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 why 2 by 2 could be 5? Can you predict what 2 by 10
Choose a symbol to put into the number sentence.
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,. . . .
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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!
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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!
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?
Can you complete this jigsaw of the multiplication square?
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?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here is a chance to play a version of the classic Countdown Game.
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
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
If the answer's 2010, what could the question be?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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.
Number problems at primary level that require careful consideration.
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 design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
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?
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.
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?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.