Area of Circles and Composite Shapes

Teachers' Notes

The programme supports the teaching of this topic by exploiting the ability of television to create and manipulate images to illustrate the mathematical techniques covered. It includes visual decomposition of many composite shapes commonly seen in examination questions and also provides real-life applications of the topic. Complex area calculations are shown using clear, step-by-step methods that lead the student through each stage of the solution.

The programme could be used as an introduction to more involved area problems, or to provide interest, contextual content and visual support alongside classroom work on this topic. Students may benefit from viewing short sections of the programme as they progress through the different stages and then view the entire programme to summarise the main points. It could also be used as a revision tool or to consolidate understanding at the end of the topic.

It is expected that students will have already been introduced to the circumference of a circle and . They may also have performed some straightforward calculations involving area of a circle prior to viewing. The formula for the circumference of a circle is assumed and the programme begins by using this to derive the area formula (through a visual demonstration of sectors being rearranged to create a rectangle). The content moves quickly on to quite complex calculations of composite shapes, so viewers need to be comfortable with the calculation of simple areas (rectangles, triangles and circles) in order to follow the examples given.

The calculations shown in the programme are performed using a scientific calculator. The use of the button, the need to use the radius in area calculations, how and when to round, units of area and common approximations for (3.14 and 3.142) are specifically addressed. The use of mental methods, rough estimates and suitable approximations of are not covered and this could be discussed either before or after viewing.

At the end of the drinks can item, students are invited to consider how many rows of discs are stamped out each day and to find the value of the waste produced if aluminium costs roughly £2.10 per square metre. The factory produces 6 million cans per day and each row makes 14 cans. Jamie calculated that the waste aluminium per row was 267cm² (a row was 173cm by 14cm and the discs had diameters of 14cm).

The answers to Worksheet 1 could be used as the basis for a discussion after viewing. For revision purposes, students may find it useful to have their own copy of the Key Facts and Exam Tips section of these notes. These could be edited and amended to meet individual needs.