Objective To begin to think about number and algebra in relation to areas of compound shapes.

I will be successful if: -I am able to express areas using algebra -I am able to simplify algebraic expressions

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

Think about this shape; Or like thisIt could be made like this 2a2a + 2b a + b 2a + 2b = 2(a + b)

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

How did you find g? If this has area a and I take away area bI’m left with area a - b This has area a + (a – b) Which is time2a - b 4(2a - b) ORtimes1 234

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 and the area of the quadrant is b area b Then the area of this shape is b+ab+ OR a + 2b So what about these? area a + 2b area 4a - 2barea 3a - barea 2a

MISSION IMPOSSIBLE Mr Ranson’s safe

YES! MY KEY WORKS This has area 8a8a+3b3b-4b4b Which is 8a - b OR a + 2b 4a - 2b 3a - b + + ________________ a + 4a – 3a +2b - 2b - b Which is 8a - b ________________

Can you do this shape in the same way? area 11a+3b3b- 2b2b 11a + b a + 2b 2a2a + + 3a - b 4a - 2b a + 2b + + ________________ 11a + b