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?

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!

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

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?

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

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

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

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

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

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

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?

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?

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

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?

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?

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

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

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

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?

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

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?

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

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

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

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?

A game for 2 players. Practises subtraction or other maths operations knowledge.

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

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?

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?

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?

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

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!

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?

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.

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?

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

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?

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.

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

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

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