Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
My measurements have got all jumbled up! Swap them around and see
if you can find a combination where every measurement is valid.
Measure problems at primary level that require careful consideration.
Measure problems for primary learners to work on with others.
Measure problems for inquiring primary learners.
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.
I cut this square into two different shapes. What can you say about
the relationship between them?
Measure problems at primary level that may require determination.
How many centimetres of rope will I need to make another mat just
like the one I have here?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
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 ways can you find of tiling the square patio, using square
tiles of different sizes?
Can you draw a square in which the perimeter is numerically equal
to the area?
An investigation that gives you the opportunity to make and justify
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
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?
How many tiles do we need to tile these patios?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
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
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?
What do these two triangles have in common? How are they related?
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?
Grandpa was measuring a rug using yards, feet and inches. Can you
help William to work out its area?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
This article for teachers gives some food for thought when teaching
ideas about area.
An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you maximise the area available to a grazing goat?
A task which depends on members of the group noticing the needs of
others and responding.
A simple visual exploration into halving and doubling.
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Look at the mathematics that is all around us - this circular
window is a wonderful example.
Explore this interactivity and see if you can work out what it
does. Could you use it to estimate the area of a shape?
Use the information on these cards to draw the shape that is being described.