# Lesson 2

Create Your Own Number Line

## Warm-up: Which One Doesn’t Belong: Fractions on Number Lines (10 minutes)

### Narrative

This warm-up prompts students to compare four images. It gives students a reason to use language precisely. 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 tick marks, labels, unit fractions, whole numbers, and length.

### 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 your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

Which one doesn’t belong?

### Activity Synthesis

• “Let’s find at least one reason why each one doesn’t belong.”

## Activity 1: Create Your Own Number Line (25 minutes)

### Narrative

The purpose of this activity is for students to use their fraction reasoning skills to practice locating fractions on a number line. Students should be in groups, but the groups should stay small enough that every member will have a chance to share their ideas. Be sure to space groups so that each has their own area to work in. Students write the fractions on their tape. Students will use the number line they create in the next activity.

As they place the different numbers students think about the meaning of the numerator and denominator in the fractions and how whole numbers can be written as fractions (MP7).

MLR8 Discussion Supports. Synthesis: At the appropriate time, give groups 2–3 minutes to plan what they will say when they present to the class. “Practice what you will say when you share your number line with the class. Talk about what is important to say, and decide who will share each part.”
Advances: Speaking, Conversing, Representing
Action and Expression: Develop Expression and Communication. Synthesis: Identify connections between strategies that result in the same outcomes but use differing approaches.
Supports accessibility for: Memory

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 3-4 students needs a roll of tape and a marker.

### Launch

• Groups of 3–4
• “Today you are going to work with your group to create a number line and place fractions on it. Be prepared to share your methods with the class.”
• Give each group a roll of tape and a marker.

### Activity

• 10–15 minutes: small-group work time
• Monitor for methods that groups use to locate the points, such as:
• starting with benchmark numbers, such as unit fractions or whole numbers
• considering whether fractions are larger or smaller than 1
• considering whether fractions are equivalent to whole numbers
• comparing fractions with the same numerator or denominator

### Student Facing

Create a long number line on the floor.

Locate and label each fraction on the number line. Be prepared to explain your reasoning.

• 0
• 1
• 2
• $$\frac{1}{2}$$
• $$\frac{1}{3}$$
• $$\frac{6}{2}$$
• $$\frac{12}{3}$$
• $$\frac{1}{4}$$
• $$\frac{5}{4}$$
• $$\frac{6}{6}$$
• $$\frac{5}{6}$$
• $$\frac{9}{8}$$
• $$\frac{15}{8}$$
• $$\frac{5}{3}$$
• $$\frac{18}{6}$$
• $$\frac{2}{8}$$

### Activity Synthesis

• Have each group share a method they used or a fraction they placed, based on what you noticed during the activity. Encourage groups to use their number lines when demonstrating their reasoning.
• “Did any groups use a similar strategy?”
• “Did any groups place that fraction in a different way?”
• “Which fractions were easier to locate?”
• “Which fractions were harder to locate?”
• Keep number lines displayed for the next activity.

## Activity 2: Make a Statement (10 minutes)

### Narrative

The purpose of this activity is for students to use the number line they created in the previous activity to make comparison statements about fractions. Students use the symbols $$>$$, $$=$$, and $$<$$ to record comparisons between pairs of fractions.

### Launch

• Groups of 3–4
• “Now you are going to work with your group to write comparison statements based on your number line.”

### Activity

• 8–10 minutes: small-group work time
• Monitor for a variety of student-generated statements of each type to share during the synthesis.

### Student Facing

Write 6 fraction comparison statements about the numbers on your number line. Include 2 statements for each symbol ($$>$$, $$=$$, and $$<$$).

1.
2.
3.
4.
5.
6.

Choose 2 statements you wrote. Use numbers, pictures, or words to show that they are true.

### Activity Synthesis

• Have each group share at least one comparison statement they came up with and their reasoning. Be sure to share at least one statement that uses each symbol.

## Lesson Synthesis

### Lesson Synthesis

“How did you decide how long your number line should be? Does it matter?” (We looked at the largest number we had and made sure it would fit on the number line. Yes, because you had to make sure all the numbers would fit on the number line.)

“The number line of one group is noticeably longer than that of another group. Does that affect the comparison statements that each group could make?” (It wouldn’t affect the comparison statements for one group working on their own number line, but if two groups tried to compare fractions with number lines with different lengths, their statements could be wrong.)