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Finding the area and arc length of sectors following on Perimeter and Area where students first learn about circles. Throughout this unit on sectors students develop their algebra skills by deriving and changing the subject of the arc length and area formulae. This unit takes place in Term 3 of Year 11 for foundation students.

**Prerequisite Knowledge**

- 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;

**Success Criteria**

- Calculate arc lengths, angles and areas of sectors of circles
- Understand and use standard mathematical formulae; rearrange formulae to change the subject
- Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

**Key Concepts**

- A sector is a fraction of 360° of the entire circle.
- Students need to have a secure understanding of using the balance method when rearranging formulae. Recap inverse operations, e.g., x^2=>√x.
- When generating formulae it is important to associate mathematical operations and their algebraic notation with key words.

**Common Misconceptions**

- 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.
- Students often have difficult generating formulae from real life contexts. Encourage them to carefully break down the written descriptions to identify key words.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]