Conjecturing and generalising

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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.