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

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?

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?

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!

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?

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

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?

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

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?

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

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

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

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. . . .

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

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

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?

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

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

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

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?

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.

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.

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?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

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.

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?

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!

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

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

There were 22 legs creeping across the web. How many flies? How many spiders?

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

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

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.

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

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?

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

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?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

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?