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 make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
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!
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you hang weights in the right place to make the equaliser
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Choose a symbol to put into the number sentence.
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
An old game but lots of arithmetic!
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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
If you have only four weights, where could you place them in order
to balance this equaliser?
Find all the numbers that can be made by adding the dots on two dice.
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 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?
Number problems at primary level that require careful consideration.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you make square numbers by adding two prime numbers together?
Ben has five coins in his pocket. How much money might he have?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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 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!
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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!
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 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?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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.
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same