No of aliens 12345678910 Number of fingers Number of toes Number of legs Number of ribs Number of arms.

No of aliens

1 2 3 4 5 6 7 8 9 10

Number of fingers

Number of toes

Number of legs

Number of ribs

Number of arms

Now to write the formulae!

Write formulae to show the number of each body part on n aliens.

Copy and complete the following...

Fingers on n aliens = 6n

Toes on n aliens =

Legs on n aliens =

Ribs on n aliens =

Arms on n aliens =

How many squares can you find on a chessboard?

Working systematically....

64 1 x 1 squares

49 2 x 2 squares

Can you see any patterns?PROVE that you are right!

Walt: Explore different possibilities in order to solve a problem.

Use our knowledge of the properties of number in order to solve problems.

Use a symbol to stand for an unknown number.

We found there are 204 squares on a chessboard where the length ofone side is 8 squares (8 x 8).

Imagine a new chessboard has been invented that has a length of 25 squares (25 x 25).

How many squares are there in this new chessboard?!

Length of one side (x)

Total number of individual (1 x 1)squares

Total number of squares (n)

1

2

3

4

5

6

7

8

9

10

Imagine your data is like a function machine.

Where... x = length of one siden = total number of squares

You know the input (x) and the output (n), but what is happening in the function machine?

Can you spot any patterns in your data to help you solve the problem? Use your knowledge of the properties of numbers to help you.

n = x(x +1)(2x +1)

6n = total number of squaresx = length of one side

Can you work out from this the total number of squares in a chessboard measuring 25 x 25 squares?