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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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

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?

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

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

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?

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Try this matching game which will help you recognise different ways of saying the same time interval.

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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

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

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?

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.

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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?

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

Can you fill in the empty boxes in the grid with the right shape and colour?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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

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

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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 to have an ordered approach.

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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

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?

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

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?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?