Conjecturing and generalising

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Have a look at this table of how children travel to school. How does it compare with children in your class?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.