# Lesson 9

Compare Numbers on the Number Line

## Warm-up: Estimation Exploration: Hundreds (10 minutes)

### Narrative

The purpose of this Estimation Exploration is for students to practice the skill of making a reasonable estimate for a point on a number line based on the location of other numbers represented. Students give a range of reasonable answers when given incomplete information. They have the opportunity to revise their thinking as additional information is provided. Revealing the actual answer is not necessary because leaving it open ended provides an opportunity to focus on reasonableness and not just one right answer.

### Launch

• Group of 2
• Display the image.
• “What number could be represented by the point on the number line?”
• “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Record responses.
• “We had a lot of different guesses, because we don’t have a lot of information.”
• Add 3 tick marks to the number line, so that it looks like this:
• “Based on this new information, do you want to revise or change your estimates?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.
• “How did your estimation change?”
• 30 seconds: quiet think time
• Share responses.

### Student Facing

What number could this be?

1. Record an estimate that is:
too low about right too high
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2. Record an estimate that is:
too low about right too high
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

## Activity 1: Compare Comparisons (20 minutes)

### Narrative

The purpose of this activity is for students to make sense of different methods they can use to compare three-digit numbers. They analyze the thinking of others and make connections across representations (MP2, MP3). Although students have compared numbers using different representations in prior units, this activity offers them the opportunity to consider using the number line as a tool to compare three-digit numbers. In the synthesis, students will discuss which representation makes it easier to see the comparison. While students could make a case that each of the representations was easier for them, the focus is on Jada’s way, the number line.

MLR8 Discussion Supports. Display sentence frames to support partner discussion. “_____ and _____ are the same/alike because . . .” and “_____ and _____ are different because . . . .”

• Groups of 2

### Activity

• “Diego, Jada, and Clare were asked to compare 371 and 317. They each represented their thinking differently.”
• “Take some time to look over their methods.”
• 2 minutes: independent work time
• “Discuss with your partner how their methods are the same and different.”
• 4 minutes: partner discussion
• 6 minutes: partner work time

### Student Facing

Each student compared 371 and 317, but represented their thinking in different ways.

Diego

• I see 3 hundreds for each number.
• 317 only has 1 ten, but 371 has 7 tens.
• $$371 > 317$$

Clare

• Each has 3 hundreds.
• 371 has 7 tens, but 317 only has 1 ten.
• $$317 < 371$$

• I can see that 371 is farther to the right on my number line, so I know it is greater than 317.
• $$371 > 317$$

1. What is the same and different about these students’ representations?

Discuss with a partner.

Estimate the location of 483 and 443 on the number line. Mark each number with a point. Label the point with the number it represents.

3. Use $$>$$, $$=$$, or $$<$$ to compare 483 and 443.

______________________________

### Student Response

If students write comparison statements that are not true, ask them to read their statements and consider asking:
• “How did you decide which number was greater?”
• “How does your statement match the number line?”

### Activity Synthesis

• “Clare, Diego, and Jada represented their thinking in different ways. Whose method made it easier to see that 371 is greater than 317? Explain.” (Jada’s because you just have to look at which number is farther to the right. You can see 371 is farther from 0. Diego’s because I use diagrams and I can see quickly that the hundreds are the same and there are more tens, but some things were the same.)
• As needed, “Jada and Diego wrote $$371 > 317$$, but Clare wrote $$317 < 371$$. Who do you agree with? Explain.” (They both mean the same thing. 371 is greater than 317, so 317 is less than 371.)

## Activity 2: Compare in Different Ways (15 minutes)

### Narrative

The purpose of this activity is for students to compare three-digit numbers based on different representations. Students continue to make connections and deepen their understanding of place value as they compare numbers using base-ten diagrams and number lines. They have the opportunity to reflect and share about the representation that makes the most sense to them and how they can use it to justify their thinking (MP3). This understanding will be helpful in upcoming lessons when students choose their own methods to compare three-digit numbers.

Representation: Develop Language and Symbols. Support understanding of the problem by inviting students to act it out. For example, recreate a number line using index cards and string. Have students hold a given number and find their appropriate spot on the number line.
Supports accessibility for: Memory, Conceptual Processing

• Groups of 2

### Activity

• “In the last activity, we saw that Jada found it helpful to use the number line to explain that 371 is greater than 317.”
• “In this activity, you will compare three-digit numbers and explain your thinking using the number line.”
• 6 minutes: independent work time
• 4 minutes: partner discussion

### Student Facing

1. Locate and label 420 and 590 on the number line.

Use $$<$$, $$>$$, and $$=$$ to compare 420 and 590.

______________________________

2. Estimate the location of 378 and 387 on the number line. Mark each number with a point. Label the point with the number it represents.

Use $$<$$, $$>$$, and $$=$$ to compare 378 and 387.

______________________________

3. Diego and Jada compared 2 numbers. Use their work to figure out what numbers they compared. Then use $$<$$, $$>$$, and $$=$$ to compare the numbers.

______________________________

4. Which representation was most helpful to compare the numbers? Why?

### Activity Synthesis

• Display the images for 432 and 423.
• “What is the same or different about seeing these numbers on the number line compared to looking at a base-ten diagram?” (The one farthest to the right is greater. With the diagram you have to count to see which one has more. The number with more hundreds or tens is farther to the right on the number line.)

## Lesson Synthesis

### Lesson Synthesis

“Today we used a number line to compare three-digit numbers.”

Display 543 and 345.

“If I wanted to compare 543 and 345, how would the number line help me see which is less and which is greater? Explain.” (On a number line, 345 would be closer to zero and 543 is located farther to the right of 345. It would be easy to see that 345 is less than 543.)