If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you find the chosen number from the grid using the clues?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Can you use the information to find out which cards I have used?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

What two-digit numbers can you make with these two dice? What can't you make?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Can you replace the letters with numbers? Is there only one solution in each case?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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?

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you find all the different ways of lining up these Cuisenaire rods?

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

Number problems at primary level that require careful consideration.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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.

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

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

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

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

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?

What happens when you try and fit the triomino pieces into these two grids?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?