My fourth grade students finished up a unit on volume about a month ago. This past week I gave the same group a cumulative assessment on the first two units. After grading the assessment I started to notice trends. Many students had issues with converting square units to cubic units. Students also mislabeled units related to measurement.

This is my first year using a new version of a district-adopoted math resource. This year’s scope-and-sequence had students encountering area first and then volume was discussed in a completely separate part of the unit. I believe that isolation made students think that problems in the different sections were either 1) related to area or 2) related to volume. The assessments that I graded indicated that students needed some bolstering in applying area and volume. Combining them would be a bonus.

Early this week I came across Graham’s Tweet about test questions.

I clicked on the article and found some amazing questions. I definitely geeked out after trying out a few. These types of questions made me think beyond one math skill or idea and I thought it would move students in that direction too. I decided to use the area question with my students.

You see, in the past students have been given the length, width, and height, and then asked to use a formula (often given to them) to find the volume. In this case, students were given the area and had to use that to find the side lengths. This type of task in Graham’s Tweet was definitely different problem for them.

I gave each student a copy of the sheet and had them work on it individually for about 10 minutes. Students initially thought of adding all the area sides together, but then they realized that adding them wouldn’t help in the process. I redirected students to look at what the question is asking. There were a few minutes of frusturation as students were looking for ways to find the length, width, and height.

Students were then put in groups to work out the problem. Eventually, students started to think of factors as they started to investigate numbers that work for the length. Some went the route of using a factor rainbow, while others used a trial-and-error method.

More frustration ensued, but students still moved forward. A few groups were confident that they had a solution. I briefly looked over all the responses and saw that no one had the correct answer, but I pokerfaced it and had the students work it out at home. That evening some of the students tackled the problem and came back with a solution. I was impressed with the perseverance and also how these students applied their understanding of area to find volume.

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