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Unit 4

Ten Times As Much

Lesson 10

From Hundredths to Hundred-thousands

Expressions and Equations

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Let's write equations to show the relationship between the digits in multi-digit numbers.

Unit 4 ● Lesson 10

Learning

Goal

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Related Numbers

Unit 4 ● Lesson 10 ● Warm-up

Find the value of each expression mentally.

  • 650 + 75
  • 5,650 + 75
  • 50,650 + 75
  • 500,650 + 75
  • Which parts of the number change when we add 75?
  • How do we know without adding if digits in a number are going to change?

Number Talk

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

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Alike but Not the Same

Unit 4 ● Lesson 10 ● Activity 1

  1. Complete the table with the value of the 8 in each number.

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  • Describe the relationship between the value of the 8 in each number.
  • Write a multiplication or division equation to represent the relationship between the values of the 8 in two different numbers in the table.

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

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Alike but Not the Same

Unit 4 ● Lesson 10 ● Activity 1

Let’s share some multiplication and division equations.

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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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More and More Money

Unit 4 ● Lesson 10 ● Activity 2

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Diego’s class is counting collections of play money during a math class. There are four types of bills: tens, hundreds, thousands, and ten-thousands.

Diego found 9 of each type of bill. He organized each type into a stack, creating four stacks.

  1. How much money is in each stack of bills?
    1. 9 tens
    2. 9 hundreds
    3. 9 thousands
    4. 9 ten-thousands
  2. Describe the relationship between the values of each stack of bills.
  3. How is the value of the stack of thousands related to the value of the stack of ten-thousands? Write an equation for that relationship.

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

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More and More Money

Unit 4 ● Lesson 10 ● Activity 2

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  • Clare had 21 bills of each type. How much money is in each stack of bills Clare has?
    • 21 tens
    • 21 hundreds
    • 21 thousands
    • 21 ten-thousands
  • What is the value of the 2 in each stack of bills?
  • How is the value of the 2 in the stack of thousands related to the value of 2 in the stack of ten-thousands? Write an equation for that relationship.

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

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Ten Times As Much

Unit 4 ● Lesson 10

Today we wrote multiplication and division equations to represent the relationship between the digits in different places in multi-digit numbers.

  1. 2,000 ✕ 10 = 200
  2. 2,000 ✕ 10 = 20,000
  3. 20,000 ÷ 10 = 2,000
  4. 20,000 ✕ 10 = 200,000
  5. 200,000 ÷ 10 = 200

Which of these equations represent the relationship between the digit 2 in the stacks of hundreds, thousands, and ten-thousands?

Can you write a new equation that correctly describes the relationship between the digit 2 in two of the stacks?

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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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Same Digit, Different Place

Unit 4 ● Lesson 10

Here are two numbers: 872,000 and 700,208

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  1. ​
    1. What is the value of the 2 in each number?
    2. Write a multiplication or division equation to show the relationship between these two values.
  2. ​
    • What is the value of the 7 in each number?
    • Write a multiplication or division equation to show the relationship between these two values.

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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.