standard_description: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Warm-up
This warm-up reviews the volume work students had done previously to prepare for the work in this lesson. It reinforces the idea of using unit cubes and fractional-unit cubes as a way to measure the volume of a rectangular prism.
Launch
Give students 2–3 minutes of quiet work time. Follow with a class discussion.
Student Facing
How many cubes with an edge length of 1 inch fill this box?
[IMG]
If the cubes had an edge length of 2 inches, would you need more or fewer cubes to fill the box? Explain your reasoning.
If the cubes had an edge length of
\(\frac 12\)
inch, would you need more or fewer cubes to fill the box? Explain your reasoning.
Student Response
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Activity Synthesis
Select several students to share their responses and reasoning. After each person explains, ask students to indicate whether they agree. To involve more students in the discussion, consider asking:
“Who can restate ___’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”
“Do you agree or disagree with the reasoning? Why?”
Tell students that they will use their understanding of the volume of rectangular prisms to solve other geometric problems.


aligns: no