Standard #: MAFS.7.G.2.4 (Archived Standard)

Students are asked to solve a problem involving the circumference of a circle.

Students are asked to write the formula for the circumference of a circle, explain what each symbol represents, and label the variables on a diagram.

Students are asked to write the formula for the area of a circle, explain what each symbol represents, and label the radius on a diagram.

Students are asked to solve a problem involving the area of a circle.

Students are asked to complete and explain an informal derivation of the relationship between the circumference and area of a circle.

• Recognize and use common 2D representations of 3D objects.
• Identify and use the appropriate formula for finding the circumference of a circle.

Students will help a volunteer coordinator choose cleanup projects that will have the greatest positive impact on the environment and the community.  They will apply their knowledge of how litter can impact ecosystems along with some math skills to make recommendations for cleanup zones to prioritize.  Students will explore the responsibilities of citizens to maintain a clean environment and the impact that litter can have on society in this integrated Model Eliciting Activity.  

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.  Click here to learn more about MEAs and how they can transform your classroom.

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

This set of geometry challenges focuses on creating circles and calculating area/circumference as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor

Students will calculate unit rate & circumference, compare & order decimals, convert metric units, and round decimals. Bubble Burst Corporation has developed some chewing gum prototypes and has requested the students to assist in the selection of which gum prototypes will be mass produced by using both quantitative and qualitative data to rank the prototypes for Bubble Burst Corporation.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

7th grade math/science lesson plan that focuses on the concept of circumference and rotation relationship. Culminates in a problem-solving exercise where students apply their knowledge to the "rotations" field in programming a LEGO/NXT robot to traverse a set distance.

This lesson is designed to be a fun and creative way to introduce math vocabulary (radius, diameter, and circumference) related to circles. Students will create a story board (comic strip) to retell the story using targeted vocabulary, and then demonstrate understanding of the relationships among radii, diameter, and circumference by completing the worksheet.

In my experience, lower performing students struggle to not confuse radius, diameter, and circumference. My learning objective in this lesson is to have them correctly remember the "parts" of a circle and that a diameter is comprised of 2 radii. I frequently refer back to the story in later lessons when they are having difficulty identifying radius or diameter.

Students will learn what a "net" is, draw nets of three dimensional shapes, accurately calculate the surface area of their nets, and put them together to create an original person or pet.

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best plan for installing tile floor considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

This is the final lesson of the unit , "Makeover, Home Edition." This lesson is designed to teach students the applicability of finding area of composite figures as well as understanding the importance of ratios in the real world. Part I (#48705) dealt with determining backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into this backyard. Part III (#49025) dealt with creating a scale drawing of the backyard.

In this lesson, students will develop an understanding of the meaning of pi and how it relates to the relationship to circumference and diameter. This is a hands-on activity where students measure circular objects and calculate the relationship of the circumference to the diameter.

"Students will learn the relationship between the radius and diameter of a circle and the relationship of the diameter and the circumference of a circle. Students will also find the approximate circumference of a circle, given either the diameter or radius." (from MATH Can Take You Places)

Using volume in the real world

This lesson includes measurement activities that help students understand where the value of pi originated, as well as activities that help students apply the value of pi to real-life scenarios.

Explore the origins of Pi as the ratio of Circumference to diameter of a circle. In this interactive tutorial you'll work with the circumference formula to determine the circumference of a circle and work backwards to determine the diameter and radius of a circle.

Explore how to calculate the area of circles in terms of pi and with pi approximations in this interactive tutorial. You will also experience irregular area situations that require the use of the area of a circle formula.

Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive tutorial.

A math teacher describes the relationship between area and circumference and gives examples in nature.

How many times larger is the area of a large pizza compared to a small pizza? Which pizza is the better deal? Michael McKinnon of Gaines Street Pies talks about how the area, circumference and price per square inch is different depending on the size of the pizza.

Download the CPALMS Perspectives video student note taking guide.

An architect discusses how he uses circumference and area calculations to accurately create designs and plans.

A dance costume designer describes how she uses circumference and area calculations to make clothing for the stage.

A math teacher presents an idea for a classroom activity to engage students in measuring diameter and circumference to calculate pi.

A science teacher demonstrates stepwise calculations involving multiple variables for designing robots with desired characteristics.

Students derive the formula for area of a circle using worksheet in the attachment section of this resource or using the provided URL.

Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area.

This video shows how the area and circumference relate to each other and how changing the radius of a circle affects the area and circumference.

In this video, students are shown the parts of a circle and how the radius, diameter, circumference and Pi relate to each other.

This video shows how to find the circumference, the distance around a circle, given the area.

In this video, watch as we find the area of a circle when given the diameter.

This interactive lesson introduces students to the circle, its attributes, and the formulas for finding its circumference and its area. Students then perform a few calculations to practice finding the area and circumference of circles, given the diameter.

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems.

• In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related.
• The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and record in a table the data for radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis.
• The Problems section contains questions for students to solve and record their answers in the correct unit.

(NCTM's Illuminations)

Explore the origins of Pi as the ratio of Circumference to diameter of a circle. In this interactive tutorial you'll work with the circumference formula to determine the circumference of a circle and work backwards to determine the diameter and radius of a circle.

Explore how to calculate the area of circles in terms of pi and with pi approximations in this interactive tutorial. You will also experience irregular area situations that require the use of the area of a circle formula.

Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive tutorial.

A math teacher describes the relationship between area and circumference and gives examples in nature.

Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area.

This video shows how the area and circumference relate to each other and how changing the radius of a circle affects the area and circumference.

In this video, students are shown the parts of a circle and how the radius, diameter, circumference and Pi relate to each other.

This video shows how to find the circumference, the distance around a circle, given the area.

In this video, watch as we find the area of a circle when given the diameter.

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems.

• In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related.
• The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and record in a table the data for radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis.
• The Problems section contains questions for students to solve and record their answers in the correct unit.

(NCTM's Illuminations)

A math teacher describes the relationship between area and circumference and gives examples in nature.

Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area.

This interactive lesson introduces students to the circle, its attributes, and the formulas for finding its circumference and its area. Students then perform a few calculations to practice finding the area and circumference of circles, given the diameter.