8/6/2019 Playing With Blocks

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Playing with Blocks

Warm up: some students multiply numbers in their head by visualizing rectangles. Examples:

Drawapictureof3226ORfigureitoutinyourheadusingthisidea.

Background: Some teachers wanted a way to picture or visualize algebra. So they took the idea above to

invent Algebra Blocks. (Also called Algebra Tiles.) The idea is not that youd use these blocks your wholelife, but that they can help you understand the symbols and the ideas better if you can picture them.

Two related questions here:

Whatdoesthishavetodowiththemultiplyingstuff?

Whyisx2asquareandxastick?

Use: Mathematicians take ideas like take a number, double it, and add 3 and put it into symbols: 2x+3.Now we can also put it into blocks.

14

4

10

10

100

5

15

40

50

20

1415=100+40+50+20=210

16

6

10

20

200

3

23

so1623=200+120+___+___=_______

120

x2

x 1

Whatwouldthesymbols

forthisbe?

Howwouldyoudraw

2x2+x+3?

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Block Challenge

But we started with multiplication, and thats when the blocks get really interesting.

Mathematicians use this picture to prove that (x+1)(x+2)=x2+3x+2. How does this pictureshow that?

Whatdoesthispictureshow?Whydoyouthinkso?

Howwouldyousimplifytheresult?Whatwould

mathematicianssaythispictureproves?

Problems to try: try to do theses with the blocks and record in symbols. Some of these might be hard tothink about how to show with the blocks, since were trying something new.

1) Multiply (2x+1)(2x+1)2) Multiply (x+2)(x3)3) Can you make a rectangle out ofx2+6x+9?4) Can you make a rectangle out ofx2+x6? (Tricky. Requires unsimplifying.)5) Make a rectangle of your own. What multiplication does it show?6) Can you find a set of blocks that makes two different rectangles? What are the two different

multiplications you can show with those blocks.

Pick one of the problems to explain how you did it, in your own words.

Whatdoesthispicture

show? +

Whatdoesthispictureshow?!

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