Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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!
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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?
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.
Choose a symbol to put into the number sentence.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
If the answer's 2010, what could the question be?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Investigate what happens when you add house numbers along a street
in different ways.
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 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?
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.
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
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?
Can you hang weights in the right place to make the equaliser
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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 project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Can you use the information to find out which cards I have used?
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
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?
Investigate this balance which is marked in halves. If you had a
weight on the left-hand 7, where could you hang two weights on the
right to make it balance?
This challenge extends the Plants investigation so now four or more children are involved.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the