standard_description: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
problem_activity: Narrative
The purpose of this activity is for students to apply their knowledge from previous activities to draw arrays to match multiplication expressions. Have connecting cubes or counters available for students who need them. In the launch, students use their bodies to make an array for the expression
\(4\times6\)
. Feel free to adjust this expression to better fit the number of students in your class.
Launch
Groups of 2
Display
\(4\times6\)
“Work together as a class to use your bodies to create an array for this multiplication expression.”
If the number of students does not exactly match the product, ask extra students to monitor the array and be prepared to explain where they see parts of the expression in the array.
3–5 minutes: whole-class work time
Activity
“Work with your partner to draw an array for each multiplication expression. Be ready to share connections you notice between the multiplication expressions and arrays.”
2–3 minutes: partner work time
Student Facing
Draw an array for each multiplication expression. Be prepared to share your reasoning.
\(2\times3\)
\(5\times2\)
\(4\times4\)
Student Response
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Advancing Student Thinking
If students draw equal groups that are not arrays, consider asking:
“How did you use the expression to create your drawing?”
“How could we rearrange your drawing into an array?”
Activity Synthesis
Share an array or two for each expression.
“What connections did you and your partner see between the multiplication expressions and arrays?” (The factors tell us how many things are in each row and column. For
\(2\times3\)
, we drew an array with 2 columns that have 3 things in each column. For
\(2\times3\)
, we drew an array with 2 rows that have 3 things in each row.)


aligns: no