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 for inquiring primary learners.
I cut this square into two different shapes. What can you say about
the relationship between them?
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.
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
Measure problems for primary learners to work on with others.
How many centimetres of rope will I need to make another mat just
like the one I have here?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
What do these two triangles have in common? How are they related?
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
Measure problems at primary level that may require determination.
Measure problems at primary level that require careful consideration.
What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.
Can you draw a square in which the perimeter is numerically equal
to the area?
Explore this interactivity and see if you can work out what it
does. Could you use it to estimate the area of a shape?
Look at the mathematics that is all around us - this circular
window is a wonderful example.
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 shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
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?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
Can you maximise the area available to a grazing goat?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
Grandpa was measuring a rug using yards, feet and inches. Can you
help William to work out its area?
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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 total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Can you work out the area of the inner square and give an
explanation of how you did it?
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
A follow-up activity to Tiles in the Garden.
Explore one of these five pictures.
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
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?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
What happens to the area and volume of 2D and 3D shapes when you