Area of rectangles for a mixed ability maths class

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.

Difference between perimeter and area

Area of rectangles for a mixed ability maths class

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.

Area of rectangles for a mixed ability maths class

Area of rectangles for a mixed ability maths class

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 cm2.  What could the dimensions be?”

Area of rectangles for a mixed ability maths class

More able

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

Area of rectangles for a mixed ability maths class

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.

LengthWidthAreaPerimeter
12 cm8 cm
9 mm12 mm
6 in30 in^2
15 m46 m
11 cm7 cm^2
25 m36 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.

LengthWidthAreaPerimeter
av
2x5r
55(c + 15)
2c + y10c + 2y
4ff^2 - 1
1820 - 2c - 4c^2

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

Assessing progress and leading on to composite areas
Area of rectangles for a mixed ability maths class

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.

 

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

Mr Mathematics Blog

Teaching Mathematics for a Growth Mindset

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach.  The feeling of success is addictive.  The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it.  Teaching […]

Equation of Straight Line Graphs

To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis.  Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]

Arithmetic and Geometric Sequences

Students learn how to generate and describe arithmetic and geometric sequences on a  position-to-term basis.  Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term. This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs. Arithmetic […]