This image is from the “Grocery Store, Stamps and Measuring Strips” Context for Learning unit. I love this unit and think it is a great way to introduce multiplication to students. At the end of the unit, students are asked to look at this image. (Note: I am only including part of the image because this is not my work and I don’t want to violate copyrights!)
We had done all the proportional reasoning work before this: figuring out how tall or long everything on a city street (trees, a bus, a few buildings) might be in relationship to 4 foot tall Antonio. It was time for some final assessment.
“How many design elements are on the curtain?” I asked. One image shows a full extended shade, with 16 (maybe 20? I forget) oranges in an array. The grade 3’s easily told me the total, and explained how they had counted. Lots of multiplying I was very happy to note. But they said there were 14 stars on this shade, and 12 or maybe 18 diamonds* on the other curtains. They debated it for a while. Then I said, “What if I stretched that shade so it covered the whole window, just like this one with the oranges?”
Blank stares. The 5 of them looked at each other. They looked at me. They recounted the 14 stars and 18 diamonds*. They weren’t sure what I was asking. “Well, we can see part of the window in each of these, and there is light coming through. But what if the curtain was closed? What if we could see the whole shade?”
They thought some more. They used their fingers to measure. They finally decided that if there were 12 on one curtain, there must be 12 on the other, and 2 groups of 12 = 24. . The roller shade wasn’t as easy, but once they figured out the curtain they had a strategy. “I think,” said one, “that there would be 3 more rows of stars. So thats 7+7 doubled, plus 7 more.” OH MY GOODNESS! Proportional reasoning AND partial products??? I could not have been happier. Everyone agreed, then took turns explaining how they’d counted the stars and diamonds.
I’m calling this unit a success!
*We are calling them diamonds instead of rhombuses because they don’t have parallel sides that are straight, and the angles aren’t right for rhombuses.
7 thoughts on “Proportional Reasoning is so cool!”
Can I sneak into your classroom and steal you for my kids? I am really struck by how clearly you know what you’re looking for in your observations. I suspect that I would have seen children counting on their fingers. Your gleeful identification of proportional reasoning and partial products is evidence of your depth of understanding of the development of mathematical thinking. Enviable knowledge!
There is always room for more kids my classroom. Well, actually there is a finite amount of room, but we could squeeze a few more in. 🙂
It is great to see young minds at work.
You are the math teacher that I wish I’d had! 🙂 You rock!
Why thank you. I do really enjoy teaching math. 🙂
Wow! I’m so impressed with this math talk too! I could learn a thing or two! Loved listening in on these math conversations!