This week’s activity is based on an old exam question that I now often put on one of our tests. And generally the kids are fine until they have to design a box that uses less cardboard than the original. Most of them leave this totally blank (I usually tell them I will not accept their test until they at least draw a box and label each side with a measurement).

So after the test, I decided we should physically build this problem. Physically manipulate the contents of the box. Here’s how it went down:

**Problem 1: Volume of the toy house**

The part here that trips them up on the test is the fact that you need to use Pythagorean Theorem to find the height of the triangular base for the prism that makes the roof. Most make the (false) assumption that it is also 5cm.

**Part 2: Surface area of a box holding 20 houses**

No problems here, really, since a rectangular prism is one of the easier solids for working with surface area.

**Part 3: Draw a paper net & build a model of the house**

I remembered that last year it took my students a really long time to draw & fold these. I thought it would be better this year. Wrong. It took a full 75 minutes for them to draw 1 net, copy it onto a 2nd sheet (each student needed to build 2) & fold them both into place w/ tape.

Also, I think next time, it would be beneficial to do this part 3 first. Build a model & then ask them to estimate the volume. So that they can see its size in real life. I’ll do that semester 2.

**Part 4: Design a box that uses less cardboard**

This is the part of the test that they have so much trouble with. But given the model houses as manipulatives, they can really envision the dimensions of the box. Also they’re working in groups of 2-3 which always helps the problem solving process.

As always, here is the link to all of my materials for this lesson.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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