Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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. . . .

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

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?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

Surprise your friends with this magic square trick.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

A game for 2 players. Practises subtraction or other maths operations knowledge.

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?

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?

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

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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

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

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?

Number problems at primary level that may require resilience.

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Got It game for an adult and child. How can you play so that you know you will always win?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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?