# Lesson 1

Represent Numbers in Different Ways

## Warm-up: Which One Doesn’t Belong: Numbers within 1,000 (10 minutes)

### Narrative

This warm-up prompts students to compare numbers represented in different ways. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as place value, hundreds, tens, ones, sum, or base-ten diagram.

### Launch

- Groups of 2
- Display the image and expressions.
- “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 your partner.”
- 2-3 minutes: partner discussion
- Share and record responses.

### Student Facing

A.

B. \(300 + 70 + 1\)

C. \(300 + 60 + 10\)

D. \(400 - 30\)

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

- “What do all of these ways of showing numbers have in common?” (The parts of the number have been separated into hundreds, tens, and ones.)
- “Remember that
**expanded form**is a specific way of writing a number as a sum of hundreds, tens, and ones. It is written as a sum of the value of each digit like in B.” - “How would we write 482 in expanded form?” \((400 + 80 + 2)\)

## Activity 1: Card Sort: Numbers in Their Different Forms (15 minutes)

### Narrative

The purpose of this activity is for students to revisit numbers that are written in different forms. Students match numbers represented in different forms: base-ten numerals, base-ten diagrams, number names, and expanded form. As they make matches, students use their understanding of base-ten structure represented in many different ways (MP7).

*MLR8 Discussion Supports.*Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “I noticed ___ , so I matched . . .” Encourage students to challenge each other when they disagree.

*Advances: Listening, Speaking*

*Engagement: Develop Effort and Persistence.*Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.

*Supports accessibility for: Attention, Visual-Spatial Processing*

### Required Materials

### Required Preparation

- Create a set of cards from the blackline master for each group of 2.

### Launch

- Groups of 2
- Distribute one set of pre-cut cards to each group of students.
- Give students access to base-ten blocks.

### Activity

- “This set of cards includes numbers in different forms. Find the cards that match. Work with your partner to explain your matches.”
- 8 minutes: partner work time

### Student Facing

Your teacher will give you a set of cards that show numbers in different forms.

Match the cards that represent the same number. Record your matches here. Be ready to explain your reasoning.

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students don't match base-ten numerals to the other representations, consider asking:

- “What does each digit in the number represent?”
- “How could we use what each digit represents to match it to another representation?”

### Activity Synthesis

- Invite students to share the matches they made and how they know those cards go together.
- Attend to the language that students use to describe their matches and numbers in different forms, giving them opportunities to describe the numbers in different forms more precisely.
- Highlight the use of terms like hundreds, tens, ones, word form, expanded form, base-ten blocks, and base-ten diagrams.

## Activity 2: Numbers in Different Forms Round Table (20 minutes)

### Narrative

The purpose of this activity is for students to use place value understanding from grade 2 to decompose numbers in different ways. In small groups, students start by writing a three-digit number, and then pass their number to the group member to their right. Each time students receive the number, they decompose it in a different way. In the synthesis, students look for connections in the ways their number was decomposed, and in all the recording sheets in their group. Highlight connections that show that place value can be used to represent a number as different combinations of hundreds, tens, and ones. This will be helpful later in the unit when students add and subtract using strategies and algorithms based on place value.

### Required Materials

### Launch

- Groups of 4
- Display: 365
- “What are some ways you could decompose this number?”
- 30 seconds: quiet think time
- Share and record responses.
- Give each student a copy of the blackline master.
- “Take a minute and think of a three-digit number that you will use for this activity.“
- 30 seconds: quiet think time.
- “Now write your number in the first box on your sheet.”

### Activity

- “Pass your paper to your right and receive the paper from your left. The paper has a number in Box 1. In Box 2, show one way the number you were just passed can be decomposed.”
- 1-2 minutes: independent work time
- “Pass your paper to your right and receive the paper from your left. The paper has a number in Box 1 and one way of decomposing that number in Box 2. In Box 3, show another way the number you were just passed can be decomposed.”
- 1-2 minutes: independent work time
- “Pass your paper to your right and receive the paper from your left. The paper shows two ways of decomposing a number. In Box 4, show another way to decompose that number.”
- 1-2 minutes: independent work time
- “Pass your paper one more time. You should have your original number back.”
- “Talk to your group about which box was the most difficult for you to fill in. Share ideas about what helped you most during this activity.”
- 2-3 minutes: group discussion
- Share responses.

- “Look at what was written to represent your number. Write down any connections you notice between the different ways the number was represented.”
- 3 minutes: independent work time
- “Now, look at the recording sheets of everyone in your group. What patterns do you notice in the ways the numbers are decomposed?”
- 2-3 minutes: group discussion

### Student Facing

Your teacher will give you a recording sheet.

Part 1

- In Box 1, write a three-digit number. (Pause for your teacher's instructions.)
- In Box 2, show a way that the number could be decomposed. (Pause for teacher instructions.)
- In Box 3, show a way that the number could be decomposed that’s different from Box 2. (Pause for teacher instructions.)
- In Box 4, show a way that the number could be decomposed that’s different from Boxes 2 and 3.

Part 2

- Look at the different ways your number was decomposed on your recording sheet. What connections do you see between them?
- Look at all of the recording sheets for your group. What patterns do you notice in the ways the numbers are decomposed?

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students don't generate decompositions based on place value, consider asking:

- “How did you decompose the number?”
- “How could you use base-ten blocks to come up with other ways to decompose the number?”

### Activity Synthesis

- Have groups share the connections they saw across the sheets.

## Lesson Synthesis

### Lesson Synthesis

Display: 253

“Today we decomposed numbers in lots of different ways. What are some ways that we could decompose 253?” (\(200+50+3\), \(200+40+13\), \(100+150+3\))

Display: \(253 + 134\)

“If you were adding 253 and 134, which way of decomposing the numbers do you think would be most helpful and why?” (I think decomposing them by hundreds, tens, and ones would be most helpful so you could add hundreds and hundreds, tens and tens, and ones and ones.)

## Cool-down: Let Me Count the Ways (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.