9 Components
Big Ideas
End of Unit Assessments
Browse Components
Big Ideas
End of Unit Assessments
Big Idea:

### A circle is uniquely defined in the coordinate plane using its center and radius.

1 week

Evidence of Understanding

• describe the characteristics of any circle
• construct a circle using a compass and justify that all radii are equidistant and congruent
• explain that all points on the circle are equidistant from the center of the circle
• define radius as a relationship between a circle’s center and points on the circle
• justify circles are similar using scale factor
• reason proportionally and connect the measurements of a circle with similarity
• analyze examples and non-examples to distinguish radii, chords, tangents, and secants
• use constructions to explain the relationship between the radius and a tangent line
• construct perpendicular bisectors of chords to show they always pass through the circle’s center

• analyze characteristics of a circle in the coordinate plane
• graph a circle in the coordinate plane given its center and radius
• explore whether a point lies on a circle whose radius and center point are known
• identify and justify possible methods including the use of a compass, straightedge, the Pythagorean Theorem, the distance formula, etc.
• prove whether a point lies on a circle given the circle’s center and another point on the circle
• describe characteristics about a circle given its center, radius, points on the circle, etc.
• Example: find the area of a circle whose endpoints of its diameter lie at (2, 3) and (10, -3), or determine the diameter of a circle centered at the origin and passing through (-5, 10)

• determine the standard equation of a circle in the coordinate plane
• describe connections between a circle’s equation and and its graph in the coordinate plane
• generate the equation of a circle from its graph
• derive the equation of a circle from the Pythagorean Theorem
• describe the relationship between x, h, y, k, and the Pythagorean Theorem
• generate a circle’s equation given information about its center, radius, or points on the circle
• apply completing the square to write the equation of a circle in standard form

Develop conceptual understanding:

circle, radius/radii, equidistant, center of the circle, points on the circle, equation of a circle

Supporting terms to communicate:

similar, scale factor, coordinates, Pythagorean Theorem, completing the square

Core Resource

A core resource supports multiple days of instruction.

• Defining Circles
This incomplete Core Resource supports students in making connections between the Pythagorean theorem and the equation of circles.
Resource:
Defining Circles

This incomplete Core Resource supports students in making connections between the Pythagorean theorem and the equation of circles.

All Resources From:
• Unit 7

#### Circles

Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.

• Is It On the Circle?
Students use what they know about finding distances in a coordinate plane and right triangles to prove that a point lies on a circle through another point.
Resource:
Is It On the Circle?

Students use what they know about finding distances in a coordinate plane and right triangles to prove that a point lies on a circle through another point.

All Resources From:
• Unit 7