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Students learn how to find the area of various 2D shapes parallelograms, trapezia, compound shapes and circles. Throughout the topic links are made to algebraic reasoning and estimation. This topic takes place in Term 1 of Year 9 and links to volume and surface area later on.

**Prerequisite Knowledge**

- Know and apply formulae to calculate the area of rectangles
- Calculate the perimeters of 2D shapes, including composite shapes;
- Compare and order lengths, mass, volume / capacity and record the results using >, < and =
- Measure, compare, add and subtract: lengths (m/cm/mm); mass(kg/g); volume/capacity (l/ml)
- Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

**Success Criteria**

- Know and apply formulae to calculate: area of triangles, parallelograms and trapezia;
- Know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr
^{2}; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; - Calculate arc lengths, angles and areas of sectors of circles

**Key Concepts**

- Demonstrate a triangle as being half a rectangle so students know to use the perpendicular height in their calculation. Demonstrate a parallelogram as having an equal area to a rectangle.
- To calculate the area of composite rectilinear shapes have students break them up in different ways.
- A sector is a fraction of 360° of the entire circle.

**Common Misconceptions**

- Students often confuse area and perimeter.
- When calculating the area of a triangle or parallelogram students tend to use the slanted height rather than the correct perpendicular height.
- Arc length and area of a sector are often rounded incorrectly. Encourage students to evaluate as a multiple of pi and calculate the decimal at the end.

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]

March 26, 2019

Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]