Measuring by Magic: Shadows and Mirrors

We had some unusually warm weather a week ago and the kids were all clamoring to go outside; I said "next week" not realizing the temperature would drop so dramatically. I should have known - I've lived in New England my entire life - but I certainly wasn't going to start having class outside just because it was warm out in March! Imagine the begging I would hear in June... So, we measured using shadows when the thermometer read 30-something and opted to use mirrors in the lobby, where there was heat and high ceilings (the entryway spans all three floors).

Indirect Measurement

Before we headed outside, we looked at the diagrams and determined why this method would work. Similar triangles was an obvious answer since that's the unit we are on, but they know better than to just assume triangles are similar. Important facts: pick something that is at 90 degrees to the ground and on level ground (our flag pole is on an impossible to measure cliff), hold the meter stick vertical, the sun is reeaallly far away (doing this inside with a lamp would not work) and finally when looking in the mirror you must stand up perfectly straight. We neglected to mention accurate measurements, which I discovered when we got back to the classroom and some students were calculating in terms of feet with no spare inches. I'm pretending that's due to rushing in the cold (yes, I know the mirror activity was inside, fine, I'll note their inaccuracy when I comment on their work) and will be sure to mention it with my other classes next week. Overall it's a fun activity that gets kids looking at applications of math in a non-contrived way. I even went on a little tangent about just how hard it is to measure trees- tall, hard to climb, branches everywhere so even if you reach the top, how do you know how high you are?? Problems like these also encourage students to estimate and check how reasonable their solution is. We know the lamppost is taller than them but shorter than the building so the answer had better fit in that range.