During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Investigate the different distances of these car journeys and find out how long they take.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
If you have only four weights, where could you place them in order to balance this equaliser?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
Here is a chance to play a version of the classic Countdown Game.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Choose a symbol to put into the number sentence.
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.
Got It game for an adult and child. How can you play so that you know you will always win?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
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?
How is it possible to predict the card?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
This is an adding game for two players.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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.
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?
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?
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
Can you explain how this card trick works?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Here is a chance to play a fractions version of the classic Countdown Game.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
How can we help students make sense of addition and subtraction of negative numbers?
This article for teachers suggests ideas for activities built around 10 and 2010.