1. Introducing Tak-tiles
Algebra using areas

2. 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

3. = 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)

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

5. 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

6. 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)

7. 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

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

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