Similar Triangles and a Self-Checking Physical Challenge: Mirror, Mirror on the Floor

Yesterday in Geo, I took some advice from Dan Meyer “You Don’t Have To Be The Answer Key” and set up a fun self-checking activity based on this blog post, Eye to Eye. The premise: place a sticky note on the wall, and then place a tiny mirror on the floor between you and the wall so that you can glance into the mirror and see the sticky note. The catch is that you can’t just stand and move around until you can see it, you need to place yourself, open your eyes and look, and see if you see it! The mirrors I found in the physics department were probably 3 inches in diameter, which was perfect for a little bit of precision, but enough wiggle room that this worked. It was fun because students would be really excited that it worked! And if it didn’t, they would just go back and check their calculations without needing direction from me.

Here were the three situations (I gave them the text and then they needed to show me their diagram kind of like the ones I drew below, and calculations before they were allowed to try it physically):

1. The sticky note is 7 feet up on the wall, and the mirror is 3 feet from the wall. Where should you place yourself so you can see the sticky note in mirror?

mirror1

2. Now place yourself 5 feet from the wall, and place the mirror 4 feet from you. Where should you place the sticky note so that you can see it in the mirror?

mirror2

3. Now place yourself 5 feet from the wall, and place the sticky note 3 feet up. Where should you place the mirror so you can see the sticky note in the mirror?

mirror3

These got more difficult as they went a long, and kids did a great job with the last one solving it in a ton of different ways (most using some sort of x and 60-x on the bottom). My favorite was a boy who measured his eyes to be 63 inches off the ground.

“Well, I’m 63 inches tall, so the ratio of my height to the sticky note is 63:36, which simplifies to 21:12, but 21+12 = 33, so if I break the 60 inches on the floor into 33 pieces and then multiply that by 12, that’s how far I should place the mirror from the wall.”

Cool!