Sector Area and Arc Length

6.3

Sector Area & Arc Length

Circumference and area of a circle. Arc length and area of sector. From sector angles in degrees only.

Teacher Reference

Sector Angles, Area and Arc Length

Note: Credit for this original idea goes to Dan Meyer. If you’re not familiar with Dan Meyer’s work, please visit his wonderful website. It is full of excellent resources. His creative approach to making practical problems into interesting learning experiences for students is a treasure for educators!

Context for Teaching: Geometry is particularly difficult to teach, and this is an unusual place to start, with sector angles, area and perimeter. However, the key to success, for a Geometry student, is the ability to recognize what conceptual understanding they have that might play a role in the issue they’re facing.

Geometry requires many cognitive leaps from the students! They need to draw connections between various pieces of knowledge, without prompt, in order to be excellent problem solvers. That is perhaps what learning Geometry really does for a student. It helps develop their ability to think “outside the box.” (See what I did there?)

Big Idea

We want students to take a few known facts and develop a mathematical approach to answering a question. The question is something near and dear to their hearts … How to get the most pizza?

In doing so, students will develop an understanding of sectors and area, and may even stumble upon some understanding of dimension (area versus length). This will all happen on their own, before you help them to formalize their thinking.

Key Knowledge

Prerequisite: Students need to know how many degrees are in a circle, and what the radius, diameter and circumference are. They need to recognize that a circle is a nice approximation for a pizza.

New Information: Through review and summary, you will help students formalize their understanding of sectors and arc length. This will begin in the lesson, and continue with homework review the next day.

Pro – Tip
(for students)

Record your questions and realizations throughout the lesson. This lesson is as much about learning a successful approach to Geometry as it is about learning a few basic Geometric facts and formulas.

Lesson Plans

Click on the PDF icon to download a Lesson Guide that will pace the PowerPoint. Click on the PowerPoint icon to download the PowerPoint Lesson.

The lessons are intentionally over-built with more material than the time will allow. This way you have more options on how to best serve the needs of your students.