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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

What happens when you round these three-digit numbers to the nearest 100?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

This challenge is about finding the difference between numbers which have the same tens digit.

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?

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?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

Number problems at primary level that require careful consideration.

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

How many different shapes can you make by putting four right- angled isosceles triangles together?

This challenge extends the Plants investigation so now four or more children are involved.

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Can you find out in which order the children are standing in this line?

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?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Find all the numbers that can be made by adding the dots on two dice.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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?

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?

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?

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

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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?