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?
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Delight your friends with this cunning trick! Can you explain how
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Can you explain how this card trick works?
Find the sum of all three-digit numbers each of whose digits is
Replace each letter with a digit to make this addition correct.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
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?
What are the missing numbers in the pyramids?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
If you have only four weights, where could you place them in order
to balance this equaliser?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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
Here is a chance to play a fractions version of the classic
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Investigate the different distances of these car journeys and find
out how long they take.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Choose any three by three square of dates on a calendar page...
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
An environment which simulates working with Cuisenaire rods.
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
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
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Here is a chance to play a version of the classic Countdown Game.
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.
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!
Choose a symbol to put into the number sentence.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
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. . . .
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
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?
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?
Ben has five coins in his pocket. How much money might he have?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
These two group activities use mathematical reasoning - one is
numerical, one geometric.