MA.912.GR.7.2

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Given a mathematical or real-world context, derive and create the equation of a circle using key features.

Clarifications

Clarification 1: Instruction includes using the Pythagorean Theorem and completing the square.

Clarification 2: Within the Geometry course, key features are limited to the radius, diameter and the center.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning
Standard: Apply geometric and algebraic representations of conic sections.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.GR.7.AP.2: Create the equation of a circle when given the center and radius.

Related Resources

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

Formative Assessments

Complete the Square for Center-Radius 2:

Students are asked to find the center and radius of a circle given its equation in general form.

Type: Formative Assessment

Derive the Circle – General Points:

Students are given the coordinates of the center, (h, k), and the radius, r, of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Type: Formative Assessment

Derive the Circle – Specific Points:

Students are given the coordinates of the center and the radius of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Type: Formative Assessment

Complete the Square for Center-Radius:

Students are asked to find the center and radius of a circle given its equation in general form.

Type: Formative Assessment

Lesson Plans

Circle Reasoning:

Students use the Pythagorean Theorem (Distance Formula) to derive the Standard Equation of a Circle; then move between descriptions and equations of a circle.

Type: Lesson Plan

Run Fido, Run!:

A guided practice for deriving the equation of a circle and then identifying a location to tether a dog to maximize movement.

Type: Lesson Plan

Original Student Tutorials

Where IS that Cell Tower?:

Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial. 

Type: Original Student Tutorial

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.

Type: Original Student Tutorial

MFAS Formative Assessments

Complete the Square for Center-Radius:

Students are asked to find the center and radius of a circle given its equation in general form.

Complete the Square for Center-Radius 2:

Students are asked to find the center and radius of a circle given its equation in general form.

Derive the Circle – General Points:

Students are given the coordinates of the center, (h, k), and the radius, r, of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Derive the Circle – Specific Points:

Students are given the coordinates of the center and the radius of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Original Student Tutorials Mathematics - Grades 9-12

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.

Where IS that Cell Tower?:

Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial. 

Student Resources

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

Original Student Tutorials

Where IS that Cell Tower?:

Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial. 

Type: Original Student Tutorial

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.

Type: Original Student Tutorial

Parent Resources

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