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.”
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.