26 Squares – Sum of Squares #MFM2P

I’ve started my #MFM2P course again this year with a set of activities using the 26 Squares thought up by Al Overwijk & Bruce McLaurin (there’s a write-up about how Al uses them here). The 26 squares are a set of squares cut out of grid paper; a 1×1, 2×2, 3×3, … all the way to a 26×26 square. Each group gets one full set.

We started with the perimeter investigation that I blogged about last year.
Summary 2016.09.09 (1) (1).png

Our second activity was the area investigation that I blogged about already last year.
Summary 2016.09.13 (1).png

Our third activity involved creating right-angled triangles with our 26 squares, starting with a 3-4-5 triangle:

Students were asked “What do you notice?” about this and other right-angled triangles made from our squares. Several commented that the area of the two smaller squares add together to make the area of the largest square (well, it took some prompting to get them to express themselves w/ the proper mathematical terminology!). And they remembered from past Math classes that this is the Pythagorean Theorem with the equation a2 + b2 = c2.

I gave students the measurements of 3 sides of a triangle and asked them to verify if it is right-angled or not. I forgot to take photos, but they all had the idea of using the P.T. equation to check that the two side are equal.

Finally I gave them this problem:
A right triangle has two smaller sides measuring 28cm and 45cm.
Determine the length of the longest side:IMG_20160915_113624 (1).jpg

The homework was to practice Pythagorean Theorem on Khan Academy.

26 squares
Perimeter investigation w/ Pear Deck
Area investigation w/ Pear Deck
Sum of Squares investigation w/ Pear Deck

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)