Designing Buildings

The idea for this lesson is from Measurement in the Middle Grades, published by NCTM in 1994. It's still available here. I created this worksheet.

I purposely did not give the kids interlocking cubes to complete question 1 — wanted to see if they could count the number of windows and rooms from just the diagrams. A few students had some trouble counting the number of "windows" in Buildings D and F.

In question 2 below, students needed to create three buildings, each with a specified number of rooms and windows. I passed out interlocking cubes and isometric dot papers at this time.

While some kids could create a building, they have a tougher time drawing it on dot paper. Rapha had a suggestion for us.

Matt built this and wanted to know if it could be considered a "building." The class redefined it as "It's a building if it can stand without tipping over."

But before they attempted to draw the buildings, I asked them to give their building to at least one classmate to see if he/she would get the correct number of rooms and windows. They were very engaged to construct the buildings and draw them to complete question 2.

We were into our second day on this. At least half of the kids were now working on questions 3 and 4.

And these were some of the answers for questions 3 and 4.

They were very much into the building and drawing, so I went around to ask them what they thought of this lesson thus far:

It lets me be creative by drawing and making, see how it comes out.

It's difficult to count the windows. I check with my classmate and it's wrong!

This is awesome fun, question 4 is challenging, I'm still trying to figure it out.I'm stuck on creating Building 3, it's difficult, but I'm pretty close.

I like the different ways that I can build.

I never thought question 3 would make me think so hard like this!

Drawing is easy for me, it's more difficult to build.

The 3-D drawing got easier after Rapha helped me.

It's difficult. It's not working out (referring to creating Building 2), but it's fun to try to find it.

Very fun, I like it because I can help people with it, show them how to draw perspective.

My conversation with Sam about his paper:

Me: Help me read your answer to question 4.

Sam read it and added: Imagine a gigantic cube building... Well, all those rooms on the inside don't have windows. So, no passing the code!

Me: How big is gigantic? What size?

Sam: Hmmm... 25 cubes on each side?

Me: Okay, like 25 by 25 by 25.

Sam: Let me get a calculator.

Class was ending. I asked the students to finish this for homework. I let a few students take some cubes home because they asked. I look forward to Sam's calculations of rooms and windows for his "gigantic" cube. I look forward to our class discussion tomorrow — I've never heard both words "fun" and "difficult" to describe a lesson as often as I'd heard it here in this lesson.