A game that tests your understanding of remainders.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
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.
56 406 is the product of two consecutive numbers. What are these
Given the products of adjacent cells, can you complete this Sudoku?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
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.
Can you work out what a ziffle is on the planet Zargon?
Can you complete this jigsaw of the multiplication square?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Here is a chance to play a version of the classic Countdown Game.
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?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Resources to support understanding of multiplication and division through playing with number.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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 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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Choose a symbol to put into the number sentence.
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 your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
This problem is designed to help children to learn, and to use, the two and three times tables.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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,. . . .
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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?
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.