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Equivalent Ratios 1
Alignments to Content Standards:
6.RP.A
Task
Rubi was paid \$24 to sweep 4 walks. Which of the following can be represented by an equivalent ratio? Explain your thinking.
 \$6 to sweep 1 walk
 \$12 to sweep 3 walks
 \$30 to sweep 5 walks
Anthea hiked 6 miles in 2 hours. Which of the following can be represented by an equivalent ratio? Explain your thinking.
 4 miles in 1 hour
 12 miles in 4 hours
 9 miles in 3 hours
IM Commentary
The purpose of this task is for students to reason about whether two ratios are equivalent. The solution shows two of many possible diagrams that students might draw to help them reason about these ratios, but there is no one right way to represent the problems. What matters is that students can explain their reasoning and, if they have drawn a diagram, how the diagram reflects their solution.
Should students struggle to get started, we suggest showing a representation of \$24 for 4 walks that is familiar to the class, and ask a student to point out for the class how you can see \$6 for 1 walk within the representation.
Solution
Rubi was paid $24 to sweep 4 walks. This is equivalent to:
 $6 to sweep 1 walk
 $30 to sweep 5 walks
You can see each of these ratios in the following diagram:
You can also see that \$12 to sweep 2 walks is equivalent to these, so \$12 to sweep 3 walks cannot be.
Anthea hiked 6 miles in 2 hours. This is equivalent to:
 12 miles in 4 hours
 9 miles in 3 hours
You can see each of these ratios in the following diagram:
You can also see that 3 miles in one hour is equivalent to this ratio, so 4 miles in one hour cannot be.
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