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 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!
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?
Choose a symbol to put into the number sentence.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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!
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 arrange 5 different digits (from 0 - 9) in the cross in the
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
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 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?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you complete this jigsaw of the multiplication square?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
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.
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,. . . .
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
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?
Here is a chance to play a version of the classic Countdown Game.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
What is happening at each box in these machines?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Amy has a box containing domino pieces but she does not think it is
a complete set. She has 24 dominoes in her box and there are 125
spots on them altogether. Which of her domino pieces are missing?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
Use the information to work out how many gifts there are in each