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?

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!

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

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

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

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?

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

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.

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

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

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?

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

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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?

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

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?

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

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

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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 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?

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

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!

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

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.

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

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?

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.

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

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

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

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.

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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