I bought this lovely red book — and the blue one too — from the Shell Centre for Mathematical Education back in 2007 and paid a pretty penny to get it shipped from Nottingham, UK.

[07/04/14: This book is now available for free download.]

I noticed immediately that the book and the “Masters for Photocopying” were not of the size 8 1/2 by 11 inches (purple paper) that I’m familiar with. They were of size ‘A4’ or 210 by 297 millimeters. Not a big deal. I ran the masters through the copy machine and was pleased with an identical set in the “right” letter size.

Fast forward to 2012. I pulled out the activity above called “Warmsnug Double Glazing” and thought it’d be great for my 6th graders. The first page of the two-page worksheet has diagrams of “windows,” each one labeled with a letter and a price (in pounds of course).

Two questions are posed on the worksheet:

**How have Warmsnug arrived at the prices of these windows?****One window has been given an incorrect price, which one is it and how much should it cost?**

The second page gave too much information — and direction — given to the kids so I ignored it.

I did some pre-measurements of the windows before the students came in and got “weird” numbers, like 3.7 cm by 1.2 cm, give or take. Oh well, the British likes their students to work with decimals. More power to them. And anyway, this will drive home my point that “nobody promises you whole numbers.”

Here are windows *A* and *B* on the page.

I randomly assigned the students to groups of three. As they began the activity, we discussed these key points:

- The price of each window depends how much glass is used.
- The price also depends on how much frame is needed to hold the glass panes in place.
- The frame costs more than the glass.
- Finding the amount of glass is finding its area.
- Finding the amount of frame is finding its lengths.
- Measure in centimeters to the nearest tenth.
- Keep an organized table of measurements and calculations.
- Divide up the work among group members — maybe each person is assigned 5 windows.

The kids seemed to be working hard.

But there wasn’t a whole lot of talking — like they normally do with an activity like this. I yelled at two students because they weren’t busy measuring. I love these kids, and I hate yelling at any one of them.

I wanted to check in with the whole class to see how close the measurements were among the different groups. We went over window *A* together. While the groups were within one square centimeter for the glass area; their measurements were all over the place for the frame lengths.

The bell rang. For homework, I asked each student to measure at least three windows.

Two hours ago I sat down at my computer to do some more lesson planning. I stared at the red book on my bookshelf and instantly felt flushed with dread and shame. I said something like, “O shit. Size A4. Size A4. I shrank A4!! No wonder the windows were a pain to measure!!” (Or a pane to measure. Get it? Haha. I hate myself.)

Bright and early tomorrow I will make copies of the original master AS IS!! I will give my 6th graders their favorite candies. I will shower them with apologies and ask for their forgiveness.

The lesson itself is demanding already for 6th graders. They are really dealing with system of equations, two variables, the price of glass per square centimeter and the price of frame per centimeter. I will ask them lots of questions, guide them, help them along. I’m hopeful that these 6th graders can grasp this activity and get a head start on this important and useful algebra 1 topic.

What they didn’t need was to have a terrible entry point into the lesson by having to needlessly measure to the tenth of a centimeter. Oh, look, the length of window *A* on size A4 paper is exactly 8 centimeters!

Then I found the same lesson online! However, they revised the worksheet — the windows are now on **grid paper**. That’s nice, but I want the students to measure with a good old ruler. They also have 3 different worksheets, each progressively more challenging.

Aside from my screw-ups, I sincerely recommend this lesson — it’s a different way to approach system of equations that incorporates lengths and areas and measuring and manipulating data.

The activity went so much better today!! Four groups had figured out the cost per square unit of glass and cost per unit of frame. We will wrap this up on Monday.

My scanner won’t scan 1:1 or I don’t know how to do it, so I just recreated the WINDOWS worksheet. (The correct answers to the original worksheet is $2/unit of frame and $1/square unit of glass. This was challenging enough for my 6th graders.)

But with older (algebra 1) students, you may want to change the price of each window to make it more challenging — maybe have the frame cost $4/unit and the glass cost $3/unit.Therefore I purposely did not indicate prices on the windows I’d drawn above. Here is a warmsnugs Excel sheet that I made to make it easy for you to just pick a certain set of prices for the windows depending on what you want each unit of frame/glass to cost.

**Don’t forget to mark one the windows with an incorrect price!** Window *I* in the original lesson has the wrong price.

system of equations The Language of Functions and Graphs Shell Centre Warmsnug Double Glazing asking questions problem solving A4 paper area perimeter ratios proportions

## One Trackback

[…] I did this last year. Really great lesson. I’m adding an extension of having kids create a set of 8 windows and price them accordingly, give the price of each one, including 1 of them as incorrect. So, pretty much duplicate the lesson with their own pictures and pricing scheme. […]