Your Basket 0 items - £0.00

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.

June 5, 2019

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values. Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

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 […]