Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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
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!
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 the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
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?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Can you hang weights in the right place to make the equaliser
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Find all the numbers that can be made by adding the dots on two dice.
Choose a symbol to put into the number sentence.
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Ben has five coins in his pocket. How much money might he have?
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?
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?
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.
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?
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?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
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!
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?