Calculating arcs and areas of sectors in circles

This lesson develops the concept of finding areas of sectors. In particular students will:

• Find perimeters, areas, and arc lengths of sectors using formulas
• Find the relationships between arc lengths, and areas of sectors after scaling
• Using radians

The initial challenge shows three concentric circles with twelve equally spaced rays dividing the circles. There are a series of questions exploring the area of the sectors.

There then follows an exploration of the relationship between the angle of a sector in radians, the fraction of a circle, and the area of the sector.

The final activity is a domino card loop consisting of six cards. Each domino has a diagram with three concentric circles. The circles are divided into eight equal angles at the centre. The activity explores the relationship between arc lengths and areas of sectors after scaling.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.