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?
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?
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.
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?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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 each work out the number on your card? What do you notice?
How could you sort the cards?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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!
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.
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?
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
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!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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 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?
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
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.
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 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?
An old game but lots of arithmetic!
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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.
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?
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?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
This activity focuses on doubling multiples of five.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
56 406 is the product of two consecutive numbers. What are these
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.