This week, I decided to create a 3-act task on proportional figures. I decided to use body measurements to represent the diameter of the proportional circles. I thought my students might get the idea of ratios more easily this way and that they would be able to see that my new shape was 1.5 times bigger directly with the body measurement I used.
To my surprise, they most of them found the ratio by comparing the area of the circles. I wonder if it is because they previously developed a metaphor about area being the size of a shape.
As for the outside measurement, I decided to create a path for my dog. To give a little context, I have a small dog who likes to sniff around the tree on my lawn. Now in Schefferville, it is snowshoes season (we need snowshoes to walk around). My snowshoes are around 70cm long.
When she goes outside, my dog is tied with a long leash. Because my dog is small, she needs trails to be able to walk around the lawn.
I want my dog to be able to get closer to the tree (she loves to sniff over there), but I don’t want her to be able to reach the driveway next to it. Thus, I decided to measure the length of the leash with my number of steps (with snowshoes) and then use this number of steps (length) to create her a path that does not make the driveway accessible. It was useful to measure with snowshoes because my path is not straight forward. It allowed me to measure the length of a path mixed with curves and straight lines.
I think that the idea of mathematics a realm of “pure” thoughts also brought the idea of the need for precision. The metric system allows us to be precise in our measurement, but it is not always the most efficient way to measure. It was much quicker and efficient to create a path for my dog by measuring with snowshoes than using a measuring tape because I was able to make straight lines and curved lines while measuring. It is also much easier to remember that my snowshoe is about 70cm long and to visualize this distance in my head than a meter, and I know it is true for my students as well (see reflection below).
I have noticed a within looking at body measuring there is a theme of convenience and efficiency in the discussion of when or why we use it. I love that you took this outside and used the snowshoes to create this the path with both straight and curved lines.
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Thinking about when we use the metric system and seek that kind of precision has me considering how much I use it and reflecting on when do we really need to use it. Throughout this week I have been thinking of the ways to incorporate the body more but additionally I have been thinking of moving towards less of a consistent emphasis on the metric system when working in with my class on measurement and more intentionally using it to model a real world approach.
Thanks Noemi and Colleen! I love that you took this outdoors too, Noemi. And what a great purpose and measurement source: your snowshoes and your dog's leash! There's a very important discussion within your group and the class about the relationship between precision and estimation, and how these interact in our practical lives. This might be a great discussion to have with your students as you try out some of these measurement activities!
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