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

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

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do 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?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

This challenge extends the Plants investigation so now four or more children are involved.

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

An environment which simulates working with Cuisenaire rods.

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

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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?

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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

Investigate what happens when you add house numbers along a street in different ways.

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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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

This task follows on from Build it Up and takes the ideas into three dimensions!

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

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

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 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!

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

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?

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.