Lesson 21: Area of a rectangle Strategies for calculating the area of a rectangle including simple decimal multiplication

Do Now Using Task sheet 21a students must group or order the shapes by the amount of space they take up (i.e. their area). These two shapes are intended to promote discussion and address miscon- ceptions. Students may think that the area of the circle is 9 and the rectan-

gle 1. It is important to address this and ensure that students understand how these two shapes differ from the others in the task.

Encourage students to discuss and explain why they have chosen a specific grouping or order.

Coach input Formally introduce the concept of Area as the amount of space a flat shape takes up. Ask students to give all the properties of a rectangle—4 sides, 4 rights angles, opposite sides are parallel and of equal length. Do students agree that a square is a special type of rectangle? A square exhibits all the properties of a rectangle plus an additional property that all four sides are the same (similarly a square is also a rhombus). Ensure that you expose students to less familiar aspects or views of rectangles, you could also choose to discuss the conventions for labelling some of the properties given:

For the talk task students need only to recognise that they can find the area by counting the num- ber of squares in the shape, although some may already be aware of the formula for the area of a rectangle.

Talk Task Give students 20 blocks or a geoboard if available (or simply use squared paper) and ask them to create rectangles with areas from 1 to 20.

Some areas, for example 3, can only be represented in one way: Whereas an area of 12 can be represented in each of the ways below:

or or

Encourage students to think of as many possibilities as possible to represent each area. “Which numbers have the most possibilities?” “Is it true that larger numbers have more possibilities?” “What kind of numbers only have one option?” Further to this encourage students to identify strategies for calculating the area. They might count the number of boxes in each row and use repeated addition, whilst some might recognise that they can use multiplication Students should be encouraged to discuss their work and to explain their methods. Developing lan- guage and reasoning skills should be an important theme running through all coaching sessions.

Develop Learning A Formally introduce the formula for calculating the area of a rectangle

Area = Length x Width

Demonstrate using a rectangle with each square labelled, and a further rectangle with just the sides labelled. Discuss the fact that the area is the same regardless of which dimension comes first (the commutative property of multiplication). It is important to emphasize that area is measured in square units. For example the notation for square centimetres is cm2.

5cm 2cm

7cm

6cm

Independent Learning A Task sheet 21b can be utilised at this stage. Whilst this is an independent task, coaches should ask students to explain their answers, perhaps choosing one question in each section to discuss.

Develop Learning B The next step is to introduce students to rectangles where one side is not a whole number:

Encourage pupils to consider how they could calculate the area of this shape—they could do it by counting the squares (with the

3cm darker segments equal to a half), or by repeated addition (3.5 +

3.5 + 3.5 or 3 + 3 + 3 + 1.5), or they may attempt to use the for- mula and calculate 3.5 x 3. 3.5cm Some students may be able to do simple decimal multiplication mentally, but it is important that they have an effective written method for more challenging calculations.

3 . 5 Encourage students to estimate the answer prior to calculating it. Students may recognise that the number of decimal places in the answer is equal to the total number of decimal places in the question. x 1 3 They may require further guidance on this prior to commencing Task sheet 1 0 . 5 21c

Independent Learning B Task sheet 21c can be utilised at this stage. Whilst this is an independent task, coaches should ask students to explain their answers, perhaps choosing one question in each section to discuss.

Plenary Coaches can summarise findings or extend the strategies learnt today by looking at the area of com- pound shapes and more challenging decimal numbers. Another interesting task is to give students a length of string (say 16cm) and ask them to construct rectangles and find their area. What dimen- sions must the rectangle have to achieve the greatest area? (It should be a square) Any of the task sheets could be used for interim homework allowing students to practise their skills and consolidate their learning. Do share any useful resources with members of the Mathematics Mastery community via the online toolkit.

Teacher notes: