

Unit 6 ● Lesson 9

Today we learned different ways of recording partial products to multiply four-digit by one-digit numbers. We made connections between a diagram and using algorithms that use partial products.

4 ✕ 5,342

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  • Who can make a connection between the two ways to solve the problem?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Partial Products

Unit 6 ● Lesson 9

Find the value of 5 ✕ 1,023. Show your reasoning.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.