Lesson 9

Equal Pieces

Warm-up: Which One Doesn’t Belong: Pieces of Shapes (10 minutes)

Narrative

This warm-up prompts students to carefully analyze and compare images. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of shapes and pieces of shapes. To help all students distinguish the composite shapes from the smaller shapes they are made up of, invite students to clarify or show what they mean when they describe attributes of the shapes they see in each image.

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: Build a Circle (10 minutes)

Narrative

The purpose of this activity is for students to recognize the difference between equal-size pieces and unequal-size pieces. Students work together to make circles from the pieces they are given. After some circles have been made, students discuss what they notice about each circle. Both circles have four pieces, however one has equal-size pieces and the other doesn't.
MLR8 Discussion Supports. Synthesis. Display sentence frames to support whole-class discussion: “These pieces are/are not equal because…” and “These pieces do/do not make a circle because…”

Required Materials

Materials to Copy

• Pieces of Circles

Required Preparation

• Cut out the pieces of the circles on the blackline master. Each copy has enough pieces for 8 students.

Launch

• Give each student one piece of a circle.
• “Today we are going to make circles. Each circle will be made up of four pieces. You will walk around and find three other people who have pieces that fit with yours to make a circle.”
• “If you try to put your piece together with three other pieces and they don’t make a circle, find other people with different pieces and try again.”
• “When you have made a circle, leave it on the table, and sit down so we know you are done.”

Activity

• 5 minutes: whole-class work time
• Monitor for a group that makes a circle with equal-size pieces and one that makes a circle with unequal-size pieces.

Student Facing

Synthesis:

Which of these shows equal pieces that make a circle?

Activity Synthesis

• Display the two different circles that were made, or the images in the student book.
• “We made these two circles. What do you notice about them?” (One of them has pieces that all look the same. One has a tiny piece and some bigger pieces. They both have four pieces but the pieces are different sizes.)

Activity 2: Fold into Equal Pieces (15 minutes)

Narrative

The purpose of this activity is for students to fold circles and squares into two or four equal pieces. To make equal pieces, some students may partition the shape by folding it down the middle (and folding again for fourths) and matching up the edges of the shapes. There are several ways students may fold their square into equal pieces--vertically, horizontally, or diagonally--although each way gives different shaped pieces, they all result in four equal pieces. There are many ways to fold the circle but the size and shape of the pieces when it is folded are all the same (MP8).

Required Materials

Materials to Gather

Materials to Copy

• Circles and Squares

Required Preparation

• Consider having extra shapes cut from the blackline masters for students who may need more than one of each shape.

Launch

• Give each student a copy of the blackline master and scissors.

Activity

• 10 minutes: independent work time
• Monitor for students who line up the edges and fold the square horizontally, vertically, or diagonally, and a student who folds the circle.

Student Facing

1. Cut out one circle and one square.

Fold each shape so that there are 2 equal pieces.

Be ready to explain how you know your shape has 2 equal pieces.

2. Cut out one circle and one square.

Fold each shape so that there are 4 equal pieces.

Be ready to explain how you know your shape has 4 equal pieces.

Activity Synthesis

• Invite previously identified students to share.
• “Is your paper folded so that each piece is the same size? How do you know?” (Yes, the pieces line up perfectly. No. when I fold it on the line, one piece is bigger.)
• Consider cutting out the pieces and laying them on top of one another to show whether or not they are the same size.

Activity 3: Halves or Fourths (10 minutes)

Narrative

The purpose of this activity is for students to be introduced to the terms halves and fourths. In the launch, students explore examples and non-examples of shapes split into halves and fourths and develop a shared understanding of what these terms mean (MP6). Students then draw lines to partition shapes into halves or fourths. During the synthesis students learn that the term 'quarters' means the same as fourths. Fourths and quarters will be used interchangeably throughout this section.

Action and Expression: Develop Expression and Communication. Give students access to a straight edge or ruler.
Supports accessibility for: Fine Motor Skills, Visual-Spatial Processing

Launch

• Groups of 2
• Display the categories of shapes from the student workbook.
• “Here are some shapes split into pieces.”
• “What do you notice?” (One table shows shapes split into two pieces and the other table shows shapes split into four pieces. The pieces are equal in the first group.)
• 1 minute quiet think time
• 2 minutes: partner discussion
• Record responses.
• “Based on what you observed, what do you think split into halves means? What do you think split into fourths means?”
• 1 minute quiet think time
• Record responses.
• Halves are the pieces created when a shape is split into two pieces that are the same size. Fourths are the pieces created when a shape is split into four pieces that are the same size.”

Activity

• 4 minutes: independent work time
• Monitor for students who accurately partition the shapes into fourths in different ways.

Student Facing

1. Split each shape into halves.
2. Split each shape into fourths.
3. Split each shape into fourths.
4. Split each shape into halves.
5. Split each shape into halves.
6. Split each shape into fourths.

Student Response

Students may split the shapes into halves accurately by drawing a vertical or horizontal line down the middle of each shape. These students may attempt to create fourths, for the rectangles and circles, using the same technique by guessing-and-checking. Ask these students to explain their method and what they hope to achieve. Consider asking:

• “How many pieces are you trying to create?”
• “How can you make sure they are the same size?”
• “How would you fold this shape to make __ equal pieces?”
• “How can you use the table of shapes we looked at earlier to help plan how to make __ equal pieces?”

Activity Synthesis

• Invite previously identified students to share.
• “Do all of these shapes show fourths? How do you know?” (Yes, each of the shapes have 4 equal pieces. Each of the pieces are the same size.)
• “When we split a shape into four equal-sized pieces, the shape is split into fourths. We can also say the shape is split into quarters.”

Lesson Synthesis

Lesson Synthesis

Display the two circles from activity 1.

“Tyler says both circles are split into fourths. Do you agree? Why or why not?” (Fourths are four equal pieces. The first circle is split into fourths because the four pieces are all the same size. The second circle has four pieces but they are not the same size, so it is not split into fourths.)

What is another way to describe how the first circle is split?” (It is split into quarters.)