Exploring Volume and Surface Area

Today in MFM2P we had a challenge. I gave each table group the task of working as a design team to create a rectangular prism to meet my specifications. It needed to be made of card stock (old file folders) and tape, and it needed to have the volume of 300 cubic centimetres.

Groups had access to rulers, protractors, calculators, scissors, folders and tape.

As groups they had some choices to make about what the dimensions should be. We had talked about volume earlier. We know that the volume is the insides of a 3D shape. We know that for prisms it is calculated by the area of the base multiplied by the height, or specifically for rectangular prisms volume=(length)(width)(height). It took a while to find dimensions that would work, and then the struggle was with how to cut out the pieces to build it, and what pieces we’d need.

Some drew each side separately and taped them all together. Some made a foldable net.

When we got them assembled the goal was to check to see if the volume met my criteria of 300 cubic centimetres, and then I asked them to report on the surface area of paper required to build them.

Some groups had time to make several different boxes. And some realized after they made the box, that it wasn’t quite right, so they had to be redone. This small one has a volume of 90 cubic centimetres. It’s pretty cute though.

one group got really creative and persevered to make a box that was 100cm x 3cm x 1cm.

We will keep working on this tomorrow and consolidate with talking about how prisms with the same volume don’t always have the same surface area. We’ll arrange them to see any patterns, and connect the idea to surface area to volume ratio and how that’s important in packaging, and also in biology.

This task was pretty open ended, which caused some struggles getting started. We managed emotions like frustration pretty well, and we are continuing to work on our collaboration skills and working as a team to get tasks accomplished. We’re making headway on our clean-up skills which is allowing us to take more risks with hands on tasks.

I was quite intrigued to see this box being built at the end of class. We’ll have lots to chat about when we come back to this tomorrow.