Today we pulled out the 26 squares and students were asked what they could make with them. There were houses, stars, stacks of presents, a horse and a triangle. They then all had to make triangles. Could they make a triangle with any three squares? They said "Yes!". So I pulled out two small squares and one large square and could not connect the corners. In groups, they had to figure out a rule for how to choose 3 squares that would form a triangle. This was a little like pulling teeth, being a little after 8 am. I circulated and choose examples like squares of side length 8, 13 and 21 and showed them that if I connected the outside corners I then needed to make the two shorter sides completely flat against the third side to connect those corners. What was special about the squares I chose? Someone figured out that 8 + 13 = 21 (or whatever the values were for that group) and then they said that the two shorter sides had to be longer than the long side. "Write that down!" We talked about what kind of triangles they would be able to make with the 26 squares which took us to right triangles.
Which squares could you use to make right triangles. I offered them grid whiteboards to help form right angles and some groups did pretty well at finding combinations that worked. Some were close so I pointed them in the right direction "It's not 16-20-25, but try replacing the 16." Eventually this is what we came up with:
Tomorrow we will finish the tables and consolidate all of this.