Describing patterns and sequences

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

MatildaMatildaMatil... What is the 1000th letter?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Explore one of these five pictures.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?