Welcome back,  today I will be explaining the process of answering the driving question:

“How can we test the pythagorean theorem and the law of reflection?”

First off, what is the pythagorean theorem? The pythagorean theorem is the sum of the legs of a triangle that equal the hypotenuse (the side opposite from the right angle). 

After learning some more about triangles and the law of reflection we learned how we were going to prove it-by creating a laser triangle display! (more about that later). Creating a display all by yourself and doing the math and other things would be a lot of work so we were put into groups. The people in my group were,

Jupiter, Luca, Frankie, Mackenzie, and of course me.

Now onto the big load of work…

To show a bit more of what the display was supposed to be for this project here is ours:

It is basically a cardboard base decorated to a certain theme (your choice), then a triangle gets drawn on and you put a mirror on two corners of the triangle and the laser at the corner with no mirror.

After getting into our groups we had a little bit of awkward silence, but soon after we started working. The first thing we did was find a good pythagorean triple to use to create the triangle. The one we used was: 6² + 8² = 10²

Luca drew out the triangle as we all planned out the design and theme, and once we had the triangle down we started creating our design plan. Since we got blue paper to cover the base we decided the theme should be the sky (a group already did the sea). Here is some of the process:

Getting the laser to line up with the mirrors was hard, the goal was to get the laser back to “home base” (back to the laser pointer). To make it easier we had the laser supported in a support actually for the mirror. When we put it in the support we would move it around to try and angle it correctly so it would bounce from mirror to mirror. I found that it worked better when it was being angled a little bit up. The laser was finicky though, if you left it on too long it would burn out. Sadly our laser burnt out quite fast even though we didn’t even use it for that long. 

Finally, after finishing up the board and adding the final decorations we ended up with this:

Then the next day we transferred it over to Mr. Grosses room and added smoke to it. The reason for this is because when the laser’s on you can’t see it very well, but when you add smoke and turn the lights off you’re able to see the beams of light very well. Sadly, our laser died so we didn’t get very many good photos but here are some of the ones we took.

I think that we were able to prove the law of reflection and the pythagorean theorem. Even though our triangle didn’t work well in the dark we did get the light to bounce of all mirrors in the correct angle and direction.

Here is a mind map of some of the things I wondered at the start of the year and then I answered some of my questions and put down some things I learned.

.｡.:*☆Answering the core competencies☆*:.｡.

1. Questioning and predicting:  Demonstrate a sustained intellectual curiosity about a scientific topic or problem of personal interest

I think I used my class time effectively and I payed attention to what was being explained, questioning myself along the way. For example, I questioned if  using a pythagorean triple would make it easier to create a laser triangle outline. 

2. Communicating and Representing: Represent mathematical ideas in concrete, pictorial, and symbolic forms

I think I did ok in this since I understood the simulators yet I wasn’t the best at using them. But I was helpful when creating the display which was hands-on. 

3. Applying and innovating: Cooperatively design projects

When our laser burnt out we had to disassemble our display. We worked together quickly and got it done fast. We had to do it twice but each time it worked out fine, and our design never got compromised by our misshaps. We listened to each other’s design ideas and I feel each group member’s “voice” was heard when creating it because everyone pitched in.