Lesson 8
Are All Pieces Created Equal?
Warmup: Number Talk: 5 Ones (10 minutes)
Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting multiples of 5 from multiples of 5. These understandings help students develop fluency and will be helpful later in this unit when students will learn to tell time to the nearest 5 minutes. Monitor for the different ways students use the relationship between the numbers in each expression to choose their strategy. For example, students may subtract by place when both numbers have a 5 in the ones place or look for ways to count on by 5 and 10 (MP7).
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategies.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
 \(25  15\)
 \(40  15\)
 \(65  25\)
 \(60  35\)
Student Response
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Activity Synthesis
 “What patterns did you notice when finding the value of these expressions?” (All the expressions were subtracting a number that had a 5 in the ones place. All the numbers are numbers we say when we count by 5, so we can count by 5 and 10 to find the values. When both numbers had a 5 in the ones place, I just subtracted the tens and knew there would be 0 ones. When only one number had a 5 in the ones place, I thought about adding on to make it easier.)
Activity 1: Make Quarters and Halves (20 minutes)
Narrative
The purpose of this activity is for students to explore different ways to partition rectangles into halves and fourths. They notice that when they partition two equalsize rectangles into fourths or halves in different ways the resulting pieces may have different attributes. In the synthesis, students explain why the equal pieces of the same whole could look very different even though they have the same size, so long as the original shape was split into the same number of equal pieces (MP3, MP7).
Advances: Conversing, Reading
Launch
 Groups of 2
 “Lin wanted to partition this square into quarters. She started by splitting the square into halves.”
 Display the square partitioned into halves.
 “After she drew the first line, she tried 3 different ways to make fourths.”
 Display the 3 squares split into 4 pieces.
 “Which of these shows fourths or quarters? Explain.” (B is the only one that shows four equal pieces, so they are fourths. The other 2 show 4 parts, but they are not equal.)
 30 seconds: quiet think time
 1 minute: partner discussion
 Share and record responses.
Activity
 “Now you will have a chance to explore different ways to partition shapes to make fourths or quarters and halves.”
 “Work on your own to partition your shapes and answer the questions about the pieces. Then compare your work with your partner.”
 6 minutes: independent work time
 4 minutes: partner discussion
 Monitor for students who show different ways to partition the rectangle into fourths (see Student Responses).
Student Facing
Lin wanted to partition this square into quarters. She started by splitting the square into halves.
After she drew the first line, she tried 3 different ways to make fourths.
 Which of these shows fourths or quarters? Explain and share with your partner.

Name the shaded piece.
Shape A has a ________________ shaded.
Shape B has a ________________ shaded.

Show 2 different ways to partition the rectangle into quarters or fourths. Shade in a fourth of each rectangle.
 Show 2 different ways to partition the square into halves.
Shade in a half of each square.
Student Response
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Activity Synthesis
 Invite previously identified students to share their rectangles partitioned to make fourths.
 Display students’ work.
 “Each of these students believe they have split the rectangle into fourths or quarters. Who do you agree with? Explain.” (The pieces look different in each rectangle, but they all show fourths because each rectangle is split into 4 equal pieces.)
Activity 2: Make Equal Pieces (15 minutes)
Narrative
The purpose of this activity is for students to consider different ways to partition a circle or rectangle into thirds. They continue to deepen their understanding that equal pieces of the same whole can look different. Monitor for the ways students reason that the equal pieces of the same whole may look different, but they are the same size to share in the lesson synthesis (MP3, MP7).
Supports accessibility for: Memory, Language, Organization
Launch
 Groups of 2
Activity
 “Lin, Mai, and Andre were asked to shade in one third of a shape. Look at their images and choose the ones that show one third shaded. Explain how you know or if you disagree.”
 2 minutes: partner discussion
 “Now work independently to complete the last 2 problems.”
 6 minutes: independent work time
 Monitor for students who have a clear explanation for Diego’s brother to share in the lesson synthesis.
Student Facing
 Lin, Mai, and Andre were asked to shade in a third of a shape.
Lin
Mai
Andre
Do all their shapes show a third shaded? Explain and share with a partner.
 Partition the rectangle into thirds and shade a third of the shape.
 Diego’s dad made 2 square pans of cornbread and sliced them up for the family.
Diego’s Brother
Diego’s
Diego’s little brother was upset because he thought his piece of cornbread was smaller than Diego’s. What would you tell him?
Student Response
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Advancing Student Thinking
If students agree that both Diego and Diego’s brother each got a fourth, but disagree that they got the same amount because the shape of their pieces is different, consider asking:
 “How are the pieces of cornbread Diego and his brother have the same and different?”
 “Do you see a way you could break apart Diego's brother's piece and put it back together so it's the same shape as Diego's piece?”
Activity Synthesis
 Invite previously selected students to share.
 “How is it possible that both students have shaded a third if they don’t look the same?” (Their thirds might not look the same when compared to each other, but they each partitioned the rectangle into 3 equal parts and shaded one part.)
Lesson Synthesis
Lesson Synthesis
“Today, you learned that if a shape is partitioned into the same number of equal pieces, but in different ways, the pieces of the shapes will have the same name, even though they look different.”
Display or draw:
Invite previously selected students to share their reasoning.
“Since both pans are the same size, we know that both brothers got a fourth of the pan even though it looks different. The pieces look different, but it's the same amount.”
Cooldown: Paint a Picture (5 minutes)
CoolDown
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