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!

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?

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?

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

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

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?

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?

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

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

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

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

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?

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

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?

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

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

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?

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?

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?

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

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

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

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?

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?

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

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.

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

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

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?

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?

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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

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?