This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
If you have only four weights, where could you place them in order
to balance this equaliser?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Choose a symbol to put into the number sentence.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Can you hang weights in the right place to make the equaliser
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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!
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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!
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Use the number weights to find different ways of balancing the equaliser.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?