Hello everyone! Today I’ll be sharing my 2nd summative post for scimatics on my blog. The final task for this project was to test the Pythagorean Theorem an the law of reflection by creating a laser display! Our driving question for this project was: “ How can we test the law of reflection and the Pythagorean theorem?
Now before making the laser display right away, we needed to learn about light and the law of reflection, as well as the Pythagorean theorem.
When we first launched into this project, which was in late November for the record, we did a fun entry event against the other scimatics class across the hall. It was a mock up laser tag game, where there were two teams. Each team had to set up their target ( plastic container ) and their barrier (wood), somewhere in the classroom. Then, with our laser and the help of two mirror stands, you took turns trying to hit the other class’s target. And even when the other class’s target was blocked by a wood barrier, we figured out how to position the mirrors to hit the target. I really liked this entry event because it got me questioning about lasers.
I created a project start mind map with some of my need to know questions, and added to it as the project went along:
Then we practiced the pythagorean Theorem by doing some math textbook pages. But what is the pythagorean Theorem?
The pythagorean Theorem was discovered long ago, in Greece, by a boy named Pythagoras. He discovered a unique relationship between the sides of right angle triangles. The theory states that the square of the length of the hypotenuse is equal to the the sum of both other sides of the triangle, squared.
In mathematical formula: a2 + b2 = c2
- a = side of a right triangle
- b= side of a right triangle
- c = hypotenuse
We cut out squares to try to visually depict the the Pythagorean theorem formula.
By practicing solving problems using the Pythagorean theorem, we also learned about square rooting ( √ ) , perfect squares ( 25 is a perfect square because 5x 5= 25 and 5 is a whole number ) and what Pythagorean triples are.
Then we learned about the science part of this project, which is the law of reflection.
I learned that there are 3 different types of mirrors: convex mirrors ( curved outward), concave ( curved inward), and plane mirrors ( flat mirrors). Depending on what mirror, the light reacts and reflects differently.
The law of reflection states that the angle of incidence is equal to the angle of reflection. The normal is an imaginary line perpendicular to the mirror or reflecting surface, and the angle between the normal and the incident ray is the same as the normal to the reflected ray. Also, the incident ray, the normal and the reflected ray all lay on the same plane. To help you visualize:
Now armed with a bunch of new information on the Pythagorean theorem and how light behaves, it was time to prove our knowledge! Before creating our final laser display, we each did an individual lab report. Our driving question was: “ How can we test the law of reflection and the Pythagorean Theorem, using the online optics simulator?”. My science teacher in seventh grade told the class to make sure our lab reports had every step be very detailed, so that if you handed the steps to your sibling or to someone else in the school, they could be able to follow the steps. I’m super proud of my lab report, because the steps are very clear and I explained most of my thought process. I also included possible sources of error in using the online optics simulator. Here are some of my diagrams that I include in my lab report. 
My milestone 4 triangle measurements didn’t prove the Pythagorean theorem, but the answers were so close to being precise. After several more tries, I was only able to prove the law of reflection using the finicky website.
Now let’s get building our laser displays !
For this final task, everyone was put into a group of 3-4 people. My group consisted of Chris, Caden, Hayden and I. The first step in making this imaginary creation come to life was to decide on the measurements of our triangle. We researched possible pythagorean triples, and decided on 28, 45 and 53 for the lengths of the sides of our right angle triangle. Then we calculated the angle at which the mirrors should be placed at two out of three vertex’s of our triangle, to prove the law of reflexion.
My teamwork skills showed as I took a leadership role in making sure we were being productive and using our 3 class times to design, create and make our laser display come to life. When someone asked me what they should be doing, I told them what I think they could help with. I brought posca markers / paint pens to add some color to our basic black background paper.
Here are some photos of the making of our displays:
When all the laser displays were complete and we were able to power up the laser, we got to go into the other scimatics classroom with our displays. Mr. Gross turned off the lights and sprayed smoke onto our laser triangle displays, and the laser shined so bright, you could clearly see the outline of your triangle. It didn’t capture the coolness as well in photos but just to give an idea:
Overall, some people’s displays looked more visually appealing than ours, which I was worried would take off marks, but our triangle proved both the Pythagorean theorem and the law of reflection, and that’s what the project criteria was. The triangle measurements are labeled and traced in white so that the writing stands out. Our laser followed the traced outline of our triangle precisely and connected back to the start. I loved how you could see dust particles moving because they were illuminated by the laser.
Curricular competencies and the answer to our driving question:
Questioning and predicting: Demonstrate a sustained intellectual curiosity about a scientific topic or problem of personal interest
Throughout this project, I’ve been interested in all the new information I’ve gained. I have been participating in class discussions, group projects and even the correction of our worksheets. When it came to homework, I would try to get as much work done in class to avoid having to do it at home. When building our final laser displays, I was constantly working or trying to figure out the next steps.
Communicating and Representing: Represent mathematical ideas in concrete, pictorial, and symbolic forms
I relate this curricular competency to my milestone four lab report, because I developed my own scientific procedure with detailed step by steps. By using my measurements and math as proof, I was able to come to a conclusion about the law of reflection and the Pythagorean theorem. An opportunity for further growth in this competency would be to explain my math calculations and a bit about the behaviour of light into further detail.
Applying and innovating: Co-operatively design projects
This competency has to do with teamwork while designing our laser triangle. Our group was pretty organized and assigned people to bring so and so materials into class. I think we definitely could’ve made our display prettier and done more with our 3 class times. Our laser triangle worked though, and our measurements must’ve were correct, because the laser followed the path of our traced triangle.
We were able to prove to answer our driving question: “ how can we prove the law of reflection and the Pythagorean theorem?” There are actually several ways you can prove both of these, but the way we proved both the Pythagorean theorem and the law of reflection was by creating a right angle triangle with a laser/ our laser display.
Anyway… if you made it to the end of this post… you’re amazing! Thanks for reading my blog post, I know this ones was extremely long. I wonder what our next scimatics project is going to be… stay tuned!