A challenging activity focusing on finding all possible ways of stacking rods.
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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.
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.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
In how many ways can you stack these rods, following the rules?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
This article for teachers suggests ideas for activities built around 10 and 2010.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
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?
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!
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
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 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.
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?
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?
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
Can you find ways of joining cubes together so that 28 faces are
Can you create more models that follow these rules?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
How many models can you find which obey these rules?
Explore one of these five pictures.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
A follow-up activity to Tiles in the Garden.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Have a go at this 3D extension to the Pebbles problem.
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?
An investigation that gives you the opportunity to make and justify
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?