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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
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 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"?
An activity making various patterns with 2 x 1 rectangular tiles.
What is the largest cuboid you can wrap in an A3 sheet of paper?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
Investigate what happens when you add house numbers along a street
in different ways.
What do these two triangles have in common? How are they related?
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 happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
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?
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
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?
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?
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?
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?
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?
Why does the tower look a different size in each of these 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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
How many tiles do we need to tile these patios?
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
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?
If the answer's 2010, what could the question be?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?