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Programme Of Study For Key Stage 3 Mathematics

These are the Transum resources related to the statement: "Pupils should be taught to derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)"

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Area and Perimeter Area and perimeter of composite shapes video for GCSE Maths.
- Area and Perimeter of a Rectangle Questions on the areas and perimeters of rectangles which will test your problem solving abilities.
- Area of a Trapezium Check that you can find the area of a trapezium and use the trapezium area formula for problem solving.
- Areas of Composite Shapes Find the areas of combined (composite) shapes made up of one or more simple polygons and circles.
- Formulae Pairs Find the matching pairs of diagrams and formulae for basic geometrical shapes.
- Surface Area Work out the surface areas of the given solid shapes.
- Volume Work out the volumes of the given solid shapes.

Here are some exam-style questions on this statement:

- "
*The trapezium and rectangle shown here have the same perimeters. The diagrams are not drawn to scale and the measurements are in centimetres. Calculate the area of the trapezium.*" ... more - "
*The diagram shows a water tank in the shape of a trapezoidal prism.*" ... more

Click on a topic below for suggested lesson starters, resources and activities from Transum.

- Area See also the topic called Mensuration. Pupils should not only be able to apply area formulae but they should also have a good understanding of what area means. This can be achieved by beginning the study of area with plenty of practical examples. The Pin Board provides an open-ended interactive experimental activity to secure a good fundamental understanding of area. Though many examinations now provide formulae sheets it is still important that pupils know the common formulas for finding the areas of basic shapes. They should use these formulae in context to find areas of basic and compound shapes and be able to give answers using appropriate units. Pupils will also learn to find the surface areas of three dimensional shapes, use scale to determine areas from maps and solve real world problems involving areas.
- Circles This is all to do with pi and why it is such an important number. From finding the circumference and area of circles to problem solving and investigation. Pupils will begin by learning the names of the parts of a circle then, either through investigation or practical activity, discover that the circumference of a circle is always just a little more than three times the length of the diameter whatever the size of the circle. A brief walk through history leads them to find out how to use this knowledge (and a more accurate version of pi) to find the circumference and areas of circles. This can then be developed to find the area of a sector, area of a segment, area of an annulus and the area of the region between a circle and a square in more complex problem solving situations. More mathematics related to the circle can involve angle theorems, loci and algebra.
- Mensuration Mensuration is the branch of Mathematics dealing with measurement of angles, length, area, and volume. It is linked closely to the topic of Estimation and related to the topics of Angles, Shape and Shave (3D). It is essential for pupils to have an understanding of the units used to measure which include both the more common metric units and the Imperial units still in common usage. We have found a good teaching strategy is to ask each of the pupils to "Bring to the next Maths lesson some visual aid which will help the rest of the class remember the size of a unit of measurement". See Memorable Measures below for the printable resources. This activity provides an association with a unit, a visual aid and a known person which is a great memory enhancer.