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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Can you complete this jigsaw of the multiplication square?
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
Here is a chance to play a version of the classic Countdown Game.
Choose a symbol to put into the number sentence.
An old game but lots of arithmetic!
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
There were 22 legs creeping across the web. How many flies? How many spiders?
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!
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This article for teachers suggests ideas for activities built around 10 and 2010.
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?