Numbers arranged in a square but some exceptional spatial awareness probably needed.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
A description of some experiments in which you can make discoveries about triangles.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
A challenging activity focusing on finding all possible ways of stacking rods.
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
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. . . .
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?
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 article (the first of two) contains ideas for investigations.
Space-time, the curvature of space and topology are introduced with
some fascinating problems to explore.
How many triangles can you make on the 3 by 3 pegboard?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
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
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?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
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.
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
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 ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
A follow-up activity to Tiles in the Garden.
In how many ways can you stack these rods, following the rules?
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?
It starts quite simple but great opportunities for number discoveries and patterns!
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. . . .
An activity making various patterns with 2 x 1 rectangular tiles.
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.
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.
Explore one of these five pictures.
Can you create more models that follow these rules?
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?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
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?
What do these two triangles have in common? How are they related?