Explore one of these five pictures.
A follow-up activity to Tiles in the Garden.
Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
It starts quite simple but great opportunities for number discoveries and patterns!
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
If the answer's 2010, what could the question be?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Arrange your fences to make the largest rectangular space you can.
Try with four fences, then five, then six etc.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
An investigation that gives you the opportunity to make and justify
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
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.
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.
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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?
What do these two triangles have in common? How are they related?
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?
A description of some experiments in which you can make discoveries about triangles.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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!
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?
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?
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?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position
yourself so that you are 'it' if there are two players? Three
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
Why does the tower look a different size in each of these pictures?