Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
Given the products of adjacent cells, can you complete this Sudoku?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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 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?
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 replace the letters with numbers? Is there only one
solution in each case?
Here is a chance to play a version of the classic Countdown Game.
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?
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 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!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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 problem is designed to help children to learn, and to use, the two and three times tables.
Can you work out what a ziffle is on the planet Zargon?
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.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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.
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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 any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
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,. . . .
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
A game that tests your understanding of remainders.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
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. . . .
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Choose a symbol to put into the number sentence.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you work out some different ways to balance this equation?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost 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?