Falling Bridges (extra activity)

We had planned a special "Falling Bridges" activity based on some 3-letter acronym teaching style.

I began by talking about the importance of math in building structures, then showed a couple of video clips about the Tacoma Narrows Bridge collapse.



After the video we looked at a worksheet where an engineer determined a value for what the bridge can hold, and Sam made a sign with an improper value. We looked at how rounding error can drastically effect the end result of a problem.

After teaching a couple sections I changed my wording in the presentation of the problem and had the students pretend to be judges trying to figure out who is at fault for the bridge collapse. This activity engaged the students and I would like to rework the activity to increase how engaged students are.

9.3 part 2: 30-60-90 triangles

Here we used isometric dot paper to run an experiment similar to the one from 9.3 part 1. This experiment involved creating triangles that had the base 'a' and hypotenuse '2*a' with integer values. Using the Pythagorean theorem we notice that the second leg was 'a*sqrt(3)'.

After looking at the case were the base was a=1,2,3,4,... students started to piece together the pattern.

Now both of the "special" right triangles were covered and we took a little bit of time to look at how to find the other two sides given one of the other sides of this triangle.

9.3 part 1 (Isosceles Right Triangles)

I took chapter 9.3 and broke it into two parts. First we looked at isosceles right triangles. We used square graph paper to compute the hypotenuse of some isosceles right triangles, and we noticed a pattern to extend to any isosceles right triangle. So the students figured out that if both legs have length 'a' then the hypotenuse has length 'a*sqrt(2)'. Now to figure out how to get the 'sqrt()' symbol to work in web-pages and blogs. I'm surprised more people don't use math symbols all the time...

9.2 Converse of the Pythagorean Theorem

Here we looked at how we can use the Pythagorean theorem to determine if a triangle is a right triangle. So we use the Pythagorean theorem in reverse. We also learned about some common Pythagorean triples.

If a^2 + b^2 = c^2, then we have a right triangle.

There was time to do homework in class.

Chapter 9.1 The Theorem of Pythagoras

This chapter begins the Pythagorean theorem for the students.

We went over that if you have a right triangle you know that the three sides have the relationship a^2 + b^2 = c^2, where a and b are the legs, and c is the hypotenuse.

We learned to find the length of the hypotenuse given 'a' and 'b'. And we learned to find the length of a leg (a or b) given the other leg and they hypotenuse.

This was basic and repeated many times over the semester.

Chapter 9 (Tri Square Rug Game)

We used the tri-square rug game to begin the unit on the Pythagorean theorem. Unfortunately my class didn't take well to this. There was a lot that the students needed to cut out, and would probably go more smoothly if things were cut out and prepared for students ahead of time.

Also the game doesn't make sense to the kids. I would like to try and create a game that we could modify into a tri-square game. I think that if we had a game, and played it, then it would connect better with the students.