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

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

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?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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?

An activity centred around observations of dots and how we visualise number arrangement patterns.

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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?

How many possible necklaces can you find? And how do you know you've found them all?