(2x – 1) (3x + 2)

(2x – 1) (3x + 2)

(2x – 1) (3x + 2)

(2x – 1) (3x + 2) 6x 2

(2x – 1) (3x + 2) 6x 2 + x

(2x – 1) (3x + 2) 6x 2 + x - 2

Use the tiles to show these multiplications. Make a sketch of your model. Label the dimensions clearly. Draw arrows to show any tiles that add to zero. Write the product. 1.2x(x – 1) 2.(x + 1)(x + 2) 3.(x – 2)(3x + 3) 4.(x – 3)(x + 3) 5.(2x + 2)(2x – 2) 6.(x + 3)(x + 3)

(x – 1) 2x “This was kind of an easy one, but if they didn’t put it into a rectangle now, this would surely be a problem later on. So I pushed the tiles together into a rectangle for them and told them that thy needed to pay attention to how the tiles on the dimensions were related to the tiles forming the product. As I rearranged the pieces, I told them it was like a puzzle and to think about it. I wasn’t sure they knew what I was talking about but at least they had a rectangle now.”

“I was beginning to get nervous. The groups had been working for about half the period and I saw only one group that had completed more than half of the problems with the correct picture and symbol solutions on their worksheets. My hints did not seem to be getting them moving in the right direction.”

“When I asked the group that was farthest along if they could explain to the class how they got their answers, Malcolm, the group leader, explained to me that they had worked the problems using the FOIL method from yesterday and then figured out by trial and error how to fit the tiles together to make a rectangle. Part of me wanted to scream when I heard that.”

(2x + 2)(2x – 2) Hakeem:First you gotta get all the pieces for 2x + 2 and for 2x – 2. MB:What’s the next step? Tonya:Put the first parentheses down the side and the second one across the top. MB:What should the 3 rd step be? Malcolm:Ms. Butler I just figured it out. Can I show it?

(2x – 2) (2x + 2) “Look, you can figure out what pieces to use just by matching up the lengths going down and going across. See, you need this much going down and this much going across so it has to be one of these square ones. And you just do that until you got ‘em all.”

(2x – 2) (2x + 2) “Does the +2 and the -2 mean you should do something different?”

(2x – 2) (2x + 2) “Oh, yeah, these ones have to flip over because they are underneath the shaded blocks.”

“When I thought about this lesson later, I had mixed feelings. On the one hand, I was happy to see Malcolm get up in front of the class, especially since he actually came up with the right answer. On the other hand, when I really thought about what he had said in his explanation, I had to ask myself, how mathematical was it? Was he making any of the connections I was hoping for? Was anyone else?”