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

Place the numbers 1 to 10 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 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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.

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

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

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?

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

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

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?

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

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

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?

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?

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

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 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. . . .

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?

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

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

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.

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 task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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!

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

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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?

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

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?

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

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?

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

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

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

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

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?

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

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?

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?