Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?