The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.

Students Can (Evidence Outcomes):

HS.G-CO.A. Congruence: Experiment with transformations in the plane. 

• State precise definition of circle, based on the undefined notions of point and distance around a circular arc. (CCSS: HS.G-CO.A.1)

HS.G-C.A. Circles: Understand and apply theorems about circles.

• Prove that all circles are similar. (CCSS: HS.G-C.A.1)

• Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. (CCSS: HS.G-C.A.2)

• Prove properties of angles for a quadrilateral inscribed in a circle. (CCSS: HS.G-C.A.3) 

HS.G-GPE.A. Expressing Geometric Properties with Equations: Translate between the geometric description and the equation for a conic section.

• Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. (CCSS: HS.G-GPE.A.1)

HS.G-GPE.B. Expressing Geometric Properties with Equations: Use coordinates to prove simple geometric theorems algebraically.

• Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). (CCSS: HS.G-GPE.B.4)

HS.G-GMD.A. Geometric Measurement and Dimension: Explain volume formulas and use them to solve problems. 

• Give an informal argument for the formulas for the circumference of a circle and area of a circle. Use dissection arguments and informal limit arguments. (CCSS: HS.G-GMD.A.1)

HS.G-MG.A. Modeling with Geometry: Apply geometric concepts in modeling situations. 

• Apply concepts of density based on area in modeling situations (e.g., persons per square mile). (CCSS: HS.G-MG.A.2)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

Assessments:

• Chapter 10 Assessment (PDF), Chapter 11 Assessment (PDF)

• SAT Suite Educator Question Bank (Content Domain: Geometry and Trigonometry)

• Additional Assessment Tasks

Instructional Resources & Notes:

• Big Ideas Geometry Chapters 10-11 (skip Lessons 10.6, 10.8)

• Supplemental Lesson Resources: Chapter 10, Chapter 11

• Additional Modeling Tasks

  • Cost of a Driveway, People, People Everywhere, You Broke My Table!, On a Roll, Viewing Distances (References: Completing the Modeling Cycle, Advice on Modeling)

• Notes:

  • Students do not need to construct a tangent to a circle in Lesson 10.1 or construct a square inscribed in a circle in Lesson 10.4; these are optional and can be reserved for Honors Geometry classes only.

  • Lesson 10.8 (Focus of a Parabola) addresses evidence outcomes in Precalculus with Trigonometry. Lesson 10.8 should be skipped.

  • Students do not need to convert between degree and radian measure in Lesson 11.1 (Circumference and Arc Length).

  • Even though finding areas of sectors of circles (Lesson 11.2) is part of the (+) evidence outcomes in the Colorado Academic Standards, it can be assessed on the SAT.

Algebra 1 Review:

In addition to the Review & Refresh exercises included with each Big Ideas Geometry lesson, the following resources can be used for curating frequent, ongoing mixed review exercise sets of key Algebra 1 concepts and skills. These resources focus on linear equations, linear functions, systems of equations & inequalities, exponential functions, quadratic functions, and quadratic equations:

• Big Ideas Algebra 1 Additional Practice

• Using Your Algebra Skills Lessons

• Algebra Warm-Ups for Geometry Teachers (Geoff Krall)

• SAT Suite Educator Question Bank (Content Domains: Algebra, Advanced Math)