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?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Can you make square numbers by adding two prime numbers together?

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?

A game for 2 players. Practises subtraction or other maths operations knowledge.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

These two group activities use mathematical reasoning - one is numerical, one geometric.

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

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?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

An environment which simulates working with Cuisenaire rods.

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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?

Number problems at primary level that require careful consideration.

Use the number weights to find different ways of balancing the equaliser.

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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.

You have 5 darts and your target score is 44. How many different ways could you score 44?

If you have only four weights, where could you place them in order to balance this equaliser?