This Warm-up prompts students to carefully analyze and compare shapes that are split into pieces. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about characteristics of shapes and pieces of shapes. To help all students distinguish the composite shapes from the smaller shapes of which they are made, 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 the shapes.
“Pick 3 shapes that go together. Be ready to share why they go together.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Share and record responses.
Student Task Statement
Which 3 go together?
A
B
C
D
Student Response
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Advancing Student Thinking
Activity Synthesis
Display Shape D.
“If this was a piece of paper, how could you fold it to make these pieces?” (Take the bottom right corner and fold it up to the top left corner.)
Repeat with Shape A.
Activity 1
10 mins
Build a Circle
Standards Alignment
Building On
1.G.3
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
The purpose of this activity is for students to recognize the difference between equal and unequal 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 . . . .” Advances: Speaking, Representing
Launch
Give each student one piece of a circle.
“Today we are going to make circles. Each circle will be made up of 4 pieces. You will walk around and find 3 people who have pieces that fit with yours to make a circle.”
“If you try to put your piece together with 3 other pieces and they don’t make a circle, find people with different pieces and try again.”
“When you have made a circle, leave it on the table, and sit down to show you are done.”
Activity
5 minutes: whole-class work time
Monitor for a group that makes a circle with four equal pieces and one that makes a circle with unequal pieces.
Student Task Statement
Synthesis:
Student Response
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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 circle has pieces that all look the same. The other circle has a tiny piece and some bigger pieces. Both have 4 pieces but the pieces are different sizes.)
Activity 2
15 mins
Fold into Equal Pieces
Standards Alignment
Building On
Addressing
1.G.3
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
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. There are many ways to fold the circle so that the size and the shape of the pieces when it is folded are the same (MP8).
Launch
Give each student a copy of the blackline master and scissors.
Activity
Read the Task Statement.
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 into equal pieces.
Student Task Statement
Cut out 1 circle and 1 square.
Fold each shape so that there are 2 equal pieces.
Be ready to explain how you know your shape has 2 equal pieces.
Cut out 1 circle and 1 square.
Fold each shape so that there are 4 equal pieces.
Be ready to explain how you know your shape has 4 equal pieces.
Student Response
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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
10 mins
Halves or Fourths
Standards Alignment
Building On
Addressing
1.G.3
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
The purpose of this activity is to introduce students to the terms halves and fourths. In the Launch, students explore examples and nonexamples 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 Activity 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 book.
“Here are some shapes split into pieces.”
“What do you notice?” (One table shows shapes split into 2 pieces, and the other table shows shapes split into 4 pieces. The pieces are equal in the first group of both tables.)
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 equal parts. Fourths are the pieces created when a shape is split into four equal parts.”
Activity
Read the task statement.
4 minutes: independent work time
Monitor for students who accurately partition the shapes into fourths in different ways.
Student Task Statement
Split each shape into halves.
Split each shape into fourths.
Split each shape into fourths.
Split each shape into halves.
Split each shape into halves.
Split each shape into fourths.
Activity Synthesis
Invite previously identified students to share.
“Do all of these shapes show fourths? How do you know?” (Yes, each shape has 4 equal pieces. All pieces are the same size.)
“When we split a shape into four equal pieces, the shape is split into fourths. We can also say that the shape is split into quarters.”
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 4 equal pieces. The first circle is split into fourths because the 4 pieces are the same size. The second circle has 4 pieces that 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.)
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