MFM2P - Day 14 (Sum of Squares)

We did another counting circle as a warm up today. We started at 57 and went down by 3 each time. At one point I stopped them (at student A) and asked what number we would be at when we reached <student 4 away from current student> (student B). Some counted down by 3 for each student from student A to student B, others counted the number of students to get to student B, multiplied that by 3 then subtracted the result from the number for student A. They did this well.

Back to our list of right triangles and their areas. We spent more time than I thought we would discussing how to recognize the longest side in a right triangle. This is what they were looking at:

and one student said "the bottom line" was the longest then changed his answer to "the bottom line and the diagonal line" were the same length. We talked about isosceles triangles and figured out that if both angles were 90° we would not have a triangle. They told me that the sum of the angles in a triangle was always 180° so I asked them what they knew about the two non-right angles in the triangles. They figured out that together they would be 90° so each would have to be less than 90°. Combining that with the fact that the longest side is always across from the largest angle, we found the hypotenuse!

They were now ready to use the Pythagorean theorem, known to them as the Sum of Squares, to find missing side lengths. First, they cut out and glued an example in their exercise books:

We worked through the connection between the areas as some had already forgotten and I we worked through how to find a missing side length. They practiced with 3 more examples; one had them find the length of the hypotenuse, the other two had them find the length of one of the legs (two are shown below).

Once they did those correctly (there were a lot of errors - finding the perimeter instead of area, dividing by 4 instead of taking the square root...) they got a sticker (because even 15-year olds like stickers) and started working on this handout which we will continue tomorrow.