Number problems at primary level that require careful consideration.

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?

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

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

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?

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

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?

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

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

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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!

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

My coat has three buttons. How many ways can you find to do up all the buttons?

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

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?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

What could the half time scores have been in these Olympic hockey matches?

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?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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 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?

Investigate the different ways you could split up these rooms so that you have double the number.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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