Circles and Circumference – Advanced Lesson


Circles and Circumference – Advanced Lesson explains how to find the circumference of a circle. There are two equations or formulas students can use to solve these problems. By the end of the lesson, students will be able to use both expressions to find the circumference of any circle. They will also discover how to find the radius or diameter using a given circumference.

There are a couple of suggestions in the “Options for Lesson” section that you may want to use in the lesson. Instead of physical objects, for instance, you can draw circles on paper or on the board for students to use. Another option is to have students guess the circumferences of their heads.

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What our Circles and Circumference – Advanced Lesson lesson plan includes

Lesson Objectives and Overview: Circles and Circumference – Advanced Lesson teaches students how to find the circumference of a circle. Students will learn the equation and how to apply it. By the end of the lesson, they should be able to recall the equation and find the circumference of a circle. This lesson is for students in 6th grade.

Classroom Procedure

guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the orange box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The supplies you will need for this lesson include string, scissors, and objects with circles.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional adjustment to the lesson activity is to draw circles on paper instead of using physical objects. You can also have your students guess the circumference of their heads!

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.


Circle and Circumference: Advance Lesson

The Circles and Circumference lesson plan includes two content pages. We call the perimeter of a circle its circumference. It measures the total distance around a circle from a starting point. We can use two different formulas to calculate circumference: C = πd or C = 2πr.

By knowing both formulas, you can use either the diameter (the line that goes from one side of the circle to the other through the midpoint) or the radius (halfway across the circle, from the center point to the side) to find the circumference. Two radii (2r) equals one diameter (d), so the two formulas are basically the same.

The lesson then walks students through two example problems, one that shows them how to find circumference using the radius and one that shows how to find it using the diameter.

In the first example, you need to find the circumference of a circle with a radius of 2m. You’d use the formula C = 2πr, substituting 2 for r. The equation is C = 2π2. You then use the order of operations to solve. The final answer is C=12.56 m2.

In the second example, you need to find the circumference of a circle with a diameter of 13cm. You’d use the formula C = πd, substituting 13 for d. The equation is C = π(13). You then use the order of operations to solve. The final answer is C=40.82 cm2.


The Circles and Circumference lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.


For the activity, students will follow specific steps listed on the worksheet. First, they will choose a circular object but not pick it up. They will guess the length of circumference by cutting a piece of string to what they believe is the correct length. Then they can pick up the object and wrap the string around it to compare the actual length with their guess. They will measure their guess to the nearest quarter inch. Then they will measure the diameter of the object to the nearest quarter inch to find the actual circumference. Finally, they will write how close their guess was. They will repeat this process with three more objects.


The practice worksheet requires students to find the circumference of nine different circles. The circles label either the radius or diameter value. Students will use 3.14 for pi and whichever formula they want to solve each problem. Finally, given a specific circumference, they will work backward to find the diameter and radius and show their work.


The homework assignment has two sections. The first section, similar to the practice, has three circles for which students will need to find the circumference. The second section requires that students find two circular objects in their house. Students will trace the circles and calculate their circumferences.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information


6th Grade


Advanced, Math

State Educational Standards

LB.MATH.CONTENT.6-Advanced Lesson

Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.