I cut this square into two different shapes. What can you say about
the relationship between them?
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.
Here are many ideas for you to investigate - all linked with the
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
How many tiles do we need to tile these patios?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Explore ways of colouring this set of triangles. Can you make
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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
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 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?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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 cuboid you can wrap in an A3 sheet of paper?
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?
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?
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 players ...?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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?
This problem is intended to get children to look really hard at something they will see many times in the next few months.
Why does the tower look a different size in each of these pictures?
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 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.
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
An investigation that gives you the opportunity to make and justify
Bernard Bagnall describes how to get more out of some favourite
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?
If the answer's 2010, what could the question be?
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?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
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?
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
Investigate these hexagons drawn from different sized equilateral
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.