Lesson 5
Expanded Form of Numbers
Warmup: 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 threedigit 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 baseten structure when they look for the value of each digit in a 3digit 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.
 \(800 + 90 + 7 = 897\)
 \(156 = 50 + 100 + 6\)
 \(407 = 70 + 400\)
 \(632 = 22 + 10 + 600\)
Student Response
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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 Threedigit Numbers (20 minutes)
Narrative
The purpose of this activity is for students to write threedigit 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 threedigit 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 threedigit numbers in terms of its digits and the operation of addition (MP7).
Advances: Speaking
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 threedigit 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 threedigit 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 baseten diagrams in expanded form and as a threedigit number.”
 7 minutes: partner work time
Student Facing

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 threedigit number:
_______________
Write each number as the sum of hundreds, tens, and ones, and as a threedigit number.

Expanded form: _________________________
Threedigit number: _________________________

Expanded form: _________________________
Threedigit number: _________________________

Expanded form: _________________________
Threedigit number: _________________________

Expanded form: _________________________
Threedigit number: _________________________
Student Response
For access, consult one of our IM Certified Partners.
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 baseten numerals and expanded form. Students work with a partner to arrange number cubes to create the largest or smallest threedigit 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 threedigit numbers.
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 threedigit numbers.”
 “Roll the number cubes. Use the digits you roll to make threedigit 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 threedigit 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 threedigit number and in expanded form.”
 Write the number as a threedigit 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

Roll the number cubes.
Make the largest number possible.
Write it as a threedigit number. ___________
Write it in expanded form.

Roll the number cubes.
Make the smallest number possible.
Write it as a threedigit number. ___________
Write it in expanded form.

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 threedigit number. ___________
Student Response
For access, consult one of our IM Certified Partners.
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 threedigit 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 \(400 + 20 + 6\))
Cooldown: Threedigit Numbers in Expanded Form (5 minutes)
CoolDown
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