What statements can you make about the car that passes the school
gates at 11am on Monday? How will you come up with statements and
test your ideas?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
This activity asks you to collect information about the birds you
see in the garden. Are there patterns in the data or do the birds
seem to visit randomly?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
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!
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
In my local town there are three supermarkets which each has a
special deal on some products. If you bought all your shopping in
one shop, where would be the cheapest?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What is the largest cuboid you can wrap in an A3 sheet of paper?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Here are many ideas for you to investigate - all linked with the
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Investigate the numbers that come up on a die as you roll it in the
direction of north, south, east and west, without going over the
path it's already made.
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many models can you find which obey these rules?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
Why does the tower look a different size in each of these pictures?
How many tiles do we need to tile these patios?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
In how many ways can you stack these rods, following the rules?
These pictures were made by starting with a square, finding the
half-way point on each side and joining those points up. You could
investigate your own starting shape.
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
If the answer's 2010, what could the question be?
Follow the directions for circling numbers in the matrix. Add all
the circled numbers together. Note your answer. Try again with a
different starting number. What do you notice?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Investigate the different ways you could split up these rooms so
that you have double the number.
Investigate these hexagons drawn from different sized equilateral
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
Investigate the number of faces you can see when you arrange three cubes in different ways.