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 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 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 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 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. . . .

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?

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

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

This challenge extends the Plants investigation so now four or more children are involved.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

Delight your friends with this cunning trick! Can you explain how it works?

Can you explain the strategy for winning this game with any target?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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

An environment which simulates working with Cuisenaire rods.

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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

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?

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.

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?

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?

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 arrange 5 different digits (from 0 - 9) in the cross in the way described?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?