Part 1: The Mattresses
I asked the kids to guess how the size of the little rectangles on paper compare to the real mattresses. (It’s 2% of actual.) We ignored the thickness.
Then I asked them what the scale factor would be. Many didn’t know.
Next, with a partner, I had them cut out a set of 5 mattresses from construction papers, a different color for each size. Each paper mattress needed to be 8% of the original.
I almost threw out this cutting part because I didn’t really have a follow-up for these pieces, but seeing how some struggled with measuring and cutting that I’m glad I kept it in. Here’s a set 8_of_actual_mattresses (of the 8%) that we used as a key to check for precision.
Based on the given price of a certain size mattress, how much should the other sizes [of the same type] cost? And they had to explain how they arrived at the prices, based on what criteria.
Part 2: The Flat Sheets
The Bedding handout. To give them more practice with “finding the percent of,” I told them that flat sheets are made so that the width is 160% wider and the length is 130% longer than the width and the length of each sized mattress, respectively. Knowing this, find the dimensions of each sheet.
Then I gave them the price per square foot of each brand of sheets set, and they needed to figure out the rest.
I thought it went well. (When I spend too much time creating a lesson, I convince myself and the kids that it’ll be awesome. It kinda works.)
A very simple rates/proportions lesson, but I’m reminded of some key things:
- The kids weren’t cutting for the sake of cutting — we’re not here to make stuff pretty, we’re here to make things accurate, and in doing so things look pretty. They had to use a ruler to mark two end points before drawing a segment. They had to understand the significant digits allowed by a simple ruler. Decimals are still tricky for some. Junior high boys are more clumsy with scissors. It’s smart to draw the rectangle in the corner of the paper instead of smack dab in the middle of the paper.
- Student to his partner, “Finding the perimeter doesn’t make sense. We have to find the area because that’s the material you sleep on.”
- Eight percent is not point-eight.
- Their proportional reasoning is still developing.
- Dividing by 12 is not how you change square inches to square feet.
- “But that’s what the calculator says” is a poor excuse on any day of the week.
The idea of unit rate needed a lot of attention and review. Kids weren’t sure to divide price by area, or divide area by price. What I learn regularly is kids will take two numbers and operate on them, but they don’t know what the answer means and what unit the answer carries.