Analyse these beautiful biological images and attempt to rank them in size order.
Can you draw the height-time chart as this complicated vessel fills with water?
How efficiently can you pack together disks?
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
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.
Can you find the area of a parallelogram defined by two vectors?
Explore one of these five pictures.
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
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. . . .
A task which depends on members of the group noticing the needs of others and responding.
An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
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. . . .
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?
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. . . .
Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'. Show that the sum of the areas of the two crescents equals the area of triangle ABC.
Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .
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 square carpet.
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
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?
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. . . .
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 work out the area of the inner square and give an explanation of how you did it?
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?
Can you maximise the area available to a grazing goat?
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?
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
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?
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.
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.
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.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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!
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .
Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Determine the total shaded area of the 'kissing triangles'.
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
Can you find the areas of the trapezia in this sequence?
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Derive a formula for finding the area of any kite.
If I print this page which shape will require the more yellow ink?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
What is the same and what is different about these circle questions? What connections can you make?
Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.