standard_description: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
problem_activity: Narrative
The purpose of this activity is for students to put together pattern blocks to form larger shapes in more than one way. Students create hexagons using different combinations of pattern blocks. In the synthesis, students discuss whether the same pattern blocks in different orientations should be considered as different ways to make a hexagon (MP3). There is no one correct answer to the question. The goal is for students to notice and discuss that the same pattern blocks are arranged in different orientations.
MLR8 Discussion Supports.
To support the transfer of new vocabulary to long-term memory, invite students to chorally repeat these words in unison 1–2 times: more, fewer, the same as.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Pattern blocks
Launch
Groups of 2
Give each group of students pattern blocks.
“Work with your partner to find many different ways to make hexagons with pattern blocks. Tell your partner about the shapes that you use each time using ‘more’, ‘fewer’, or ‘the same number’.”
Activity
6 minutes: partner work time
Student Facing
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Student Response
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Advancing Student Thinking
If students find one or two ways to fill in the hexagon pattern block puzzle:
“Tell me more about which pattern blocks you used to make the hexagon.”
“Can you use these green triangle pattern blocks to make this red trapezoid pattern block? How can that help you find another way to fill in the hexagon?”
Activity Synthesis
Invite students to share different ways they made a hexagon.
As students share, say “Tell your partner about the shapes that they used using ‘more’, ‘fewer’, or ‘the same number’.”
Display all of the ways to make a hexagon that students have shared.
“Are there any other ways to make a hexagon with pattern blocks?”
Display 2 hexagons created with 2 blue rhombus pattern blocks and 2 green triangle pattern blocks in different orientations:
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“Han and Clare shared these ways to make a hexagon with pattern blocks. Are these the same way to make a hexagon or a different way? Why do you think that?” (They are the same because they used the same pattern blocks but put them in different spots. It looks like they flipped it. They are different because the pattern blocks are in different places, so they look different.)


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