# Lesson 10

One of the Pieces, All of the Pieces

## Warm-up: Which One Doesn’t Belong: Split Shapes (10 minutes)

### Narrative

This warm-up prompts students to compare four shapes split into pieces. It gives the teacher an opportunity to hear how students use geometric vocabulary and talk about the characteristics of the shapes in comparison to one another (MP6).

### Launch

• Groups of 2
• Display 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: Color a Piece (10 minutes)

### Narrative

The purpose of this activity is to introduce the language of a half of and a fourth of a shape. Students begin by applying the language of halves and fourths, or quarters, to partition each shape. Students are asked to describe “how much” of each shape is shaded to elicit a variety of responses that include half, fourth, or quarter, including the phrases “of the square” or “of the circle.” Monitor for a variety of words and phrases to share in the synthesis including:

• phrases that reference the pieces only (“one piece”).
• phrases that reference that some, but not all of the shape is shaded (“part of it,” “a little bit”)
• phrases that name the pieces (“a half,” “a fourth,” “a quarter”)
• phrases that name the pieces in reference to the whole shape (“a half of the square,” “a fourth of the circle”)

All responses should be shared and compared in the synthesis to help build students understanding of the new vocabulary and the concept of fractional pieces of a whole (MP6).

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• 2 minutes: independent work time.
• 2 minutes: partner discussion
• Monitor for a range of ways to describe the amount shaded such as “some is shaded,” “one piece of the square is shaded,” “one out of two pieces is shaded,” or “a half is shaded.”

### Student Facing

1. Split the square into halves.

Color in one of the halves.
How much of the square is colored in?
2. Split the circle into fourths.

Color in one of the fourths.
How much of the circle is colored in?

### Activity Synthesis

• Invite previously identified students to share for each problem. Sequence the students in the order described in the narrative.
• “One piece of a shape split into two pieces that are the same size is called a half. One piece of a shape split into four pieces that are the same size is called a fourth.”
• For each shape, invite students to describe how much is colored in. (A half of the square is colored in. A fourth of the circle is colored in.)

## Activity 2: Card Sort: Shaded Pieces (15 minutes)

### Narrative

The purpose of this card sort is for students to connect words and phrases to visual representations of partitioned shapes. Students begin by sorting the cards in a way that makes sense to them, and then are invited to sort the shapes based on the language that can be used to describe them. In the activity synthesis, the phrases “two of the halves” and “four of the fourths” are introduced to describe shapes where all pieces are shaded in.

Keep cards D and N available to use during the lesson synthesis.

As students sort the shape cards they look for structure, namely the number of pieces making up each shape, whether or not the pieces are equal, and the number of those pieces that are shaded (MP7).

MLR2 Collect and Display. Circulate, listen for and collect the language students use as they describe the shapes. On a visible display, record words and phrases such as: “shaded,” “half,” “fourth,” “quarter,” “equal,” “not equal,” “whole,” “shape.” Invite students to borrow language from the display as needed, and update it throughout the lesson.

### Required Materials

Materials to Copy

### Required Preparation

• Create a set of Shaded Parts Cards for each group of 2.

### Launch

• Groups of 2
• Give each group a set of cards.
• “Sort your cards in a way that makes sense to you. Then explain how you sorted them.”
• 3 minutes: partner work time
• Share responses.

### Activity

• “Now, sort the cards into the categories shown on your paper. Think about what words you can use to describe the shape on each card. Write the letter of each card in the space for it's category.”
• 5 minutes: partner work time

### Student Facing

1. Sort the cards into categories in a way that makes sense to you. Explain how you sorted the cards.

2. Sort your cards into these categories.
Write the letter of each card in the space for its category.

A fourth or quarter is shaded

Not equal pieces

### Activity Synthesis

• Display card J.
• “How can we describe this shape?” (It is a square. It is cut into halves. The whole shape is shaded.)
• “When a shape is split into halves and they are both shaded, we say the whole shape is shaded or two of the halves are shaded.”
• Repeat with card E.
• “When a shape is split into fourths and they are all shaded, we say the whole shape is shaded or four of the fourths are shaded.”

## Activity 3: Describe Equal Pieces (10 minutes)

### Narrative

The purpose of this activity is for students to match language to visual representations of rectangles and circles partitioned and shaded in different ways.

Representation: Access for Perception. Read each of the phrases aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language, Conceptual Processing

• Groups of 2

### Activity

• “You may use the phrases more than once.”
• 6 minutes: partner work time

### Student Facing

Here are some ways to describe the shapes.

• split into fourths
• split into halves
• split into quarters
• two of the halves shaded
• four of the fourths shaded

Label each shape with at least one phrase from the lists.

1.

2.

3.

4.

5.

6.

7.

### Activity Synthesis

• Display the circle with four of the fourths shaded.
• “Let’s list all the ways we could describe this shape.” (It’s split into fourths. It is split into quarters. Four of the fourths are shaded.)
• Repeat with other shapes as time permits.

## Lesson Synthesis

### Lesson Synthesis

Display cards D and N.

“How are the shapes the same? How are they different?” (They are both rectangles. They are both split into halves. They are split differently. One has a half shaded and one has two of the halves shaded.)