Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
Choose a symbol to put into the number sentence.
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
This activity focuses on doubling multiples of five.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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 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?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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 complete this jigsaw of the multiplication square?
If the answer's 2010, what could the question be?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
An old game but lots of arithmetic!
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Can you replace the letters with numbers? Is there only one
solution in each case?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
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?
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
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?