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

3. 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 =

4. How many squares can you find on a chessboard?

5. Working systematically.... 641 x 1 squares 492 x 2 squares Can you see any patterns? PROVE that you are right!

6. 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.

7. We found there are 204 squares on a chessboard where the length of one 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?!

8. 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

9. Imagine your data is like a function machine. Where...x = length of one side n = 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.

10. n = x(x +1)(2x +1) 6 n = total number of squares x = length of one side Can you work out from this the total number of squares in a chessboard measuring 25 x 25 squares?