Aim To begin to think about number and algebra in relation to areas of compound shapes. Tak-tiles

NfER:- Achievement of 15-Year-Olds in Wales: PISA 2012 National Report They are less strong on questions that focus on aspects of space and shape or that require them to formulate situations mathematically in order to solve a problem.

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

So this shape has area y x Adding Areas y x This shape has an area of x This shape has an area of y x + y

What are the areas of these? y + y x + x = 2x = 2y y + y + y + y = 4y x + x + x = 3x

Think about this shape; Or like this It could be made like this 2x2x 2y x + y 2x + 2y = 2(x + y) 2 lots of (x + y)

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

How many different ways can you find of writing the areas of these shapes? a) b) c) sheet Solutions – other variations are possible in the answers e.g. the order of x and y terms. 2x + 2y = 2( x + y ) 2x + 4y = 2( x + 2y ) 9x + 3y = 3( 3x + y )

d) 3x + 6y = 3( x + 2y ) e) 6x + 2y = 2( 3x + y ) f) 12x + 8y = 4( 3x + 2y ) g) challenge 8x - 4y = 4( 2x - y )

How did you find g? This has area x I take away area y I’m left with area x - y This has area x + (x – y) Area of the full shape is Lots of2x - y 4(2x - y) OR 1 234

Sheet handout So now can you do these?

Sheet handout So now can you do these?

area x + 2y area 4x - 2y area 3x - y area 2x area x + 2y Solutions

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) Questions g and h are your first challenge.

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) Questions g and h are your first challenge. With support lines

So now can you do these? Remember to write them in as many different ways as you can find!! a) b) c)d) Solutions – other variations are possible in the answers e.g. the order of x and y terms. 4x – 4y = 4( x – y )x 2x + 2y = 2( x + y ) 3x

e) f) g) h) 2x + y x + y 2y - x

Shape 1 Work out the area of the shape in terms of x and y.

Shape 1 All of the lines have been drawn. Work out the area of the shape in terms of x and y. (With support lines)

Shape 1 All of the lines have been drawn. Work out the area of the shape in terms of x and y. Solution 7x

Shape 2 Work out the area of the shape in terms of x and y.

Shape 2 Some lines have been drawn. Complete the lines to work out the area of the shape in terms of x and y.

Shape 2 The construction lines have been drawn. Work out the area of the shape in terms of x and y.

Shape 2 12x Solution Some lines have been drawn. Complete the lines to work out the area of the shape in terms of x and y.

Shape 2 Some lines have been drawn. Complete the lines to work out the area of the shape in terms of x and y. 12x Solution

Challenge Shape 3 Work out the area of the shape in terms of x and y.

Challenge (with some support) Shape 3 Some lines have been drawn. Complete the lines to work out the area of the shape in terms of x and y.

Challenge (with further support) Shape 3 The construction lines have been drawn. Work out the area of the shape in terms of x and y.

Challenge Shape 3 Solution 8x – 3y 2 The construction lines have been drawn. Work out the area of the shape in terms of x and y.

Challenge Shape 4 Work out the area of the shape in terms of x and y.

Challenge with some support Shape 4 Some lines have been drawn. Complete the lines to work out the area of the shape in terms of x and y.

The construction lines have been drawn. Work out the area of the shape in terms of x and y. Challenge (with further support) Shape 3

Challenge Shape 4 Some lines have been drawn. Complete the lines to work out the area of the shape in terms of x and y. Solution 6x + 3y 2