This Warm-up prompts students to compare four shapes that have been partitioned and examine the features of the shapes and the partitions. In making comparisons, students have a reason to use language precisely (MP6). The observations here prepare students to explore fractions later in the lesson and enable the teacher to hear how students describe the features that they see. During the Activity Synthesis, ask students to explain the meaning of any terms they use, such as “partition,” “whole,” “parts,” “pieces,” “equal,” and “halves.”
Launch
Groups of 2
Display the image.
“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.
Which 3 go together?
A
B
C
D
Student Response
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Advancing Student Thinking
Activity Synthesis
“Why can’t we say that D is split into halves?” (The pieces or parts aren’t the same size. The pieces have to be equal.)
“Another word we can use to say something was split into pieces or parts is 'partition.' Partition means to split into parts.”
Activity 1
Standards Alignment
Building On
2.G.A.3
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
The purpose of this activity is for students to revisit ideas about how to partition shapes into halves, thirds, and fourths. Students sort a set of shapes into categories, based on their shared attributes. Look for students who distinguish shapes that have been partitioned into equal-size parts and shapes that have not. This distinction will be used to review what it means for a part of a shape to be a half, a third, or a fourth.
Sorting the shapes gives students an opportunity to identify important common characteristics or structures, in this case the number and the size of the parts (MP7). When students specify that halves, thirds, and fourths of a shape need to be equal in size, they are attending to precision (MP6).
Students will use the cards again during the Lesson Synthesis.
MLR2 Collect and Display. Collect the language students use while sorting the shapes. Display words and phrases, such as “partition,” “split,” “parts,” “equal parts,” “equal-size parts,” “halves,” “thirds,” “fourths,” “whole,” and so on. During the Activity Synthesis, invite students to suggest ways to update the display. “What are some other words or phrases we should include?” Encourage students to borrow language from the display as needed. Advances: Conversing, Reading
Launch
Groups of 2
Give each group a set of cards.
“Take a minute to look at the cards. What do you notice? What do you wonder?” (There are different shapes. The shapes are split or partitioned. Why are they partitioned into different numbers of pieces or parts? Why are some of the pieces or parts equal and some are not?)
1 minute: quiet think time
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Activity
“Work with your partner to sort the shapes on the cards into categories in a way that makes sense to you. Be ready to explain the meaning of your categories and why the shapes in each category belong together.”
8 minutes: partner work time
Monitor for groups that sort shapes, based on whether the shapes are partitioned into equal parts.
Your teacher will give you a set of cards that show some shapes that are partitioned, or divided into parts.
Sort the cards into categories in a way that makes sense to you. Be ready to explain the meaning of your categories.
Student Response
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Activity Synthesis
Invite groups to share their categories and the shapes in the categories.
Choose as many different types of categories as time allows, but ensure that one set of categories distinguishes between shapes partitioned into equal parts and shapes that are not.
Attend to the language that students use to describe their categories and shapes, and give students opportunities to describe more precisely how shapes are partitioned.
Highlight the use of terms, such as “halves,” “thirds,” “fourths,” and “equal-size pieces or parts.”
Activity 2
Standards Alignment
Building On
Addressing
3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Understand a fraction as the quantity formed by 1 part when a whole is partitioned into equal parts; understand a fraction as the quantity formed by parts of size .
The purpose of this activity is for students to partition rectangles into thirds, fourths, sixths, and eighths before learning the names “sixth” and “eighth.” Students do so by folding rectangular strips of paper into equal-size parts. While folding, students may notice that thirds can be further partitioned to make sixths and that fourths can be further partitioned to make eighths, which will be explored more in a future lesson. The focus of the Activity Synthesis should be on naming sixths and eighths, as they are new terms for students.
Students will use the partitioned rectangles during the Lesson Synthesis.
Action and Expression: Develop Expression and Communication. Provide access to pre-formatted papers that will be folded into rectangles. For each rectangle, papers with dotted lines show students where to fold. Supports accessibility for: Social-Emotional Functioning, Visual-Spatial Processing
Launch
Groups of 2
“We just looked at some shapes that were partitioned. Now you’re going to partition some rectangles into equal parts.”
Give each student 4 rectangles.
Activity
“We are going to partition these rectangles by folding them. Fold each rectangle into 3, 6, 4, or 8 equal parts. Draw lines where you folded to partition the rectangles. Be prepared to share how you folded your rectangles.”
3–5 minutes: independent work time
“Now, share how you folded your shapes with your partner.”
2–3 minutes: partner discussion
Monitor for and select to highlight during the Activity Synthesis students who used partitioning into 3 or 4 equal parts to partition into 6 or 8 equal parts.
Fold each rectangle your teacher gives you into 3, 6, 4, or 8 equal parts. Draw lines where you folded to partition the rectangles. Be prepared to share how you folded your shapes.
Student Response
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Advancing Student Thinking
Activity Synthesis
Select previously identified students to share how they folded the rectangles into 6 and 8 equal parts.
Consider asking:
“How did you use the partitions of 4 equal parts to partition into 8 equal parts?”
“How did you use the partitions of 3 equal parts to partition into 6 equal parts?”
“Does anyone want to add an observation to the way _____ partitioned?”
Display poster:
number of equal parts
name of each part
2
half
3
third
4
fourth
6
8
“When we partition a shape into 6 equal parts, each part is called a ‘sixth.’ When we partition a shape into 8 equal parts, each part is called an ‘eighth.’“
Add “sixth” and “eighth” to the chart, and keep it displayed.
Lesson Synthesis
“In the past, we’ve used the term ‘half’ to refer to each part when a whole shape is partitioned into two equal parts. We’ve used ‘third’ to refer to each of three equal parts, and ‘fourth’ to refer to each of four equal parts.”
“Today, we learned to use ‘sixth’ to refer to each part when a whole shape is partitioned into 6 equal parts and ‘eighth’ when the whole is partitioned into 8 equal parts.”
“In addition to using words to describe these equal parts, we also can use numbers.”
Write each fraction as it is named:
“One-half can be written as the number .”
“One-third can be written as the number .”
“One-fourth can be written as the number .”
“How would we write one-sixth and one-eighth as numbers?” ( and )
“The numbers that we use to describe the equal parts of a whole are called fractions. Each fraction has two parts separated by a bar.”
“What do you think the part below the bar represents?” (the number of equal parts that make up the whole)
“What about the 1 above the bar?” (the one in “one-half,” “one-third,” and so on)
Display a square partitioned into two equal parts, with each part labeled with , such as:
“We can label the equal parts in a shape with fractions. If this square is the whole shape or one, each part is one-half.”
“Find all the cards from the first activity that show a shape partitioned into two equal parts. Let's label each half with the fraction .”
“Let’s label the parts in each of your rectangles with fractions.”
Standards Alignment
Building On
2.G.A.3
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
