Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Choose a symbol to put into the number sentence.
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!
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place the numbers 1 to 10 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
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 is an adding game for two players.
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!
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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?
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?
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?
An environment which simulates working with Cuisenaire rods.
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?
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
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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 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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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 use the numbers on the dice to reach your end of the number line before your partner beats you?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.