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. . . .
A description of some experiments in which you can make discoveries about triangles.
What do these two triangles have in common? How are they related?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
What is the largest cuboid you can wrap in an A3 sheet of paper?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
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?
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 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?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
Here are many ideas for you to investigate - all linked with the
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
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?
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?
Why does the tower look a different size in each of these pictures?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many tiles do we need to tile these patios?
In how many ways can you stack these rods, following the rules?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Formulate and investigate a simple mathematical model for the design of a table mat.
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. . . .
How many models can you find which obey these rules?
Can you create more models that follow these rules?
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.
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 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?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
"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 ...?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.