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?

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

Investigate what happens when you add house numbers along a street in different ways.

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

What do you notice about these squares of numbers? What is the same? What is different?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

Number problems at primary level that require careful consideration.

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

In this game for two players, the aim is to make a row of four coins which total one dollar.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

This number has 903 digits. What is the sum of all 903 digits?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Can you find different ways of creating paths using these paving slabs?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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.

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.