# Lesson 4

Compare Numbers on a Number Line

## Warm-up: Number Talk: Subtract Fives (10 minutes)

### Narrative

The purpose of this Number Talk is for students to subtract with multiples of 5. As students share strategies based on place value or related to adding on or subtracting multiples of 5, record their thinking using a number line diagram. Students connect their mental strategies to the representation of moving a length of 5, 10, or 20 from one number to another on the number line. The understandings elicited here will be helpful in later lessons when students represent sums and differences on number lines.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Record answers and strategy. Use a number line diagram when possible.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$35 - 5$$

• $$35 - 10$$

• $$35 - 15$$

• $$35 - 25$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How did the first 2 expressions help you think about the last 2?” (I know that $$5 - 5 =0$$ because all of the ones are being taken away. Then I just take the tens from the tens.)

## Activity 1: Compare the Numbers (20 minutes)

### Narrative

The purpose of this activity is for students to compare two numbers and justify their comparison based on the location of each number on the number line. Using the number lines students created in a previous lesson, students represent numbers by placing counters as points on the number line. Students recognize that given any two numbers, the number farther to the right represents a greater value than the number to the left (MP7).

Engagement: Provide Access by Recruiting Interest. Give students a context to relate the number line to. For example, a frog jumping on lily pads, or a rabbit hopping. The counters can represent the animal hopping along the number line.
Supports accessibility for: Conceptual Processing, Attention

### Required Materials

Materials to Gather

### Required Preparation

• Each student will need their number line they made in Lesson 1.
• Each group of 2 needs 3 number cubes and 2 counters.

### Launch

• Groups of 2
• Give each group 3 number cubes and 2 counters.
• Assign Partner A and B.

### Activity

• “You will use the number line you created and work with a partner. Decide with your partner whose number line you will use.”
• As needed, demonstrate the task with a student.
• “I am Partner A. I am going to roll the 3 number cubes and find the sum.”
• “Then, I take a counter and place it on the number line to represent the sum.”
• “Now it’s my partner's turn. They do the same thing and put their counter on the same number line to represent the sum of their numbers.”
• “Then, we decide which number is greater and explain how we know.”
• “Last, we use the $$<$$ , $$>$$, or $$=$$ symbols to record our comparison.”
MLR8 Discussion Supports
• If needed, remind students to use comparison vocabulary (less than, greater than, equal to) to read the symbols and their comparisons.
• If needed, invite students to chorally repeat the phrases that each symbol represents.
• 10 minutes: partner work time
• Monitor for students who explain comparisons:
• based on lengths from 0
• using the language “to the left” and “to the right”

### Student Facing

• Partner A:
• Roll 3 number cubes and find the sum.
• Put a counter on the location of the sum.
• Partner B:
• Roll 3 number cubes and find the sum.
• Put a counter on the location of the sum on the same number line.
• Decide which number is greater and explain.
• Use $$<$$, $$>$$, or $$=$$ to compare the 2 numbers represented on your number line.
Partner A $$<$$, $$>$$, or $$=$$ Partner B

### Student Response

For access, consult one of our IM Certified Partners.

If students write comparison statements that are not true, consider asking:
• “How can you use the number line to show that ___ is greater than or less than ___?”

### Activity Synthesis

• Invite 2–3 previously identified groups to share comparisons and their explanations.
• “What do you notice about the numbers that are farther to the right?” (They were greater. They represent a greater length from zero.)

## Activity 2: Compare Larger Numbers (15 minutes)

### Narrative

The purpose of this activity is for students to use a number line to compare larger numbers. In the first activity, students compared numbers on a number line with all of the tick marks labeled. In this activity, only the multiples of 5 are labeled. Students locate and label numbers on the number line and compare them. Listen for the language students use to explain how they know a number is greater than or less than another number, including those based on the lengths the numbers represent from 0 (MP6).

### Required Materials

Materials to Gather

Materials to Copy

• Number Line to 100

### Required Preparation

• Each group of 2 needs 2 number cubes and a dry erase marker.
• Put number line recording sheets into sheet protectors. The recording sheets will be used in upcoming lessons.

### Launch

• Groups of 2
• Give each group a number line, 2 number cubes, and a dry erase marker.

### Activity

• “You are going to do some more work comparing numbers on a number line with a new partner.”
• “This time you will use a number line that goes from 0100.”
• “Each of you will roll 2 number cubes and create a two-digit number.”
• “Locate and label both numbers on the number line.”
• “Then compare the numbers using $$<$$, $$>$$, or $$=$$. Explain how you know your comparison is true.”
• 10 minutes: partner work time
• Monitor for student comparisons where both numbers are close on the number line (within 10) and where numbers are farther apart (greater than 30).

### Student Facing

• Each partner rolls 2 number cubes and makes a two-digit number.
• Locate and label your numbers on the number line.
• Use >, <, or = to compare the numbers.
• Explain why your comparison is true.
Partner A $$<, >, \text{or} =$$ Partner B

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Invite a previously identified group to share a comparison where the numbers are close.
• Display the number line from the activity to record student comparison or have students display their work so all students can see.
• “Is _____’s comparison true? Explain.” (Yes, it is true because _____ [larger number] is farther to right. It represents a longer length from 0 than the smaller number.)
• Repeat with a previously identified group with a comparison where numbers are farther apart.
• “Which comparison has a bigger difference between the two numbers? Explain.” (_____ has a bigger difference. You can tell because the length between them is much larger than the length between the other two numbers.)

## Lesson Synthesis

### Lesson Synthesis

“Today, we used number lines to compare numbers and thought about how close or far away they are from zero and each other. We used what we know about comparing lengths to compare the numbers. We also used position words like to the left or right to talk about which number was less or more.”

Display or draw: