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?
Here is a chance to play a version of the classic Countdown Game.
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?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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.
Can you complete this jigsaw of the multiplication square?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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?
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.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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. . . .
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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,. . . .
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
How would you count the number of fingers in these pictures?
Choose a symbol to put into the number sentence.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
A game that tests your understanding of remainders.
Amy has a box containing domino pieces but she does not think it is
a complete set. She has 24 dominoes in her box and there are 125
spots on them altogether. Which of her domino pieces are missing?
An old game but lots of arithmetic!
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?
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!
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?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?