Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.
A follow-up activity to Tiles in the Garden.
Analyse these beautiful biological images and attempt to rank them in size order.
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Explore one of these five pictures.
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Can you draw the height-time chart as this complicated vessel fills with water?
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
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. . . .
The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
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.
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
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?
A circle is inscribed in a triangle which has side lengths of 8, 15 and 17 cm. What is the radius of the circle?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Can you maximise the area available to a grazing goat?
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you find the area of a parallelogram defined by two vectors?
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?
In the four examples below identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
A tower of squares is built inside a right angled isosceles triangle. The largest square stands on the hypotenuse. What fraction of the area of the triangle is covered by the series of squares?
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
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!
What fractions of the largest circle are the two shaded regions?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you work out the area of the inner square and give an explanation of how you did it?
Derive a formula for finding the area of any kite.
What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.
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. . . .
Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?
Determine the total shaded area of the 'kissing triangles'.
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
A task which depends on members of the group noticing the needs of others and responding.
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
What is the same and what is different about these circle questions? What connections can you make?
How efficiently can you pack together disks?
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. . . .
Can you find rectangles where the value of the area is the same as the value of the perimeter?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?