Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
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.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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
How many tiles do we need to tile these patios?
This article for teachers suggests ideas for activities built around 10 and 2010.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
What do these two triangles have in common? How are they related?
I cut this square into two different shapes. What can you say about
the relationship between them?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
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?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
If the answer's 2010, what could the question be?
Investigate the numbers that come up on a die as you roll it in the
direction of north, south, east and west, without going over the
path it's already made.
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
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?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Bernard Bagnall describes how to get more out of some favourite
Investigate what happens when you add house numbers along a street
in different ways.
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Here are many ideas for you to investigate - all linked with the
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?
Arrange your fences to make the largest rectangular space you can.
Try with four fences, then five, then six etc.
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
"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
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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 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?
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.
Explore one of these five pictures.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
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
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
What is the largest cuboid you can wrap in an A3 sheet of paper?
An investigation that gives you the opportunity to make and justify
Investigate the number of faces you can see when you arrange three cubes in different ways.
A follow-up activity to Tiles in the Garden.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
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