When teaching proportions or similar figures I generally throw in an example or two of measuring the height of objects you wouldn't normally be able to measure using shadows or various other known distances. Since I've been on my activity/experiment kick, I wanted to go measure shadows to find the heights of trees and telephone poles. However, it's January in Michigan. Nobody wants to go outside and measure shadows, which assumes there will be a sun to cast a shadow. There are sometimes weeks that go by without seeing the sun up here.
Enter a brilliant adaptation by Jonathan Claydon for the cannot-go-outside-for-5-months-because-we-live-in-the-midwest group of people. I have my adaptation of it at the bottom of this post.
Students start be measuring each member of their group (see below). This measurement is known as the group member's 'real height'.
Enter a brilliant adaptation by Jonathan Claydon for the cannot-go-outside-for-5-months-because-we-live-in-the-midwest group of people. I have my adaptation of it at the bottom of this post.
Students start be measuring each member of their group (see below). This measurement is known as the group member's 'real height'.
Then groups drift off to the gym to find the height of objects that are too tall to measure easily. I picked three of them: the gym ceiling, the top of the backboard, and the height of the railing on the weight room. Using a ruler, group members find the 'fake height' of a each group member standing next to the too-tall object and the 'fake height' of the object. We found both measurements need to be recorded each time because of differences in how students hold the rulers.
After completing our measurements, we went back to our classroom to finish the calculations. Each group member had to find the heights of the objects using their own fake height measurements. Then groups posted a group height for each too-tall object. Lots of good conversations happened when calculated heights didn't agree. Most groups just averaged the calculated heights for each too-tall object.
Next, we figured out how we would go about agreeing on the actual height since I don't have the actual measurements myself. With our ceiling calculations, we decided to remove the group's height which was very different before averaging the heights.
Next, we figured out how we would go about agreeing on the actual height since I don't have the actual measurements myself. With our ceiling calculations, we decided to remove the group's height which was very different before averaging the heights.
The class's backboard heights weren't nearly as close. Here we thought the median might be a better descriptor of the 'real height'.
| Aside: I am horrified at the rounding in this next picture of my blackboard. I wrote the numbers students told me to write without correcting their rounding errors. In hindsight I should have forced them to be correct (or attend to precision) but we were hurrying to get done before the bell. ...Plus it makes me look like an idiot. |
Here again, the 'real heights' were all over the map. They thought the median worked out well last time and wanted to use it again.
When we talked about difficulties we encountered, several students said they had difficulty eye-baling the measurements because they couldn't hold their hands steady. When I do this again next year, I plan to hand out a jumbo paper clip to put on each student ruler to serve as a marker for the top measurement.
Thanks to http://infinitesums.squarespace.com/commentary/2011/9/30/proportions.html for the idea!
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