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!
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?
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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!
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you replace the letters with numbers? Is there only one
solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
If the answer's 2010, what could the question be?
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.
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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 your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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 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?
Can you work out some different ways to balance this equation?
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.
Have a go at balancing this equation. Can you find different ways of doing it?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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?
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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 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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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 complete this jigsaw of the multiplication square?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?