Describing patterns and sequences

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

What are the last two digits of 2^(2^2003)?