Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
How many centimetres of rope will I need to make another mat just
like the one I have here?
Measure problems for primary learners to work on with others.
Measure problems for inquiring primary learners.
Measure problems at primary level that may require determination.
Grandpa was measuring a rug using yards, feet and inches. Can you
help William to work out its area?
Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.
Look at the mathematics that is all around us - this circular
window is a wonderful example.
Measure problems at primary level that require careful consideration.
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.
Use the information on these cards to draw the shape that is being described.
How would you move the bands on the pegboard to alter these shapes?
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
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?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
A simple visual exploration into halving and doubling.
What do these two triangles have in common? How are they related?
This article for teachers gives some food for thought when teaching
ideas about area.
My measurements have got all jumbled up! Swap them around and see
if you can find a combination where every measurement is valid.
You have pitched your tent (the red triangle) on an island. Can you
move it to the position shown by the purple triangle making sure
you obey the rules?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you work out the area of the inner square and give an
explanation of how you did it?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
An investigation that gives you the opportunity to make and justify
Determine the total shaded area of the 'kissing triangles'.
It is possible to dissect any square into smaller squares. What is
the minimum number of squares a 13 by 13 square can be dissected
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
You have a 12 by 9 foot carpet with an 8 by 1 foot hole exactly in
the middle. Cut the carpet into two pieces to make a 10 by 10 foot
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Which is a better fit, a square peg in a round hole or a round peg
in a square hole?
A task which depends on members of the group noticing the needs of
others and responding.
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 follow-up activity to Tiles in the Garden.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
How many tiles do we need to tile these patios?
Bluey-green, white and transparent squares with a few odd bits of
shapes around the perimeter. But, how many squares are there of
each type in the complete circle? Study the picture and make. . . .
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
These practical challenges are all about making a 'tray' and covering it with paper.
Explore one of these five pictures.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?