# Lesson 2

Features of a Number Line

## Warm-up: Choral Count: Count by 5 (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting by 5 and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson and future lessons when students show their thinking on the number line. When students notice patterns and explain why they think they occur based on their understanding of operations and the structure of ten, they look for and express regularity in repeated reasoning (MP7, MP8).

### Launch

• “Count by 5, starting at 0.”
• Record as students count.
• Stop counting and recording at 100.

### Activity

• “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Activity Synthesis

• “Who can restate the pattern in different words?”
• “Does anyone want to add an observation about why that pattern is happening here?” ($$5 + 5 = 10$$, so when you count by 5 two times you make a new ten.)

## Activity 1: Class Number Line (20 minutes)

### Narrative

The purpose of this activity is for students to reason together about the relative position of numbers on the number line. Students place number cards on the number line, which is represented by yarn strung across the classroom. Students reason about where their number should be placed based on their understanding of the count sequence and by reasoning about the relative distance of numbers from 0 and each other. As more numbers are called, students revise their number locations to be more precise (MP6, MP7). Throughout the activity, encourage students to reflect on the length between numbers and whether it is an accurate representation of the number relationships.

It is recommended that students are called in a random order. This will provide students opportunities to revise their thinking about the position of their number when more information is added to the number line representation.

Action and Expression: Develop Expression and Communication. Some students may benefit from access to a blank number line with equally spaced tick marks on it. Students can then label the tick marks as the numbers are put on the number line to see the appropriate spacing and where the missing numbers lie.
Supports accessibility for: Organization, Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• Class Number Line Cards (0–30)

### Required Preparation

• Hang yarn across the classroom (yarn should be hung taut to resemble a line) for students to hang their number cards on.
• Create a set of number cards from the blackline master.
• Fold the number cards so they can be hung on the line.

### Launch

• Give each student a number card.
• It is not necessary to hand out all of the cards.

### Activity

• “Today, you are going to create a class number line to represent the numbers from 0 to 30.”
• “When I call you, place your number card on the number line.”
• Place the 0 card to demonstrate how to place a number on the string and to show where the number line begins.
• Invite students to hang their cards in a random order.
• When students place their numbers, ask:
• “How did you decide where to place your number on the number line?”
• “What revisions do we need to make to the number line? Why?”
• Pause to check in and revise thinking as needed. If students need prompting for justifying their reasoning for number placement based on length, consider asking:
• “How close should your number be to ___?”
• “Should your number be closer to ___ than ___?”

### Activity Synthesis

• “Number lines represent the length of numbers from 0 and help us see how close numbers are to each other.”
• “How did you adjust the location of your number as more numbers were added?” (Sometimes we had to make more room or move cards because the new number needed to fit in between numbers. The more numbers that were already on the number line, the easier it was to be precise.)
• “Looking at our number line, what final revisions could be made to make our number line more precise?”

## Activity 2: Analyze Number Lines (15 minutes)

### Narrative

The purpose of this activity is for students to analyze number lines to determine whether they represent numbers within 10 as lengths from 0. Students analyze number line diagrams that do not have equal unit intervals or have tick marks that are not properly labeled. Students discuss what needs to be added or changed in order to make these number line diagrams accurate (MP3, MP6).

This activity uses MLR8 Discussion Supports. Advances: speaking, conversing

• Groups of 3

### Activity

• “Jada, Andre, and Elena were asked to create a number line diagram to represent the numbers from 0 to 10.”
• “Look at each student’s number line on your own. Think of 1 thing you think the student did well when they represented 0–10 and 1 thing you think they should revise. Be prepared to share with your group.”
• 90 seconds: independent work time
• “Discuss each number line with your group.”
MLR8 Discussion Supports
• Display sentence frames to support small-group discussion:
• “One thing _____ did well was . . .”
• “One thing _____ should revise is . . .”
• 5 minutes: small-group discussion
• “All of the students need to revise their number lines. For each number line, write what they should do to fix it.”
• 5 minutes: independent work time
• Monitor for students who explain why each diagram needs revising by describing the labels and the space between each number.

### Student Facing

Andre’s number line

Elena’s number line

1. How should Jada revise her number line?
2. How should Andre revise his number line?
3. Elena’s number line

How should Elena revise her number line?

4. Fill in the numbers to create your own number line.

### Student Response

If students say that a number line does not need revisions, provide students with a ruler. Consider asking:

• “What is the same and what is different between ____’s number line and the ruler?”
• “How could you use the way the tick marks are spaced and labeled on a ruler to describe how ____ could revise their number line?”

### Activity Synthesis

• Display Jada’s number line diagram.
• Select previously identified students to share how Jada should revise her number line.
MLR8 Discussion Supports
• Support student use of “length” to describe revisions. For example, revoice the student statement “the numbers are wrong” as “the numbers do not show the correct lengths from 0.”
• “What are some things Jada did well when representing the numbers 0–10 on a number line?” (All of the numbers were listed and are in order. She started with 0 and used tick marks. The tick marks are equally spaced.)
• If time permits, repeat for each diagram.

## Lesson Synthesis

### Lesson Synthesis

“Today we created our own class number line and analyzed number lines. What do we need to think about when creating a number line to represent numbers?” (We should use the same amount of space between each tick mark. We should make sure labels on tick marks show the right length from 0 and are the right length from each other. We can think about a ruler to check if the number line makes sense.)