What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
A follow-up activity to Tiles in the Garden.
Numbers arranged in a square but some exceptional spatial awareness probably needed.
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.
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. . . .
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?
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?
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
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.
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
In how many ways can you stack these rods, following the rules?
A challenging activity focusing on finding all possible ways of stacking rods.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
It starts quite simple but great opportunities for number discoveries and patterns!
Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
I cut this square into two different shapes. What can you say about
the relationship between them?
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
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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?
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
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?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
An activity making various patterns with 2 x 1 rectangular tiles.
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.
If the answer's 2010, what could the question be?
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 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.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
What is the largest cuboid you can wrap in an A3 sheet of paper?
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 challenge extends the Plants investigation so now four or more children are involved.
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many models can you find which obey these rules?