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# Games at Recess

## Task

The students in Mr. Hill’s class played games at recess.

$\hskip30pt$6 boys played soccer

$\hskip30pt$4 girls played soccer

$\hskip30pt$2 boys jumped rope

$\hskip30pt$8 girls jumped rope

Afterward, Mr. Hill asked the students to compare the boys and girls playing different games.

Mika said,

“Four more girls jumped rope than played soccer.”Chaska said,

“For every girl that played soccer, two girls jumped rope.”

Mr. Hill said, “Mika compared the girls by looking at the difference and Chaska compared the girls using a ratio.”

- Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did.
- Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did.
- Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did.

## IM Commentary

In a classroom where the expectation is built in that answers to problems in context will be written as complete sentences and numerical values from a context will always be written with the appropriate units, the task may not need to explicitly model and request it as these questions do.

While students need to be able to write sentences describing ratio relationships, they also need to see and use the appropriate symbolic notation for ratios. If this is used as a teaching problem, the teacher could ask for the sentences as shown, and then segue into teaching the notation. It is a good idea to ask students to write it both ways (as shown in the solution) at some point as well.

## Solution

- Four more boys played soccer than jumped rope.
- For every three boys that played soccer, one boy jumped rope. Therefore the ratio of the number of boys that played soccer to the number of boys that jumped rope is 3:1 (or "three to one").
- For every two girls that played soccer, three boys played soccer. Therefore the ratio of the number of girls that played soccer to the number of boys that played soccer is 2:3 (or "two to three").

## Games at Recess

The students in Mr. Hill’s class played games at recess.

$\hskip30pt$6 boys played soccer

$\hskip30pt$4 girls played soccer

$\hskip30pt$2 boys jumped rope

$\hskip30pt$8 girls jumped rope

Afterward, Mr. Hill asked the students to compare the boys and girls playing different games.

Mika said,

“Four more girls jumped rope than played soccer.”Chaska said,

“For every girl that played soccer, two girls jumped rope.”

Mr. Hill said, “Mika compared the girls by looking at the difference and Chaska compared the girls using a ratio.”

- Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did.
- Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did.
- Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did.

## Comments

Log in to comment## agrannemann says:

almost 5 yearsI like the multiple expectations of how to present answers. I would suggest writing the ratio in three ways. Include 2 to 1.

## Cam says:

almost 5 yearsAgreed. I've added parenthetical remarks in the solutions with your suggestion. I think the commentary leaves it sufficiently enough up to the teacher's discretion how far to push on insisting the use of correct symbolic relation.