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

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

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

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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

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?

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.

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?

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

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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?

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

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

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?

Here is a chance to play a version of the classic Countdown Game.

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

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!

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?

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.

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.

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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

Got It game for an adult and child. How can you play so that you know you will always win?

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

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?

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.

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?

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 dice train has been made using specific rules. How many different trains can you make?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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 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?

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

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

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?

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