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

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?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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

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?

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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

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?

Number problems at primary level that require careful consideration.

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

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.

Investigate the different distances of these car journeys and find out how long they take.

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

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

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

How would you count the number of fingers in these pictures?

Number problems for you to work on with others.

Find a great variety of ways of asking questions which make 8.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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 substitute numbers for the letters in these sums?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Try out this number trick. What happens with different starting numbers? What do you notice?

Find the next number in this pattern: 3, 7, 19, 55 ...

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

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

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

Can you go through this maze so that the numbers you pass add to exactly 100?

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.

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.

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

Number problems at primary level that may require resilience.

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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?

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?

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.

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