# Lesson 1

Representations of Fractions (Part 1)

## Warm-up: What Do You Know About $\frac{1}{2}$? (10 minutes)

### Narrative

The purpose of this warm-up is to invite students to share what they know about the number $$\frac{1}{2}$$ and elicit ways in which it can be represented. It gives the teacher the opportunity to hear students’ understandings about and experiences with fractions, $$\frac{1}{2}$$ in particular. The fraction $$\frac{1}{2}$$ is familiar to students and will be central in the first activity.

### Launch

• Groups of 2
• Display the number $$\frac{1}{2}$$.
• 1 minute: quiet think time

### Activity

• 2 minutes: partner discussion
• Share and record responses.

### Student Facing

What do you know about $$\frac{1}{2}$$?

### Activity Synthesis

• “What different ways can we represent $$\frac{1}{2}$$?” (Cut an object, a rectangle, or another shape into two equal parts, mark the middle point between 0 and 1 on a number line.)

## Activity 1: Fraction Strips (20 minutes)

### Narrative

The purpose of this activity is for students to use fraction strips to represent halves, fourths, and eighths. The denominators in this activity are familiar from grade 3. The goal is to remind students of the relationships between fractional parts in which one denominator is a multiple of another. Students should notice that each time the unit fractions on a strip are folded in half, there are twice as many equal-size parts on the strip and that each part is half as large.

In the discussion, use the phrases “number of parts” and “size of the parts” to reinforce the meaning of a fraction.

Engagement: Provide Access by Recruiting Interest. Provide choice and autonomy. Provide access to different colored strips of paper students can use to differentiate each fraction.
Supports accessibility for: Organization, Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• Fraction Strips

### Required Preparation

• Each group of 2 needs 4 strips of equal-size paper (cut lengthwise from letter-size or larger paper or use the provided blackline master).

### Launch

• Groups of 2
• Give each group 4 paper strips and a straightedge.
• Hold up one strip for all to see.
• “Each strip represents 1.”
• Label that strip with “1” and tell students to do the same on one of their strips.
• “Take a new strip. How would you fold it to show halves?”
• 30 seconds: partner think time
• “Think about how to show fourths on the next strip and eighths on the last strip.”

### Activity

• 10 minutes: partner work time
• Monitor for students who notice that each denominator is twice the next smaller denominator.

### Student Facing

Your teacher will give you strips of paper. Each strip represents 1.

1. Use the strips to represent halves, fourths, and eighths.

Use one strip for each fraction and label the parts.

2. What do you notice about the number of parts or the size of the parts? Make at least two observations.

### Student Response

Students may not see the relationships between fractional parts as a result of imprecise folds on fraction strips. Consider asking: “How could we make sure that each part on a strip is equal?” and “What tools might we use to help make precise folds?”

### Activity Synthesis

• Select a group to share their paper strips and how they found the fractional parts. Ask if others also found them the same way.
• Display one set of completed strips.
• Invite students to share what they noticed about the number and size of the parts on the strips. Highlight the ideas noted in student responses.
• If no students mentions the relationships between the fractions on different strips, encourage them to work with a partner to look for some.
• If the terms “numerator” and “denominator” did not arise during discussion, ask students about them.
• Remind students that the denominator, the number at the bottom of a fraction, tells us the number of equal-size parts in 1 whole, and the numerator, the number at the top of a fraction, refers to how many of those parts are being described. Consider displaying these terms and their meanings for students to reference.
• Ask students to save the fraction strips for a future lesson.

## Activity 2: Fractions, Represented (15 minutes)

### Narrative

The purpose of this activity is for students to revisit the meaning of unit fractions with familiar and unfamiliar denominators (3, 5, 6, 10, and 12) and recall how to name and represent them.

As they draw tape diagrams to represent these fractions, students have opportunities to look for structure and make use of the relationships between the denominators of the fractions (MP7). For example, to make a diagram with twelfths they can cut each of 6 sixths in half.

To support students in drawing straight lines on the tape diagrams, provide access to a straightedge or ruler. Students should not, however, use rulers to measure the location of a fraction on any diagram.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give each student a straightedge.
• “Let’s look at some other fractions and draw diagrams to represent them. Consider using a straightedge when you draw.”

### Activity

• 7–8 minutes: independent work time
• “Discuss your responses with your partner. Be sure to talk about how you created diagrams for $$\frac{1}{6}$$, $$\frac{1}{10}$$, and $$\frac{1}{12}$$.”
• 2–3 minutes: partner discussion
• Monitor for students who:
• notice the relationship of thirds, sixths, and twelfths, and of fifths and tenths
• use the given diagrams to help partition the other diagrams

### Student Facing

1. If each full diagram represents 1, what fraction does each shaded part represent?

2. Here are four blank diagrams. Each diagram represents 1. Partition each diagram and shade one part so that the shaded part represents the given fraction.

1. $$\frac{1}{6}$$

2. $$\frac{1}{8}$$

3. $$\frac{1}{10}$$

4. $$\frac{1}{12}$$

3. Suppose you are creating a representation of $$\frac{1}{20}$$ using the same blank diagram. Would the shaded part be larger or smaller than the shaded part in the diagram of $$\frac{1}{10}$$? Explain how you know.

### Activity Synthesis

• “How did you know how to partition the diagrams in the second question?”
• Select students who use the given diagrams or the relationships between denominators to display their diagrams and share their reasoning.
• “What relationships do you see between the fractions in this activity?” (Sample responses:
• As the denominator gets larger, each fractional part gets smaller.
• A fifth is twice the size of a tenth, or a tenth is half as big as a fifth.
• Thirds, sixths, and twelfths are related in that a third is 2 sixths and a sixth is 2 twelfths. Fifths and tenths are related in the same way.)

MLR1 Stronger and Clearer Each Time

• “Share your response to the last question with your partner. Take turns being the speaker and the listener. If you are the speaker, share your response. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion.
• Repeat with 2–3 different partners.
• “Revise your initial response based on the feedback from your partners.”
• 2–3 minutes: independent work time

## Lesson Synthesis

### Lesson Synthesis

“Today we refreshed our memory about fractions. We used fraction strips and diagrams to represent some familiar and some new fractions.”

Based on students’ work during the lesson, choose the questions that need more discussion:

• “In general, what does the denominator in a fraction represent?” (The number of equal parts in 1 whole.)
• “What does the fraction $$\frac{1}{5}$$ tell us?” (The size of one part if 1 whole is split into 5 equal parts.)
• “What did you notice about the size of a fraction as the denominator gets larger?” (The size of the fraction gets smaller.) “Why might that be?” (There are more equal parts in 1 whole, so each part gets smaller.)
• “What relationships did we see between the fractions that we studied today?” (The denominators of some fractions are multiples of other fractions. A representation of one fraction can be split into two or three parts to represent another fraction.)