What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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. . . .
There are three tables in a room with blocks of chocolate on each.
Where would be the best place for each child in the class to sit if
they came in one at a time?
Formulate and investigate a simple mathematical model for the design of a table mat.
A description of some experiments in which you can make discoveries about triangles.
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?
Numbers arranged in a square but some exceptional spatial awareness probably needed.
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?
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?
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
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. . . .
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
Can you find ways of joining cubes together so that 28 faces are
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
What do these two triangles have in common? How are they related?
I cut this square into two different shapes. What can you say about
the relationship between them?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
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!
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?
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?
Investigate what happens when you add house numbers along a street
in different ways.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
What is the largest cuboid you can wrap in an A3 sheet of paper?
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"?
An activity making various patterns with 2 x 1 rectangular tiles.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Why does the tower look a different size in each of these pictures?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
It starts quite simple but great opportunities for number discoveries and patterns!
A follow-up activity to Tiles in the Garden.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
Explore one of these five pictures.