Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

Dotty Six is a simple dice game that you can adapt in many ways.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

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

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?

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?

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Here is a chance to play a version of the classic Countdown Game.

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

There are nasty versions of this dice game but we'll start with the nice ones...

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Number problems at primary level that require careful consideration.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

You have 5 darts and your target score is 44. How many different ways could you score 44?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

These two group activities use mathematical reasoning - one is numerical, one geometric.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?