Kramer Rocket Construction with Right Isosceles Triangles

I had the children draw their favorite triangles. I loved the diversity of triangles created by the children: acute, obtuse, and right triangles; scalene, isosceles and equilateral triangles. I told the Mathletes that my favorite is the isosceles right triangle otherwise known as a 45-45-90 triangle. This triangle is born from drawing a diagonal in a square. With some of the older classes, we discussed the ratio of the congruent (equal) legs and the hypotenuse (the longest side of any right triangle). This ratio is 1:1:root 2. We talked about the baseball diamond which is a 90 foot square and the distance from home plate to second base is 90 multiplied by the square root of 2, or 127 feet 3 3/8 inches.

I asked them if they would like to create their own isosceles right triangles (IRT) and we proceeded to do that with a standard rectangular piece of paper. First we folded an IRT with legs of 8.5 inches long, then four with legs of 4.25 inches, and then three IRTs with legs of 3 inches. The children noticed hexagons, pentagons, parallel folds and perpendicular folds, and beautiful symmetry. I then taught them how to trim their creation which is the paper airplane I created as a ten year old. This plane is designed to be thrown outside and I have found that throwing it vertically will produce the best results. I encouraged the children to throw their airplanes off of high places. Yes, there is a risk of littering if you cannot find the plane. My solution for this inevitable problem is to create an arbitrary ratio of 5:1; that is to pick up five pieces of garbage for every one plane lost. If you feel really guilty about littering, the ratio should be 8:1.

The attached pdf has very specific directions and different facts about the IRT. I also created a video of my hands folding this plane 

https://www.youtube.com/watch?v=SoO0Ejrxdd0&feature=youtu.be

I recommended that the children write their names on their plane and record the distance thrown.