How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Numbers arranged in a square but some exceptional spatial awareness probably needed.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
A challenging activity focusing on finding all possible ways of stacking rods.
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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 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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
An activity making various patterns with 2 x 1 rectangular tiles.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This article for teachers suggests ideas for activities built around 10 and 2010.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
In how many ways can you stack these rods, following the rules?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
Can you create more models that follow these rules?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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.
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?
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.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
This challenge extends the Plants investigation so now four or more children are involved.
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.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?