Unit 6: Length and Area: Parallelograms and Trapezia

Unit 6: Length and area: parallelograms and trapezia

Planning guidance

Unit objectives

Within this unit, students will learn to:

convert between mm2, cm2and m2
find the areas of parallelograms and trapeziums
find the areas and perimeters of composite plane figures
solve word problems involving area and perimeter

Tasks focus predominantly on exploring conversions between units and the formulae for the areas of parallelograms and trapezia. Area of parallelograms and trapezia should be explored and investigated and links should be made between their areas and the area of rectangles. Additional time may be used for consolidation of these findings. In particular, teachers may choose to spend this time practising conversions between metric units and solving word problems involving area and perimeter.

There is opportunity here to consolidate work from Year 7 on area and perimeter and properties of shapes; some key vocabulary may need reinforcing. In addition, numeracy work can be reinforced by completing much of the unit without a calculator.

This unit should take two weeks and there are two main sections of work to be completed. Within each overview page, there are a number of tasks to be completed together and which form the basis of planning for individual classes. There are many additional tasks and resources available under the documents section. All resources are provided in Smart, PowerPoint and ActivInspire formats.

Suggested Structure

The actual number of lessons spent on each section will depend on the individual class and the number of lessons available to teachers. We suggest the following based on a total of 6, 8 or 10 lessons over the fortnight:

Section / 6 lessons / 8 lessons / 10 lessons
Unit conversions (length and area) / 2 / 2-3 / 3
Areas of parallelograms and trapezia / 4 / 5-6 / 7

Length and area unit conversions

Objectives

Convert between mm, cm, m, km
Convert between mm2, cm2, m2
Working with area and perimeter
Solving complex problems involving area, perimeter and changing units

During this part of the unit students should spend time consolidating basic metric conversions of length units, before exploring conversions between units of area. Students should being by converting lengths and finding the area after and comparing answers to establish that the area conversions are not the same as the length ones.

When working on finding the conversions students should be encouraged to really develop a depth of understanding so that they are not reliant on memorising rules and formulae. Concrete and pictorial representations can be used when using the activities involving fitting tiles into a bigger shapes – for example when seeing how many 1 mm2 tiles would be needed to cover a 1 cm2 square. This should aid students in developing a strategy that they could apply when solving problems later on.

For further guidance, including the Department Tasks for this section, click Length and area unit conversion under Planning resources on the main page for this unit.

Areas of parallelograms and trapezia

Objectives:

Identify properties of parallelograms and trapezia
find the areas of parallelograms and trapezia
find the areas and perimeters of composite plane figures
solve word problems involving area and perimeter
finding the area of compound shapes

At the start of this section there is time to revise area of rectangles and triangles as well as the conversions from the earlier section. Note that the conversion element of the unit should run through this section and opportunities should be taken to consolidate earlier work.

Students are encouraged to explore the area of parallelograms and trapezia by making comparisons between shapes they are familiar with so that they understand how the areas are calculated rather than relying on learning the formulae; in this way they can develop stronger problem solving strategies for the future.

The areas of parallelograms are introduced by looking at making them from rectangles (and this would make an excellent concrete task using pre-drawn rectangles). For trapezia, students explore putting two trapezia together in order to make a parallelogram (see below) before applying their knowledge of areas of parallelograms to the shape.

Throughout the unit, there should be a clear emphasis on understanding the derivation of the areas and use of technical language, such as perpendicular height. There are also plenty of opportunities to reinforce the earlier work on units.

At the end of this section, there is time to consolidate all the work done on area so far by looking at compound shapes and exploring algebraic expressions at the same time!

For further guidance, including the Department Tasks for this section, click Areas of parallelograms and trapeziaunder Planning resources on the main page for this unit.