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.
- Assessment Limits :
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. - Calculator :
Neutral
- Clarification :
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. - Stimulus Attributes :
Items may be set in a real-world or mathematical context. - Response Attributes :
Items may require the student to draw a circle that matches an
equation in general form.
- Test Item #: Sample Item 1
- Question:
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.
- Difficulty: N/A
- Type: ETC: Editing Task Choice
Related Courses
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Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Problem-Solving Task
MFAS Formative Assessments
Students are asked to find the center and radius of a circle given its equation in general form.
Students are asked to find the center and radius of a circle given its equation in general form.
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.
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
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.
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
Original Student Tutorials
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
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
Problem-Solving Task
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.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Task
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.
Type: Problem-Solving Task