Introducing Tak-tiles

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Presentation transcript:

Introducing Tak-tiles Algebra using areas

Adding Areas This has an area of a and this has an area of b area a area b This has an area of a and this has an area of b So this shape has area a + b area a area b

= 2a + 2b 2(a + b) Think about this shape; It could be made like this Or like this a + b a + b 2a + 2b = 2a + 2b 2(a + b)

How many different ways can you find of writing the areas of these shapes? b) c) d) f) e) g)

4(2a - b) How did you do g? If this has area a and I take away area b I’m left with area a - b This has area a + (a – b) 4(2a - b) Which is 2a - b 1 3 4 2 time times OR

So now can you do these? Remember to write them in as many different ways as you can find!! a) b) c) d) e) f) g) h)

The 5 ‘easy’ Tak-tiles If the area of the square is a area a area b and the area of the quadrant is b Then the area of this shape is b + a + b OR a + 2b So what about these? area a + 2b area 4a - 2b area 3a - b area 2a

What about this shape? 8a - b 8a - b OR + + This has area 8a + 3b - 4b ________________ This has area 8a + 3b - 4b a + 4a – 3a +2b - 2b - b ________________ Which is 8a - b Which is 8a - b

Can you do this shape in the same way? 3a - b + a + 2b + 2a area 11a + 3b - 2b + a + 2b 11a + b + 4a - 2b ________________ 11a + b ________________