# Lesson 5

Expanded Form of Numbers

## Warm-up: True or False: Value of Digits (10 minutes)

### Narrative

The purpose of this True or False is to elicit insights students have about the value of the digits in a three-digit number. The reasoning students express in the task helps students deepen their understanding that numbers can be represented in different ways. This will be helpful later when students represent numbers in multiple ways in the lesson activities.

In this activity, when students describe how they use the value of each digit to determine if the equation is true, they look for and make use of the base-ten structure when they look for the value of each digit in a 3-digit number (MP7).

### Launch

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

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

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

### Activity Synthesis

• “What is different about the last equation?” (It’s not decomposed into hundreds, tens, and ones. 22 shows some tens and some ones and 10 shows another ten.)

## Activity 1: Expressions and Three-digit Numbers (20 minutes)

### Narrative

The purpose of this activity is for students to write three-digit numbers as the sum of the value of each digit, expanded form. Students connect the order and values of the addends in expanded form to the order and value of each place in a three-digit number. Use expanded form and its definition interchangeably throughout the activity so that students feel comfortable with the new vocabulary. When students represent numbers as sums by place value, they interpret the three-digit numbers in terms of its digits and the operation of addition (MP7).

MLR8 Discussion Supports. Provide all students with an opportunity to produce mathematical language by inviting students to chorally repeat “expanded form” in unison 1–2 times.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Display Andre, Tyler, and Mai’s situation and the image of their blocks.
• “What would the expression look like?”
• 1 minute: independent work time
• 1 minutes: partner discussion
• Share responses.
• Display 357 and $$300 + 50 + 7$$.
• “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.”
• As needed, discuss reasons why any expressions generated in the launch would or would not be examples of expanded form.

### Activity

• “Now you will practice writing the value of the base-ten diagrams in expanded form and as a three-digit number.”
• 7 minutes: partner work time

### Student Facing

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

Write an expression to represent the sum of their values.

__________ + __________ + __________

Write the total value as a three-digit number:

_______________

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

2. Expanded form: _________________________

Three-digit number: _________________________

3. Expanded form: _________________________

Three-digit number: _________________________

4. Expanded form: _________________________

Three-digit number: _________________________

5. Expanded form: _________________________

Three-digit number: _________________________

### Activity Synthesis

• “What is the value of $$40 + 100 + 3$$? Explain how you know.” (143. I saw there was 1 hundred, 4 tens, and 3 ones. I just rearranged it in my head like expanded form.)
• “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?” ($$100 + 40 + 3$$)

## Activity 2: Make It and Expand It (15 minutes)

### Narrative

In this activity, students represent numbers using base-ten numerals and expanded form. Students work with a partner to arrange number cubes to create the largest or smallest three-digit number. This gives students the opportunity to reason together about place value. Students recognize that placing the number cubes in order from least to greatest creates the smallest number and ordering them from greatest to least will yield the largest possible number. This reasoning will be helpful in later lessons when students compare and order three-digit numbers.

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to explain why they chose to place the digits in the order they have. Draw attention to the greatest-to-least pattern.
Supports accessibility for: Memory, Organization

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 3 number cubes.

### Launch

• Groups of 2
• Give each group 3 number cubes.
• “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.”
• Roll three number cubes.
• “I rolled a _____, a _____, and a _____.”
• “What is the smallest three-digit number I could make with these digits?”
• 30 seconds: quiet think time
• Share responses
• “After you and your partner agree on how to arrange your digits, write the number as a three-digit number and in expanded form.”
• Write the number as a three-digit number and in expanded form on the board.

### Activity

• 7 minutes: partner work time
• As students work, consider asking:
• “Do you notice a pattern in the digits when you made the smallest or largest number?”
• Monitor for students who recognize that in order to make the largest number possible they need to order the number cubes from greatest to least.

### Student Facing

1. Roll the number cubes.

Make the largest number possible.

Write it as a three-digit number. ___________

Write it in expanded form.

2. Roll the number cubes.

Make the smallest number possible.

Write it as a three-digit number. ___________

Write it in expanded form.

3. Roll the number cubes.

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

Write it in expanded form.

Write it as a three-digit number. ___________

### Activity Synthesis

• Invite 2–3 previously selected students to share the largest numbers they made.
• “How did you know if you were making the largest number possible?” (The largest digit rolled needed to be the hundreds. The next largest digit needed to be in the tens.)
• As time permits, repeat with the smallest number.

## Lesson Synthesis

### Lesson Synthesis

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

Display 426 and $$400 + 20 + 6$$.

“Explain how you know these represent the same value.” (The digits in 426 represent 4 hundreds, 2 tens, and 6 ones. That is the same as $$400 + 20 + 6$$)