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

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?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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.

Can you sort these triangles into three different families and explain how you did it?

Complete the squares - but be warned some are trickier than they look!

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Here are shadows of some 3D shapes. What shapes could have made them?

Sort the houses in my street into different groups. Can you do it in any other ways?

Can you hang weights in the right place to make the equaliser balance?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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

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

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

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

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?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

An environment which simulates working with Cuisenaire rods.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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?

My coat has three buttons. How many ways can you find to do up all the buttons?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?