My students and I have been living in fraction world lately, and I came across this math problem from a graduate level math education course that I took. I decided to pass it along to my students. I believe it originated from the 4th grade NAEP.
I am all for any problem that make kids think, and this one sure does. It requires deep mathematical understanding of fractional parts, common denominators, and fractional conversions. Immediately, most kids say, “Oh. That’s easy. It’s 6/13.” They look at you like you have three heads when you tell them to try again.
I won’t go into too many details about the answer here, but I recommend that you try it with your students. There are several ways to find the answer, and it is fascinating to watch your students work through the problem. You learn a lot about them and their thinking from a problem like this.
At Mathwire, I found an extension of this problem for my students to do to practice and extend their thinking. You can see it HERE. This activity is a bit different because the students can cover the shapes how they want. They just must have a line of symmetry and use at least 3 colors. I just added a bit more to it. Students had to answer the following questions:
1. What fraction of the shape is blue?
2. What fraction of the shape is red?
3. What fraction of the shape is green?
We did one of the pages together. I wanted to share a bit about what they did with you.