They quickly thought of 2 + 2 = 2 * 2. I liked hearing students saying that since they found one case that worked, it couldn't be always nor never. Someone also said that it worked for 0 and 0. I asked if it could work with two numbers that were different from each other. I left them thinking about that one.
Back to our 26 squares. I first asked them to make something with their squares. I saw a rocket, a caterpillar, a cat and many towers. They didn't seem to be moving toward making triangles so I asked if they could use their squares to make a mathematical shape. It took a bit, but someone finally made a triangle so I asked others to follow suit. They got the idea of how to make a triangle and that the corners needed to match up. I asked if they could make a triangle with any three squares. Most said yes. I then chose three of their squares that could not form a triangle and asked them to make one. This was followed up by me asking how you could know whether it would work. We eventually all came to the conclusion that the sum of the two shorter sides had to be longer than the long side.
On to right triangles. We defined a right triangle and I asked them to use their squares to determine whether the triangles listed (see below) seemed to contain a 90 degree angle. Here are a couple of pictures - the first one worked, the second one didn't.
They had to come up to the SMARTboard and either cross out or place a check mark next to each triangle. Here is the list (updated to remove those that were not obvious).
They filled in this handout with the nine cases that worked.
and I asked what they noticed about the areas. Many blank stares... I asked a student what he noticed about the triangle with areas 100, 576 and 676. They are all even numbers (true, but not all areas in the table were even numbers - what else do you notice?). The 3rd number is bigger than the other too (yes, by how much?)... Eventually we got to noticing the the third area was the sum of the other two.
On Monday we will see how we can use this information.
This reminds me of our PT activity http://engaging-math.blogspot.ca/2014/12/the-area-representation-of-pythagorean.html
ReplyDeleteIt does look a lot like that! We have done this for several years, but wide-open which has proven problematic. I liked giving them a list to work with.
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