My measurements have got all jumbled up! Swap them around and see
if you can find a combination where every measurement is valid.
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Measure problems at primary level that require careful consideration.
Measure problems at primary level that may require determination.
Measure problems for primary learners to work on with others.
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.
Measure problems for inquiring primary learners.
How many centimetres of rope will I need to make another mat just
like the one I have here?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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 how this pattern of squares continues. You could
measure lengths, areas and angles.
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 can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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 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?
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Look at the mathematics that is all around us - this circular
window is a wonderful example.
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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?
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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
Here are many ideas for you to investigate - all linked with the
A task which depends on members of the group noticing the needs of
others and responding.
Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).
Explore this interactivity and see if you can work out what it
does. Could you use it to estimate the area of a shape?
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. . . .
Grandpa was measuring a rug using yards, feet and inches. Can you
help William to work out its area?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Determine the total shaded area of the 'kissing triangles'.
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .
What happens to the area and volume of 2D and 3D shapes when you
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
Use the information on these cards to draw the shape that is being described.
A simple visual exploration into halving and doubling.