In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
These pictures show squares split into halves. Can you find other ways?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
If I use 12 green tiles to represent my lawn, how many different
ways could I arrange them? How many border tiles would I need each
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
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.
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
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?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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?
Bernard Bagnall describes how to get more out of some favourite
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
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?
Why does the tower look a different size in each of these pictures?
How many tiles do we need to tile these patios?
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?
This problem is intended to get children to look really hard at something they will see many times in the next few months.
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. . . .
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?
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. . . .
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?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
An investigation that gives you the opportunity to make and justify
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
What do these two triangles have in common? How are they related?
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?
Explore ways of colouring this set of triangles. Can you make
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate what happens when you add house numbers along a street
in different ways.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
What is the largest cuboid you can wrap in an A3 sheet of paper?
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 red ring is inside the blue ring in this picture. Can you
rearrange the rings in different ways? Perhaps you can overlap them
or put one outside another?
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.