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?

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

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?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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?

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

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

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?

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

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?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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

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

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

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

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

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

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

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?

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

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?

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?

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

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

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

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?

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?

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?

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?

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.

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

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

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?

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?

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?

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

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

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.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?