# Lesson 6

Represent Numbers in Different Ways

## Warm-up: Which One Doesn’t Belong: Numbers in Different Ways (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare four different representations of three-digit numbers. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about place value and different representations of numbers.

### 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.”
• 23 minutes: partner discussion
• Share and record responses.

### Student Facing

Which one doesn’t belong?

### 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 three-digit 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 base-ten diagram.
• This number has _____ hundreds, _____ tens, and _____ ones.
• The expanded form of this number is _____________________.
• The three-digit 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 three-digit number is ________________.”
• “These other forms can help us think about writing a number using number names.”
• “What is this number?” (two hundred fifty-three)
• Write the number name as the students say two hundred fifty-three.
• “Fifty-three has a hyphen because numbers with tens and ones representing 21 through 99 use a hyphen to show the 2 parts of a two-digit 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:
• base-ten diagrams
• unit form
• expanded form
• three-digit number
• number name

### Student Facing

1. Fill in the blanks to represent 248 with words.

two ___________________ forty-________________

2. Fill in the blanks to represent 562 with words.

______________ hundred _____________- _______

3. Represent this number with words.

4. Represent 627 with words.

5. Represent $$900 + 50 + 1$$ with words.

6. Represent three hundred eighteen in two different ways.

### 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 three-digit number (words, expanded form, diagrams, numerals) they deepen their understanding of the structure of the base-ten system (MP7).

MLR7 Compare and Connect. Synthesis: After the Gallery Walk, lead a discussion comparing, contrasting, and connecting the different representations of numbers. To amplify student language and illustrate connections, follow along and point to the relevant parts of the displays as students speak.
Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, comment on the group’s communication and how all members are actively engaged in creating the poster.
Supports accessibility for: Attention, Social-Emotional Functioning

### Required Preparation

• Create an anchor chart for the launch showing:
• 253 represented with a base-ten diagram
• This number has _____ hundreds, _____ tens, and _____ ones.
• The expanded form of this number is ______________________.
• The three-digit number is ________________.

### Launch

• Groups of 34
• 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 three-digit number, with a base-ten diagram, using expanded form, and using words.”
• Give each group a three-digit number to represent.
• If time permits, groups can represent the number in the additional ways suggested.
• 12 minutes: small-group work time

### Student Facing

Represent the number on your poster. Be sure to represent the number using:

• a three-digit number
• a base-ten 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

If students have representations that do not match the value of other representations on their poster, consider asking:
• “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 base-ten numeral first and compared it to the expanded form. Then I checked the others.)

“What questions do you have about three-digit numbers or any of the representations you saw today?”

## 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 base-ten 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 three-digit numbers, as a sum of the value of each of the digits, and using words.

$$300 + 50 + 7$$