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?

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?

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

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. . . .

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?

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

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

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?

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

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.

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

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?

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?

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

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?

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?

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.

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?

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.

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

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

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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

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?

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

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

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.

An environment which simulates working with Cuisenaire rods.

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?

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?

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.

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

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

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?

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