Equivalent Ratios 1

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.