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

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

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 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.

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?

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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?

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?

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

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

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

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

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?

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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?

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

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

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?

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?

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?

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

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

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?

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?

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

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?

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.

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

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

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.

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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

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

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?

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?

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?

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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?