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**Introducing Tak-tiles**

Algebra using areas

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**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

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**= 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)

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**How many different ways can you find of writing the areas of these shapes?**

b) c) d) f) e) g)

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**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

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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)

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**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

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**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

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**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 ________________

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