Unit 5

Expanded Form of Numbers

Lesson 5

Numbers to 1,000

Expressions and Equations

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Let’s represent three-digit numbers as a sum of the value of each digit.

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Unit 5 ● Lesson 5

Learning

Goal

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Value of Digits

Unit 5 ● Lesson 5 ● Warm-up

Decide if each statement is true or false. Be prepared to explain your reasoning.

• 800 + 90 + 7 = 897
• 156 = 50 + 100 + 6
• 407 = 70 + 400
• 632 = 22 + 10 + 600

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True or False

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

Expressions and Three-digit Numbers

Unit 5 ● Lesson 5 ● Activity 1

1. Andre has 3 hundreds. Tyler has 5 tens. Mai has 7 ones. They want to represent the amount they have using an expression.

What would the expression look like?

• We can represent the value of the blocks by writing a three-digit number.
• A number can also be represented as a sum of the value of each of its digits. This is called expanded form.
• Like a three-digit number, expanded form shows the sum starting with the place that has the greatest value on the left to the place with the least value on the right.

357

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300 + 50 + 7

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Launch

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

Expressions and Three-digit Numbers

Unit 5 ● Lesson 5 ● Activity 1

Write each number as the sum of hundreds, tens, and ones, and as a three-digit number.

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2. Expanded form: _________________________

Three-digit number: _________________________

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• Expanded form: _________________________

Three-digit number: _________________________

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

Expressions and Three-digit Numbers

Unit 5 ● Lesson 5 ● Activity 1

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• Expanded form: _________________________

Three-digit number: _________________________

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• Expanded form: _________________________

Three-digit number: _________________________

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

Expressions and Three-digit Numbers

Unit 5 ● Lesson 5 ● Activity 1

• What is the value of 40 + 100 + 3? Explain how you know.
• We know we can rearrange the addends to add in any order when we find the value of a sum. When a number is written in expanded form the values are written in place value order.
• How would we write 143 in expanded form?

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Activity Synthesis

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

Make It and Expand It

Unit 5 ● Lesson 5 ● Activity 2

• You and your partner will be making three-digit numbers.
• Roll the number cubes. Use the digits you roll to make three-digit number that matches the directions for each problem.
• Let’s try 1 together.
• I rolled a _____, _____, and a _____.
• What is the smallest three-digit number I could make with these digits?
• After you and your partner agree on how to arrange your digits, write the number as a three-digit number and in expanded form.

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Launch

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

Make It and Expand It

Unit 5 ● Lesson 5 ● Activity 2

1. Roll the number cubes.

Make the largest number possible.

Write it as a three-digit number. ___________

Write it in expanded form.

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• Roll the number cubes.

Make the smallest number possible.

Write it as a three-digit number. ___________

Write it in expanded form.

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

Make It and Expand It

Unit 5 ● Lesson 5 ● Activity 2

• Roll the number cubes.

Using the same digits, make a number different from your partner’s.

Write it as a three-digit number. ___________

Write it in expanded form.

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

Make It and Expand It

Unit 5 ● Lesson 5 ● Activity 2

• Let’s share some of the largest three-digit numbers we made.
• How did you know if you were making the largest number possible?

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Activity Synthesis

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

Expanded Form of Numbers

Unit 5 ● Lesson 5

• Today you represented numbers in expanded form and as three-digit numbers.

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426

400 + 20 + 6

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• Explain how you know these represent the same value.

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Lesson Synthesis

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

Three-digit Numbers in Expanded Form

Unit 5 ● Lesson 5

1. Represent the number 375 as the sum of hundreds, tens, and ones.

Expanded form: ________________________________

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• Represent 200 + 40 + 7 as a three-digit number.

Three-digit number: ____________

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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.