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?

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?

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

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

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

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

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

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.

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

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

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

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

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?

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

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?

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!

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?

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?

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.

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?

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?

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?

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

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.

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?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

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

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?

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

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?

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

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?

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

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.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

An environment which simulates working with Cuisenaire rods.