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Have you ever wondered how to teach area and circumference of a circle in 7th grade? Or how do you introduce circles to students?
Use this artistic, real-life lesson plan to teach your students about finding the area and circumference of circles. Students will learn material with artistic guided notes (interactive sketch notes), check for understanding, and practice with a doodle and color by number worksheet and a maze activity.
The lesson culminates with exploring how engineers design amusement park rides like roller coasters and Ferris wheels by applying the area and circumference of circles, ensuring they are both thrilling and safe for riders.
- Standard: CCSS 7.G.B.4
- Unit: 7th Grade → Unit 6: Plane Geometry & Angle Relationships
- Grade: 7th Grade
Learning Objectives
After this lesson, students will be able to:
Find the area and circumference of circles
Understand the relationship between the radius, diameter, area, and circumference of circles
Understand how the area and circumference of circles to real-world situations, such as designing amusement park rides
Prerequisites
Before this lesson, students should be familiar with:
Basic concepts of geometry, including shapes, angles, and measurements
Operations with decimals
Basic algebra skills, including solving for variables and manipulating equations
Materials
Pencils
Colored pencils or markers
Area and Circumference of Circles Guided Notes
Key Vocabulary
Circumference
Area
Diameter
Pi
Radius
Procedure
Introduction
As a hook, ask students how the area and circumference of circle might be important for designing amusement park rides. Refer to the last page of the guided notes as well as the FAQs below for ideas.
Use the guided notes to introduce the concept of pi, and formulas of the area and circumference of circles. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.
Walk through the key points of finding the area and circumference of circles, including understanding the relationship between the radius, diameter, and circumference of circles. In this lesson, students as asked to use 3.14 for pi, but are explained that pi is a never ending irrational number.
Check for Understanding
Have students work through the problems on the check for understanding page, either collaboratively or independently.
Walk around and spot-check student answers on the check for understanding activity.
Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.
Practice
Have students practice finding the area, circumference, diameter, radius of circles using the maze activity. Walk around to answer student questions.
Fast finishers can dive into the Doodle Math activity for extra practice. You can assign it as homework for the remainder of the class.
Real-Life Application
Bring the class back together, and introduce the concept of circles in amusement park rides. Explain that understanding the area and circumference of circles is essential for designing and building these rides, ensuring they are both thrilling and safe for riders.
Refer to the FAQs for more ideas on how to teach the real-life application of circles in amusement park rides.
Extensions
Real-Life Application Project
Ask students to brainstorm different types of amusement park rides that involve circles. Examples might include Ferris wheels, roller coasters, and spinning rides.
Have students work in small groups to design their own amusement park ride that involves circles. They should consider the area and circumference of circles in their design. After they have completed their designs, have each group present their ride to the class, explaining how they used the concepts of area and circumference to create their ride.
Additional Print Practice (Doodle Math)
A fun, no-prep way to practice area and circumference of circles is Doodle Math — it's a fresh take on color by number or color by code. It includes 3 levels of practice, and there’s one that’s perfect for St. Patrick’s Day or any time of year.
Challenge with Composite Figures (Pixel Art Google Sheets)
If you’re looking for a digital extension covering composite figures, try my Pixel Art activities in Google Sheets. They’re self checking, and perfectly themed for Valentine’s Day or Pi Day.
FAQs
The formula for finding the area of a circle is A = πr², where A is the area and r is the radius of the circle.
The formula for finding the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.
The diameter of a circle is twice the length of its radius. In other words, if you multiply the radius of a circle by 2, you get its diameter. Conversely, if you divide the diameter of a circle by 2, you get its radius.
Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is used in the formulas for finding both the area and circumference of a circle. Specifically, the formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle, and the formula for the area of a circle is A = πr², where A is the area and r is the radius of the circle.
Some real-life applications of the area and circumference of circles include designing and building amusement park rides like roller coasters and Ferris wheels, calculating the amount of material needed to construct circular objects such as pipes or wheels, and calculating the area of circular plots of land for farming.
Circles are used in designing amusement park rides because they allow engineers to create a smooth, continuous path for the ride that is both exciting and safe.
For example, the loops in a roller coaster are circular in shape, and the cars are designed to maintain a constant speed as they move through the loop. Ferris wheels also use circles to create a smooth, circular path for the riders.
Understanding the area and circumference of circles is essential for designing and building these rides in a way that ensures they are both thrilling and safe for riders.
Some strategies for teaching the area and circumference of circles include using visuals and real-life examples to help students understand the concepts, breaking down the formulas into smaller parts for easier memorization, and providing ample practice opportunities with varying levels of difficulty. Interactive activities, such as Doodle Math and mazes can also help engage students and reinforce their understanding of the material.
Other geometric concepts related to circles include chords, tangents, secants, and arcs.