Lesson 6
Represent Numbers in Different Ways
Warmup: Which One Doesn’t Belong: Numbers in Different Ways (10 minutes)
Narrative
Launch
 Groups of 2
 Display the image.
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
Activity
 “Discuss your thinking with a partner.”
 2–3 minutes: partner discussion
 Share and record responses.
Student Facing
Which one doesn’t belong?
Student Response
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Activity Synthesis
 “Which representations best help you understand the value of the number? Explain.” (A has a lot of words to read, so I prefer C. D tells you how many of each. With B you just have to count the blocks.)
 “A shows us 325 represented using only words. You will have a chance to do this in the next activity.”
Activity 1: Numbers as Words (15 minutes)
Narrative
The purpose of this activity is for students to use words to represent threedigit numbers. Students are given numbers represented in different ways and asked to represent the same number in another way, including using words. Spelling numbers might present a challenge for some students. As students learn to spell and write numbers, encourage them to say the name aloud and then write it down. Also encourage them to use what they know about place value to say and write the name. Consider using an anchor chart or poster with words, including the words for numbers 0 to 20 and the multiples of ten, to provide support in this activity and later lessons.
Required Materials
Materials to Gather
Required Preparation
 Prepare an anchor chart for the launch showing:
 253 represented with a baseten diagram.
 This number has _____ hundreds, _____ tens, and _____ ones.
 The expanded form of this number is _____________________.
 The threedigit number is _____________________.
Launch
 Groups of 2
 Display the anchor chart that shows the different forms of 253.
 Complete the chart together.
 “This number has _____ hundreds, _____ tens, and _____ ones.” (2, 5, 3)
 “The expanded form of this number is ______________________.”
 “The threedigit number is ________________.”
 “These other forms can help us think about writing a number using number names.”
 “What is this number?” (two hundred fiftythree)
 Write the number name as the students say two hundred fiftythree.
 “Fiftythree has a hyphen because numbers with tens and ones representing 21 through 99 use a hyphen to show the 2 parts of a twodigit number.”
Activity
 “For each question, work with your partner to figure out the names of each number. Think about when you will need to use a hyphen.”
 8 minutes: partner work time
 Monitor for the different ways students represent 318. Look for examples of:
 baseten diagrams
 unit form
 expanded form
 threedigit number
 number name
Student Facing

Fill in the blanks to represent 248 with words.
two ___________________ forty________________

Fill in the blanks to represent 562 with words.
______________ hundred _____________ _______

Represent this number with words.

Represent 627 with words.

Represent \(900 + 50 + 1\) with words.

Represent three hundred eighteen in two different ways.
Student Response
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Activity Synthesis
 Invite previously selected students to share their representations of 318.
 As needed, ask students how 318 could be represented in forms that you did not see them use during the activity.
 “Which representation makes the most sense to you?”
 “How can you use that representation to help you understand the others?”
Activity 2: Represent the Numbers (20 minutes)
Narrative
The purpose of this activity is for students to represent numbers in all the ways they have seen so far in this unit. Students are given a number in one form and they represent the same number in different ways. In the synthesis, students share which representations are most helpful. When students relate the different ways to represent a threedigit number (words, expanded form, diagrams, numerals) they deepen their understanding of the structure of the baseten system (MP7).
Advances: Representing, Conversing
Supports accessibility for: Attention, SocialEmotional Functioning
Required Materials
Materials to Gather
Required Preparation
 Create an anchor chart for the launch showing:
 253 represented with a baseten diagram
 This number has _____ hundreds, _____ tens, and _____ ones.
 The expanded form of this number is ______________________.
 The threedigit number is ________________.
Launch
 Groups of 3–4
 Give each group tools for making a display.
Activity
 “Each group will be given a number. Work with your group to represent that number in different ways.”
 Display the chart from the first activity.
 “Think about how you might organize your representations and make sure that each group member does their fair share.”
 “Your group should represent the number as a threedigit number, with a baseten diagram, using expanded form, and using words.”
 Give each group a threedigit number to represent.
 If time permits, groups can represent the number in the additional ways suggested.
 12 minutes: smallgroup work time
Student Facing
Represent the number on your poster. Be sure to represent the number using:
 a threedigit number
 a baseten diagram
 expanded form
 words
If you have time: Represent the number using only tens and ones. Represent the number composed in a different way.
Student Response
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Advancing Student Thinking
 “How do your representations show _____ (number given to group)?”
 “What is the same and different about all the different representations?”
Activity Synthesis
 Display the chart paper from each group.
 “Now you will walk around and see other numbers and how they were represented in different ways.”
 “Think about which representations most clearly show you the value of the number.”
 “Then, check that all of the representations show the same number.”
 5 minutes: gallery walk
Lesson Synthesis
Lesson Synthesis
“Today you had the chance to represent numbers in different ways and make connections across representations.”
“While you walked around, what representation did you look for first to help you identify the number? Why?” (I looked at the baseten numeral first and compared it to the expanded form. Then I checked the others.)
“What questions do you have about threedigit numbers or any of the representations you saw today?”
Cooldown: Words and Other Ways (5 minutes)
CoolDown
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Student Section Summary
Student Facing
In this section of the unit, we learned different ways to represent numbers that are greater than 99. We represented hundreds with baseten blocks and diagrams. We represented numbers by describing the number of hundreds, tens, and ones that make up the number. We learned to read and write numbers as threedigit numbers, as a sum of the value of each of the digits, and using words.
3 hundreds 5 tens 7 ones
357
\(300 + 50 + 7\)
three hundred fiftyseven