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? Why?
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?
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?
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.
If the answer's 2010, what could the question be?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Choose a symbol to put into the number sentence.
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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 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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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!
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
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.
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
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 find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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!
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the