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?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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.
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?
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge extends the Plants investigation so now four or more children are involved.
Have a go at this 3D extension to the Pebbles problem.
A challenging activity focusing on finding all possible ways of stacking rods.
It starts quite simple but great opportunities for number discoveries and patterns!
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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.
An investigation that gives you the opportunity to make and justify
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?
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 different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
I cut this square into two different shapes. What can you say about
the relationship between them?
What do these two triangles have in common? How are they related?
Can you find ways of joining cubes together so that 28 faces are
What is the largest cuboid you can wrap in an A3 sheet of paper?
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?
Investigate what happens when you add house numbers along a street
in different ways.
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?
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!
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
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?
If the answer's 2010, what could the question be?
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 is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Explore one of these five pictures.
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?
Can you create more models that follow these rules?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.