# MA.7.GR.1.3

Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.

### Clarifications

Clarification 1: Instruction includes the exploration and analysis of circular objects to examine the proportional relationship between circumference and diameter and arrive at an approximation of pi (π) as the constant of proportionality.

Clarification 2: Solutions may be represented in terms of pi (π) or approximately.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.GR.1.AP.3: Apply a given formula for the circumference of a circle to solve mathematical problems.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

The Meaning of Pi:

Students are asked to explain the relationship between the circumference and diameter of a circle in terms of pi.

Type: Formative Assessment

Eye on Circumference:

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

Type: Formative Assessment

Circumference Formula:

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.

Type: Formative Assessment

## Lesson Plan

Circumference/Rotation Relationship in LEGO/NXT Robots or Do I Wheely need to learn this?:

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.

Type: Lesson Plan

## Original Student Tutorials

Pizza Pi: Circumference:

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.

Type: Original Student Tutorial

Swimming in Circles:

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

Type: Original Student Tutorial

## Perspectives Video: Expert

Practical Use of Area and Circumference:

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

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Pizza Pi: Area, Circumference & Unit Rate:

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.

Type: Perspectives Video: Professional/Enthusiast

Using Geometry for Interior Design and Architecture:

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

Type: Perspectives Video: Professional/Enthusiast

Geometry for Dance Costume Designs:

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

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

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

Type: Perspectives Video: Teaching Idea

Bicycle Mathematics: Speed and Distance Calculations:

Cycling involves a lot of real-time math when you use an on-board computer. Learn about lesson ideas and how computers help with understanding performance.

Type: Perspectives Video: Teaching Idea

Robot Mathematics: Gearing Ratio Calculations for Performance:

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

Type: Perspectives Video: Teaching Idea

## Tutorials

Impact of a Radius Change on the Area of a Circle:

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.

Type: Tutorial

Circles: Radius, Diameter, Circumference, and Pi:

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

Type: Tutorial

Circumference of a Circle:

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

Type: Tutorial

## MFAS Formative Assessments

Circumference Formula:

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.

Eye on Circumference:

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

The Meaning of Pi:

Students are asked to explain the relationship between the circumference and diameter of a circle in terms of pi.

## Original Student Tutorials Mathematics - Grades 6-8

Pizza Pi: Circumference:

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.

Swimming in Circles:

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

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Pizza Pi: Circumference:

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.

Type: Original Student Tutorial

Swimming in Circles:

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

Type: Original Student Tutorial

## Perspectives Video: Expert

Practical Use of Area and Circumference:

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

Type: Perspectives Video: Expert

## Tutorials

Impact of a Radius Change on the Area of a Circle:

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.

Type: Tutorial

Circles: Radius, Diameter, Circumference, and Pi:

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

Type: Tutorial

Circumference of a Circle:

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

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

## Perspectives Video: Expert

Practical Use of Area and Circumference:

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

Type: Perspectives Video: Expert