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 — in pdf designing_buildings and docx designing_buildings — using Illuminations’ nifty isometric tool to draw the shapes.

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.

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