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Finding the area of a rectangle is such a key skill in mathematics as it leads on to many other aspects of shape, number, algebra and even handling data. In this blog I’ll take you through how I teach the area of rectangles for a mixed ability maths class in Year 7.

A common misconception for Year 7s is to confuse the area of a rectangle with its perimeter. The starter addresses this by challenging students to find the perimeter of a star, regular octagon and pentagon and hexagon.

Students are typically able to find the perimeter as a product of the number of sides and side length for the three regular shapes. Less able students may find the perimeter by long addition. Some forget to find the two missing lengths in the blue hexagon and write its perimeter incorrectly as 40 cm.

To phase in the main part of the lesson I highlight the difference between perimeter and area. I do this by counting the number of squares inside the rectangle. The majority of Year 7s know this from primary school.

As we progress, I ask the students to sketch a rectangle on their mini-whiteboard (1 whiteboard per pair so they have to work together to aid peer support). I pose two questions one for the lower and core ability and one for the most able.

**Lower and Core Ability**

“A rectangle has a fixed area of 24 cm^{2}. What could the dimensions be?”

**More able**

“A rectangle has a fixed perimeter of 36 cm. What could the different areas be?”

Rather than asking students to repetitively find the area as a product of its two sides I challenge students to find a missing length when given its area or to find both the length and width when given area and perimeter. See the table below.

Length | Width | Area | Perimeter |
---|---|---|---|

12 cm | 8 cm | ||

9 mm | 12 mm | ||

6 in | 30 in^2 | ||

15 m | 46 m | ||

11 cm | 7 cm^2 | ||

25 m | 36 m^2 |

To add further challenge for the most able I pose similar questions with algebraic dimensions.

Find the missing dimensions for these rectangles. All lengths are in cm.

Length | Width | Area | Perimeter |
---|---|---|---|

a | v | ||

2x | 5r | ||

5 | 5(c + 15) | ||

2c + y | 10c + 2y | ||

4f | f^2 - 1 | ||

18 | 20 - 2c - 4c^2 |

Ambitious? Yes, especially for Year 7 students. But it constantly surprises me how much students can understand when expectations are high.

To wrap up this lesson and lead into the next on compound areas the plenary challenges students to find the area of a composite rectilinear shape. I remind some students to find the missing lengths. Others need some help seeing the composite shape as the sum or difference of two rectangles.

Either way, by the end of the lesson students are much more confident to solve problems involving the area of a rectangle.

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