In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Sort the houses in my street into different groups. Can you do it in any other ways?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Bernard Bagnall describes how to get more out of some favourite
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Have a go at this 3D extension to the Pebbles problem.
Why does the tower look a different size in each of these pictures?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A challenging activity focusing on finding all possible ways of stacking rods.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
It starts quite simple but great opportunities for number discoveries and patterns!
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
Can you find ways of joining cubes together so that 28 faces are
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 ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
I cut this square into two different shapes. What can you say about
the relationship between them?
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
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?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
An investigation that gives you the opportunity to make and justify
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
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?
The red ring is inside the blue ring in this picture. Can you
rearrange the rings in different ways? Perhaps you can overlap them
or put one outside another?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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
What do these two triangles have in common? How are they related?
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?
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?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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?
All types of mathematical problems serve a useful purpose in
mathematics teaching, but different types of problem will achieve
different learning objectives. In generalmore open-ended problems
have. . . .