This is an activity that I used as a kind of “warm-up” to a unit on fractions with my 5th graders; I wanted to relate fractions to ratios, as well as see what the classes had remembered from the previous year. I gave out this activity, put the students in dyads (that’s groups of 2, for those of you who have forgotten their Greek, it means students work in pairs of 2.) They complete the activity sheet and then write up a summary of their findings, which they post on a wall.
You can use this activity as an assessment with 4th graders, as well as a "warm up" activity with 6th and 7th graders to ratios, proportions and fractions.
I've also included 3 samples of student responses, with commentary, to give you a guide as to how to assess the work your students do.
The next phase is to let students go from poster to poster and put in their own commentary about the accuracy and depth of the explanations. As you can see, my students are rather kind to one another, but that’s okay; by doing this, I make them more aware of how others interpreted the problem.
I think what’s interesting is that students didn’t resort to making “pies” or even drawings when working out the problem; they had remembered enough from the previous year that they could figure out the solutions without the need for diagrams. They also were able to use a variety of strategies that I had hoped they remembered from the past, including expressing ratios as fractions, comparing those fractions, simplifying fractions, and “benchmarking” fractions (that is, recognizing that one fraction was more than 1/2, another was exactly 1/2 and the third was less than 1/2.)
You’ll also notice that I was trying to address gender and racial equity issues by using females of color who don’t conform to traditional norms (that is, they are playing basketball and one of them doesn’t look very “girlish.”) These are issues we have to address in our materials: I want that girl who we used to call a “tomboy” to recognize herself and say, “hey, that’s me in that problem! I’m important!”