Students expand their knowledge of circles to establish relationships between angle measures in and around circles, line segments and lines in and around circles, and portions of circles as related to area and circumference.
In Unit 7, Circles, students expand their knowledge of circles from middle school to establish relationships between angle measures in and around circles, line segments and lines in and around circles, and portions of circles as related to area and circumference.
This unit begins with Topic A, Equations of Circles, where students make an algebraic connection to geometry by writing equations for circles and understanding how to graph and derive features of a circle from an equation. This understanding can be used to review the criteria for perpendicular lines as well as algebraic quadratic concepts such as completing the square. In Topic B, Angle and Segment Relationships in Inscribed and Circumscribed Figures, students use inscribed, circumscribed, and central angles to develop an understanding of the relationship of angle measures in and around a circle. In addition, students will develop theorems related to chords that build a basis for relationships about line segments in and around a circle. Finally, in Topic C, Arc Length, Radians, and Sector Area, students build on their understanding of area and circumference of a circle to determine lengths and areas of sectors and discover proportional and congruent relationships related to area and lengths of arcs in circles. Students will also be exposed to the idea of radians and will derive a radian.
In Algebra 2, students will use their understanding of radians and unit circle relationships to further explore trigonometric relationships. In addition, the understandings developed in this unit of circles will carry into conic sections and tangent relationships, which is studied in AP Calculus.
Pacing: 16 instructional days (14 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.
?
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
?
?
circle | radius |
diameter | equation of a circle in standard form |
complete the square | equation of a circle in general form |
transformation | translation |
dilation | chord |
central angle | tangent |
arc | Chord Central Angles Conjecture |
Thales's Theorem | semicircle |
inscribed angle | intercepted angle |
major arc | minor arc |
arc measure | Intersecting Chords Theorem |
inscribed quadrilateral | cyclic quadrilateral |
secant | point of tangency |
circumscribed angle | arc length |
radians | sector area |
?
Key: Major Cluster Supporting Cluster Additional Cluster
?
?
?