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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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!
Choose a symbol to put into the number sentence.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
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 is an adding game for two players.
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?
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?
This challenge extends the Plants investigation so now four or more children are involved.
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
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
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
Can you be the first to complete a row of three?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
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?
An environment which simulates working with Cuisenaire rods.
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?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Can you substitute numbers for the letters in these sums?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
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?
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?
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
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!
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.