All Units | Additional Cobb Honors Standards
Honors Analytic Geometry
Unit 1A: Similarity, Congruence and Proofs of Geometry
These are additional standards to be addressed in the honors course along with the Analytic
Geometry Curriculum Map and Pacing Guide.
3 weeks
Introduction:
Splitting Unit 1 up into two parts, the first part introduces some key geometric skills and contains some standards that build upon
Unit 5 & 6 of Coordinate Algebra.
Key Topics:
1. Conjecture (Honors)
2. Conditional Statements (Honors)
3. Proofs (Honors)
4. Geometric Theorems: Lines and Angles (G.CO.9)*
[Summative]
5. Polygon Congruence Transformations (G.CO.6)
6. Rigid Motion (G.CO.6)
7. Dilations (G.SRT.1a)
8. Scale Factor (G.SRT.1b)
9. Polygon Similarity Transformations (G.SRT.2)
[Summative]
*Geometric Constructions: Lines and Angles (G.CO.12)
1|L o h u i s
Cobb Honors Standard:
Use conjecture, inductive & deductive reasoning, counter examples,
and informal proofs to justify mathematical arguments.
 Essential Question(s):
How can you make or disprove conjectures?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 1 Unit 4; Glencoe Geometry Ch. 1; McDougal
Geometry Ch. 2
2. Holt-McDougal Online (Module 1, Lessons 3-5)
Cobb Honors Standard:
Use the relationships among conditional statements to justify
conjectures and reasoning.
 Essential Question(s):
1. How can you express and symbolize if-then statements?
2. How can definitions be written as biconditional
statements?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 1 Unit 4; Glencoe Geometry Ch. 1; McDougal
Geometry Ch. 2
2. Holt-McDougal Online (Module 1, Lessons 3-5)
Cobb Honors Standard:
Develop formal two-column, paragraph, and flow chart proofs to justify
geometric theorems.
 Essential Question(s):
1. What kinds of justifications can you use in writing
algebraic and geometric proofs?
2. How can you organize the deductive reasoning of a
geometric proof?
3. What are some formats you can use to organize
geometric proofs?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 1 Unit 4; Glencoe Geometry Ch. 1; McDougal
Geometry Ch. 2
2. Holt-McDougal Online (Module 2, All Lessons)
All Units | Additional Cobb Honors Standards
Honors Analytic Geometry
Unit 1B: Similarity, Congruence and Proofs of Triangles and Quadrilaterals
3 weeks
Introduction:
The second part of Unit 1 focuses on triangle similarity, proofs, and extending those proofs to quadrilaterals.
Key Topics:
1. AA Criterion (G.SRT.3)
2. Triangle Similarity Theorem Proofs (G.SRT.4)
3. Triangle Applications (G.SRT.5)
4. Triangle Congruency (G.CO.7)
5. Triangle ASA, SAS, SSS (G.CO.8)
[Summative]
6. Geometric Theorems: Triangles (G.CO.10)*
7. Triangle Concurrency (Honors)*
8. Parallelogram Proofs (G.CO.11)
9. Special Quadrilaterals (Honors)
[Summative]
*Triangle Constructions (G.CO.13)
2|L o h u i s
Cobb Honors Standard:
Explain the relationships of special points and lines of a triangle
(concurrency) and derive the Triangle Midsegment Theorem.
 Essential Question(s):
1. How can you describe the set of points equidistant from
the endpoints of a segment or from sides of an angle?
2. How can you construct the circumcenter and the incenter
of any triangle?
3. How can you find the balancing in the interior of any
triangle?
4. What are the properties of the triangle whose vertices are
the midpoints of the three sides of a triangle?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 1 Unit 5; Glencoe Geometry Ch.6; McDougal Ch. 5
2. Holt-McDougal Online (Module 6, Lessons 1-3)
Cobb Honors Standard:
Prove properties and relationships among special quadrilaterals:
parallelograms, rectangle, rhombus, square, trapezoid, and kite.
 Essential Question(s):
1. What are the geometric properties of rectangles, squares,
and rhombi?
2. What information about a parallelogram allows you to
conclude it is a rectangle, rhombus, or a square?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 1 Unit 5; Glencoe Ch.8; McDougal Ch.6
2. Holt-McDougal Online (Module 7, Lessons 3)
All Units | Additional Cobb Honors Standards
Honors Analytic Geometry
Unit 2: Right Triangle Trigonometry
3 weeks
Introduction:
Unit 2 transitions into right triangle trigonometry by first extending angle measurements to regular polygons before detailing
triangle trigonometric ratios.
Key Topics:
1. Sum of Polygon Angles (Honors)
2. Pythagorean Theorem & Converse (G.SRT.8)
3. Classifying Triangles (Honors)
4. Special Right Triangles (Honors)
[Summative]
5. Intro to Trig Ratios (G.SRT.6)
6. Complementary Angles: Sine and Cosine (G.SRT.7)
7. Solving Right Triangles + Applications (G.SRT.8)
8. Angles of Elevation and Depression (Honors)
[Summative]
Cobb Honors Standard:
Determine the sum of interior and exterior angles of regular polygons.
 Essential Question(s):
1. How do you find the sum of the interior and exterior
angles of a convex polygon?
2. How do you find the measure of each interior and
exterior angle of a regular polygon?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 1 Unit 5; Glencoe Ch. 7; McDougal Ch. 11
2. Holt-McDougal Online (Module 12, Lesson 4)
Cobb Honors Standard:
Be able to use side lengths to classify a triangle as acute, obtuse, or
right.
 Essential Question(s):
How can you use side lengths to determine whether a
triangle is acute, obtuse, or right?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Glencoe Ch. 5; McDougal Ch. 4
2. Holt-McDougal Online (Module 9, Lesson 1)
Cobb Honors Standard:
Determine the lengths of sides of 30°-60°-90° and 45°-45°-90°
triangles.
 Essential Question(s):
What are the proportions of the side lengths in 30°-60°-90°
and 45°-45°-90° triangles?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 2 Unit 5; Glencoe Ch. 13; McDougal Ch.9
2. Holt-McDougal Online (Module 9, Lesson 2)
Cobb Honors Standard:
Use angles of elevation and depression to solve application problems
involving distance.
 Essential Question(s):
How can trigonometric ratios be used to estimate distances
when you know an angle of elevation or depression?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
3|L o h u i s
All Units | Additional Cobb Honors Standards
1.
2.
Honors Analytic Geometry
Math 2 Unit 5; Glencoe Ch. 13; McDougal Ch.9
Holt-McDougal Online (Module 10, Lessons 3)
Unit 3: Circles and Volume
4 weeks
Introduction:
Emphasis is placed on the circle and its relationship with lines and angles as well as a focus on volume of various geometric solids.
Little emphasis was placed on spherical relationships and surface area and its relationship with volume.
Key Topics:
1. Circle Similarity Proof (G.C.1)
2. Angles and Lines Relationships (G.C.2)
3. Arcs and Chords Relationships (G.C.2)
4. Angles of Quadrilaterals Inscribed in a Circle Proof
(G.C.3)*
5. Tangents of Circles (G.C.4)+
6. Arc Lengths and Sectors (G.C.5)
7. Constant of Proportionality (G.C.5)
[Summative]
8. Formulas for Area & Volume (informal)
(G.GMD.1)
9. Surface Area (Honors)
10. Cavalieri’s Principle (informal) (G.GMD.2)
11. Sphere Surface Area and Volume Relationships
(Honors)
12. Solving Volume Problems + Applications
(G.GMD.3)
[Summative]
*Inscribed & Circumscribed Circles of Triangles
Constructions (G.C.3)
+Tangent Constructions (G.C.4)
4|L o h u i s
Cobb Honors Standard:
Give an informal argument for the formula for surface area for
cylinder, pyramid, cone, sphere and other geometric solids.
 Essential Question(s):
How do you find the surface area of a sphere and other
geometric shapes?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 2 Unit 6; Glencoe Ch. 12; McDougal Ch. 12
2. Review from Math 8 Curriculum
Cobb Honors Standard:
Derive a relationship between the surface area and volume of a
sphere.
 Essential Question(s):
What is its relationship, both algebraically and geometrically,
of a sphere’s surface area and its volume?
 Opening, Work Session, Closing:
Refer to attached materials.
 Text References:
1. Math 2 Unit 6; Glencoe Ch. 12; McDougal Ch. 12
2. Review from Math 8 Curriculum
3. Holt-McDougal Online (Module 11, Lessons 4)
All Units | Additional Cobb Honors Standards
Honors Analytic Geometry
Unit 4: Extending the Number System
3 weeks
Introduction:
Students pick up with rational exponents and extending the number system to encompass complex numbers. Vector
representations, both algebraically and graphically are being included.
Key Topics:
1. Rational Exponents (N.RN.1)
2. Radical and Rational Exponent Properties (N.RN.2)
3. Rational and Irrational Closure (N.RN.3)
4. Complex Numbers Derivation (N.CN.1)
[Summative]
5. Vector Representations & Complex Graphs (Honors)
6. Complex Operations + Closure (N.CN.2)
7. Complex Conjugates (N.CN.3)
8. Polynomial Operations + Closure (A.APR.1)
[Summative]
5|L o h u i s
Cobb Honors Standard:
Understand and graph complex numbers through vector
representation.
 Essential Question(s):
1. How are complex numbers represented by vectors?
2. How are vectors represented graphically?
 Opening, Work Session, Closing:
http://mathforum.org/johnandbetty/
This is an introduction to vectors that is taught in advanced
algebra. It is beneficial to understand how vectors look on
the coordinate plane.
Text References:
1. Math 3 Unit 3
2. Holt-McDougal Online (Module 13, Lessons 2)
All Units | Additional Cobb Honors Standards
Honors Analytic Geometry
Unit 5: Quadratic Functions
8 weeks
Introduction:
This is a massive unit on quadratics covering factoring, solving, graphing, comparing with linear and exponential functions, modeling,
and representing data.
Key Topics:
1. Solving Quadratic Problems (w/ Complex Solutions) (N.CN.7)
2. Factoring 𝑥 2 + 𝑏𝑥 + 𝑐 (A.SSE.3a)
3. Factoring 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 (A.SSE.3a)
4. Factoring Special Products (A.SSE.3b)
5. Standard Form (A.SSE.1a+b)
6. Vertex Form (A.SSE.2)
[Summative]
7. Graphs & Tables of Quadratic Equations (A.SSE.3)
8. Create 1-Variable Equations and Inequalities (A.CED.1)
9. Create 2-Variable Equations & Graph (A.CED.2)
10. Solving for a Particular Quantity (A.CED.4)
11. Solving by Factoring (Zeros) (A.REI.4)
12. Completing the Square (A.REI.4b)
13. The Quadratic Formula (A.REI.4a)
[Summative]
14. Systems of Equations (Quadratic and Linear) (A.REI.7)
15. Systems of Inequalities (Quadratic and Linear) (Honors)
16. Key Features (F.IF.4)
17. Domain Context (F.IF.5)
18. Average Rate of Change (F.IF.6)
19. Graph Key Features of Quadratic Functions (F.IF.7a)
[Summative]
20. Analyze Multiple Representations (F.IF.8a)
21. Comparing Functions (F.IF.9)
22. Model Functions (F.BF.1a+b)
23. Quadratic Transformations (F.BF.3)
24. Construct Models and Solve Problems (F.LE.3)
25. Represent Data (S.ID.6)
26. Line Fitting (S.ID.6a)
[Summative]
6|L o h u i s
Cobb Honors Standard:
Solve systems of quadratic and linear inequalities both
algebraically and graphically.
 Essential Question(s):
How are inequality systems of quadratics different
from linear functions?
 Opening, Work Session, Closing:
Students have already been exposed to linear
systems of inequalities, but now you want to show
both linear and quadratic equations on the same
plane and how they are solved algebraically.
 Text References:
1. Math 3 Unit 5; Holt Alg. 2 Ch. 9
All Units | Additional Cobb Honors Standards
Honors Analytic Geometry
Unit 6: Modeling Geometry
3 weeks
Introduction:
The unit takes the parts of parabolas and circles and extends them to modeling in the coordinate plane, introducing students to
conics.
Key Topics:
1. Derive Equation of a Circle (G.GPE.1)
2. Derive Equation of a Parabola (G.GPE.2)
3. Coordinates to Prove Geometric Theorems Algebraically
(G.GPE.4)
4. Understanding Loci (Honors)
[Summative]
7|L o h u i s
Cobb Honors Standard:
Locate, draw, and describe a locus in a plane or in space.
 Essential Question(s):
Describe the difference between loci in a plane and
loci in space.
 Opening, Work Session, Closing:
Introduce Loci and how it plays a role in circles and
parabolas; extend this understanding to the
introduction to conics.
 Text References:
McDougal Geometry Ch. 10; Glencoe Geometry Ch.
11 Investigation
All Units | Additional Cobb Honors Standards
8|L o h u i s
Honors Analytic Geometry