standard_description: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, Ö3) lies on the circle centered at the origin and containing the point (0, 2).
problem_activity: Narrative
The purpose of this activity is for students to build any object they want to. In the next activity, students focus only ;on rectangular prisms. As students count, they will need to make sure to count each cube once and only once. Monitor for these strategies:
Touch each cube as it is counted
Count the cubes by layer (including when there are different numbers of cubes in each layer)
Use addition or multiplication when the cubes are organized in layers
Required Preparation
Each group of 2 needs 24 connecting cubes.
Launch
Groups of  2
Give 24 connecting cubes to each group.
“In this activity, you will use unit cubes to build objects and describe how you would measure the volume.”
10 minutes: partner work time
Activity
As students work, monitor for students who build rectangular prisms to share during the synthesis.
Student Facing
Partner A: Build an object using 8–12 cubes and give the object to Partner B.
Partner B: Explain how you would count the number of cubes in the object.
Partner A: Explain if you would count the cubes in the same way or in a different way.
Switch roles and repeat.
Which objects were easiest to count? Why?
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Student Response
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Advancing Student Thinking
If students are counting all of the cubes one at a time, ask, “where do you see cubes that could be counted as a group?”
Activity Synthesis
Discuss responses to the last problem.
“Which objects were most challenging to count?” (Objects where I had to count each individual cube because it was a weird shape.)
“Which objects were the simplest to count?” (Organized shapes like towers, rectangles, cubes, or boxes.)
Invite selected students to share the rectangular prisms they built and how they counted the number of cubes.
“How did you count the cubes?” (I knew that there were 4 cubes in each layer and 2 layers so that’s 8 cubes.)
“We call these objects
rectangular prisms
. What were some ways you used to count the cubes in rectangular prisms?” (I counted the cubes in groups and then skip counted. I used multiplication to find the total.)


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