Investigate this balance which is marked in halves. If you had a
weight on the left-hand 7, where could you hang two weights on the
right to make it balance?
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
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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?
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
What do these two triangles have in common? How are they related?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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
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 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.
Investigate what happens when you add house numbers along a street
in different ways.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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?
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?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Investigate the different ways you could split up these rooms so
that you have double the number.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
If the answer's 2010, what could the question be?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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?
Why does the tower look a different size in each of these pictures?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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. . . .
In how many ways can you stack these rods, following the rules?
How many tiles do we need to tile these patios?
These pictures were made by starting with a square, finding the
half-way point on each side and joining those points up. You could
investigate your own starting shape.
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
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?
Here are many ideas for you to investigate - all linked with the
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?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.