During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This article for teachers suggests ideas for activities built around 10 and 2010.
Investigate the different distances of these car journeys and find
out how long they take.
If you have only four weights, where could you place them in order
to balance this equaliser?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
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?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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
Can you hang weights in the right place to make the equaliser
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?
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 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?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
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!
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Choose a symbol to put into the number sentence.
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.
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?
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 arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?