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# Introducing Tak-tiles - PowerPoint PPT Presentation

Introducing Tak-tiles. Algebra using areas. area a. area b. Adding Areas. area b. area a. This has an area of a. and this has an area of b. So this shape has area. a. + b. Think about this shape;. It could be made like this. Or like this. a + b. a + b. 2 a. + 2 b. =.

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### Introducing Tak-tiles

Algebra using areas

area a

area b

area b

area a

This has an area of a

and this has an area of b

So this shape has area

a

+ b

It could be made like this

Or like this

a + b

a + b

2a

+ 2b

=

2(a + b)

2a + 2b

b)

a)

c)

d)

f)

e)

g)

How did you do g? these shapes?

and I take away area b

I’m left with area a - b

If this has area a

This has area

+ (a – b)

a

4(2a - b)

3

2

4

2a - b

1

times

time

OR

Which is

So now can you do these? these shapes?

Remember to write them in as many different ways as you can find!!

b)

d)

a)

c)

e)

f)

g)

h)

area these shapes?b

The 5 ‘easy’ Tak-tiles

If the area of the square is a

area a

and the area of the quadrant is b

Then the area of this shape is

OR a + 2b

b

+

a

+

b

So what about these?

area a + 2b

area 4a - 2b

area 3a - b

area 2a

OR

a + 2b

+

4a - 2b

+

3a - b

________________

8a

+

3b

-

4b

a +4a – 3a +2b - 2b - b

This has area

________________

8a - b

8a - b

Which is

Which is

Can you do this shape in the same way? these shapes?

3a - b

+

a + 2b

+

2a

2b

11a

+

3b

-

area

+

a + 2b

11a + b

+

4a - 2b

________________

11a + b

________________