Here is the modified version of the task I gave them...
I ended up giving them three full days in class to work (many only needed 2). During this time the students had plenty of other work to do, but I allowed the extra time so they would have myself and their peers handy to ask questions. These types of experiences where students struggle (and I am all for the struggle...that is what makes students better mathematically) more than they should causes myself to reflect on the concepts and how they have previously been presented. We have done a lot of work with 3-dimensional shapes, what surface area and volume literally mean (I have a whole wall with square shapes of all sizes and a corner with cubic shapes of their counterparts) and so on...but in reflecting, my ratio of working with 2-D shapes compared to 3-D shapes was not quite equal. I will work on that in the future, and this task served as a valuable learning tool for my students and their knowledge of 3-D shapes.
To my students' credit, they really worked hard to figure this task out. We've gotten to the point where all of my posing questions and walking away has paid off because I know I have a group of students with grit...not giving up when something isn't understood immediately. That is a big improvement from where we started at the first month of 6th grade. If you are new to these tasks, students usually have a lot of "give up" in them at first, so you as a teacher cannot give in to them...you are only doing your students a disservice if you do.
Once we reinforced the idea of a cubic shape, most students progressed nicely until the final two questions. The students who started out making the conversions right away were successful on most first attempts, but I had many students who found the volume of the shapes first, and then multiplied by the conversion amount once after the volume was found. We had a discussion on why we would have to multiply by the conversion rate three times instead of one if they did the conversion afterwards...again reinforcing that idea of a cubic shape.
While time consuming, this was a wonderful task that actually hit many topics at the same time. This task also caused me to reflect on my own practice, as well as being very proud of my students for their stick-to-itiveness.
|My help sheet part one|