General Information
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Test Item Specifications
In items where the student has to complete the square to find the
center and radius of the circle, coefficients of quadratic terms should
equal 1 and all other terms should have integral coefficients.
Neutral
Students will use the Pythagorean theorem, the coordinates of a
circle’s center, and the circle’s radius to derive the equation of a
circle.
Students will determine the center and radius of a circle given its
equation in general form.
Items may be set in a real-world or mathematical context.
Items may require the student to draw a circle that matches an
equation in general form.
Sample Test Items (1)
| Test Item # | Question | Difficulty | Type |
| Sample Item 1 | Johnny wants to find the equation of a circle with center (3,-4) and a radius of 7. He uses the argument shown. There are three highlights in the argument to show missing words or phrases. For each highlight, click on the word of phrase that correctly fills the blank. |
N/A | ETC: Editing Task Choice |
Related Courses
| Course Number1111 | Course Title222 |
| 1200400: | Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 1202340: | Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 1207310: | Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) |
| 1206310: | Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 1206320: | Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 1298310: | Advanced Topics in Mathematics (formerly 129830A) (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) |
| 1206315: | Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
| 7912065: | Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current)) |
Related Resources
Formative Assessments
| Name | Description |
| 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. |
| Complete the Square for Center-Radius | Students are asked to find the center and radius of a circle given its equation in general form. |
Lesson Plans
| Name | Description |
| 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. |
| Equations of Circles 1 | This lesson unit is intended to help you assess how well students are able to use the Pythagorean theorem to derive the equation of a circle and translate between the geometric features of circles and their equations. |
| Equations of Circles 2 | This lesson unit is intended to help you assess how well students are able to translate between the equations of circles and their geometric features and sketch a circle from its equation. |
| 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. |
Original Student Tutorials
| Name | Description |
| 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. |
| 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. |
Problem-Solving Task
| Name | Description |
| Slopes and Circles | The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle. |
Student Resources
Original Student Tutorials
| Name | Description |
| 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. |
| 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. |
Problem-Solving Task
| Name | Description |
| Slopes and Circles: | The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle. |
Parent Resources
Problem-Solving Task
| Name | Description |
| Slopes and Circles: | The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle. |