Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

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

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

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

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

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

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 combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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?

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.

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

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

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?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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?

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

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Can you hang weights in the right place to make the equaliser balance?

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

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

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 short problems for you to try. Talk to your friends about how you work them out.

Try out some calculations. Are you surprised by the results?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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

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

Use these four dominoes to make a square that has the same number of dots on each side.

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

An environment which simulates working with Cuisenaire rods.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.