# Lesson 7

Make Halves, Thirds, and Fourths

## Warm-up: Which One Doesn’t Belong: Compare Equal Pieces (10 minutes)

### Narrative

This warm-up prompts students to compare four shapes. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the shapes in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as the words students use to describe shapes as composed of other shapes, split into multiple pieces, or split into equal pieces.

### 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

• 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: Fold Equal Pieces (20 minutes)

### Narrative

The purpose of this activity is for students to partition rectangles into halves, thirds, and fourths. Students fold paper shapes to guide their partitioning. Like the previous lesson with pattern blocks, students may determine that the pieces formed by the creases of their folds are equal by visual inspection. They are also encouraged to cut out the equal pieces to check whether they are close to being equal.

Most students will likely lay the pieces on top of each other to compare them. The expectation is not that they will be exact, but very close. Monitor as students fold the paper, and if students’ partitions are noticeably inaccurate, have them fold a new paper before they cut.

Engagement: Provide Access by Recruiting Interest. Invite students to generate a list of examples of food items they may cut and share with multiple people (ex: sandwich, candy bar, brownie, cake, etc.) that connect to their personal backgrounds and interests. Let the paper rectangles represent one of the items they could share. Discuss that halves are when two people share the item, thirds are for three people sharing, and fourths/quarters are when four people share the item.
Supports accessibility for: Conceptual Processing, Memory, Attention

### Required Materials

Materials to Gather

### Required Preparation

• Each student needs 3 identical paper rectangles.
• Students could use 3 sheets of construction paper as their 3 rectangles. To save paper, construction paper could also be pre-cut into equal-size rectangles.

### Launch

• Groups of 2
• Give each student 3 paper rectangles and access to scissors and rulers.
• “In an earlier lesson, we thought about how shapes could be composed using equal-size smaller shapes.”
• “Today, we are going to decompose shapes into equal pieces and name the pieces.”
• “Each of you has 3 rectangles. First, cut out each rectangle.”
• “Next, fold each rectangle in different ways. You can use a ruler to draw lines first, if it is helpful.”
• “Let’s try the first one together.”
• 4 minutes: group work time
• “You each have 2 pieces. How can you check to see if they are equal?” (If you lay them on top of each other, they are the same size.)
• Make sure students know the pieces may not be exact, but should be close to the same size.
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “When you split something into two equal pieces, what is each equal piece called?” (Each piece is a half.)
• Share responses.

### Activity

• “Now try the others on your own.”
• “After making each shape, check to see if your pieces are equal and compare with your partner.”
• Have extra paper on hand if students want to try again when making thirds.
• 10 minutes: partner work time

### Student Facing

1. Fold the rectangle to make 2 equal pieces and cut them out.

Each piece is called a ____________________.

Compare with your partner. Tell how you know the pieces are equal.

2. Fold the rectangle to make 4 equal pieces and cut them out.

Each piece is called a ____________________.

Compare with your partner. Tell how you know the pieces are equal.

3. Fold the rectangle to make 3 equal pieces and cut them out.

Each piece is called a ____________________.

Compare with your partner. Tell how you know the pieces are equal.

### Student Response

If students fold the rectangles into parts other than thirds, encourage them to first draw lines to make equal pieces. Consider asking:

• “How could using a ruler help you plan before you fold?”

### Activity Synthesis

• Invite students to share examples of the rectangle split into fourths.
• “What is the name of the equal pieces when you cut a rectangle into 4 equal pieces?” (fourths)
• “Do you know another name for each of these pieces?”(quarters)
• Invite students to share examples of their rectangle split into thirds.
• “What do you think each of these pieces may be called?”
• Share and record responses.
• “When a shape is split into three equal pieces, each piece is called a third.”
• Fold a rectangle to create a non-example of thirds, in which the pieces are not equal.
• Display the non-example.
• “What went wrong when I tried to partition this rectangle into thirds?” (It was hard to fold thirds because you can’t just fold it in the middle.)
• “When making thirds, I know the pieces are smaller than halves. I can check to see if I am on the right track before I make the crease.”
• Fold a rectangle to create thirds, demonstrating testing before making the hard creases. Display the example.
• “Sometimes it will take a few tries.”

## Activity 2: That’s Not It (15 minutes)

### Narrative

The purpose of this activity is to determine whether or not circles are partitioned into halves, thirds, or fourths. Students explain why some circles are not examples of halves, thirds, and fourths and demonstrate their understanding that it's not just the number of pieces that help determine whether to use halves, thirds, or fourths, but whether they are equal pieces of the same whole (MP3, MP6).

MLR8 Discussion Supports. Synthesis: Create a visual display for fractions. After students share their reasoning with the class, annotate the display to illustrate connections. For example, next to halves, write “2 equal pieces” and draw examples of shapes partitioned into 2 equal pieces.

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “In the first activity, we looked at examples and some non-examples of rectangles that were decomposed, or partitioned, into halves, fourths, and thirds.”
• “These circles have been partitioned into smaller pieces.”
• “Some pieces show examples of halves, thirds, and fourths, and some do not.”
• “Mark the circles that have not been partitioned into halves, thirds, or fourths with an X. Be ready to explain your choices to your partner.”
• 3 minutes: independent work time
• 4 minutes: partner work time
• Monitor for students who understand why this circle is not partitioned into thirds.
• “Now try on your own to partition the circle into thirds.”
• 3 minutes: independent work time

### Student Facing

1. Noah is looking for examples of circles that have been partitioned into halves, thirds, or fourths.

1. Put an X on the 2 circles in each row that are not examples.

halves

fourths

thirds

2. Explain why each of the shapes you marked is not an example of halves, fourths, or thirds.
2. Partition this circle into thirds.

### Activity Synthesis

• Display the images of circles from the row labeled thirds.
• “You had to decide which of these circles is partitioned into thirds. Which of these circles did you believe were not showing thirds? Explain.”
• Invite previously identified students to explain their reasoning.
• As time permits, invite students to share their responses for halves and fourths.

## Lesson Synthesis

### Lesson Synthesis

“Today you learned about making and identifying shapes that were decomposed, or partitioned, into halves, thirds, and fourths.”

“What is something you did to try to make the pieces equal when you decomposed shapes by cutting?” (I drew lines first. I folded carefully. I didn’t do a hard crease until I was sure.)

“What is something you did to try to make the pieces equal when you partitioned shapes by drawing lines?” (I made very light lines and then traced them.)