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?

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!

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.

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?

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

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

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

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?

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?

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?

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

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

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

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?

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?

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?

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

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

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.

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?

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?

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

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

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

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?

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.

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

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?

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.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

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?

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!

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

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?