Formulate and investigate a simple mathematical model for the design of a table mat.
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?
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. . . .
A description of some experiments in which you can make discoveries about triangles.
Numbers arranged in a square but some exceptional spatial awareness probably needed.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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?
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?
Explore one of these five pictures.
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
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.
Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
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?
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?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
It starts quite simple but great opportunities for number discoveries and patterns!
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A follow-up activity to Tiles in the Garden.
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?
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 must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
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 numbers?
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?
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!
Can you find ways of joining cubes together so that 28 faces are
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What do these two triangles have in common? How are they related?
If the answer's 2010, what could the question be?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
An activity making various patterns with 2 x 1 rectangular tiles.
What is the largest cuboid you can wrap in an A3 sheet of paper?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Investigate what happens when you add house numbers along a street
in different ways.
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.
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.
Why does the tower look a different size in each of these pictures?
This challenge extends the Plants investigation so now four or more children are involved.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.