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?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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?
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.
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?
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Have a go at this 3D extension to the Pebbles problem.
It starts quite simple but great opportunities for number discoveries and patterns!
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
An investigation that gives you the opportunity to make and justify
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?
If the answer's 2010, what could the question be?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you find ways of joining cubes together so that 28 faces are
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?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
A description of some experiments in which you can make discoveries about triangles.
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"?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Investigate what happens when you add house numbers along a street
in different ways.
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 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!
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
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 smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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. . . .
What do these two triangles have in common? How are they related?
What is the largest cuboid you can wrap in an A3 sheet of paper?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
In how many ways can you stack these rods, following the rules?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
How many tiles do we need to tile these patios?
Numbers arranged in a square but some exceptional spatial awareness probably needed.
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.