Number problems at primary level that require careful consideration.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Can you work out some different ways to balance this equation?

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?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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?

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?

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?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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

Have a go at balancing this equation. Can you find different ways of doing it?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Can you make square numbers by adding two prime numbers together?

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.

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?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?