ABCDEFGHIJKLMNOPQRSTUVWXYZ
1
Geometry (CP) Pacing Guide
2
Two-week summary of major instructional content and skills • 36 instructional weeks
3
4
Week(s)Unit / TextMajor ContentMajor Skills and Assessments
5
Weeks 1–2Unit 0: Geometry PrerequisitesSolving Multi-Step Equations; Solving Rational Equations; Solving Equations by Factoring; Simplifying Radicals (7 days)Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers); Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms; Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b; Simplify numerical radicals, limiting to square roots (i.e. nonperfect squares). For example, simplify v8 to 2v2
6
Weeks 3–4Unit 0: Geometry Prerequisites / Unit 1: Foundation of GeometryAlgebra Review/Summer Work Quiz; Label Points Lines and Planes; Linear Measure (6 days)Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc; Assessments/Review: Algebra Review/Summer Work Quiz
7
Weeks 5–6Unit 1: Foundation of GeometryIntro to Geometry Quiz; Distance Formula and Applications; Midpoint and Endpoint of a Line Segment (6 days)Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc; Apply the Pythagorean Theorem to find the distance between two points in a coordinate system; Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints; Assessments/Review: Intro to Geometry Quiz
8
Weeks 7–8Unit 1: Foundation of GeometryPartition a Line Segment; Coordinate Geometry Quiz; Foundations of Geometry Review/Test (6 days)Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints; Assessments/Review: Coordinate Geometry Quiz; Foundations of Geometry Review/Test
9
Weeks 9–10Unit 3: Congruence and ProofsIsoscles and Equilateral Triangles; Congruence; Proving and Applying the SAS and SSS Conruence Criteria (8 days)Use the properties of Isosceles and Equilateral triangles to solve for side lengths or angle measures; Identify the six cooresponding parts of congruent triangles/polygons; Prove triangle congruence given special congruence criteria
10
Weeks 11–12Unit 3: Congruence and ProofsProving and Applying the ASA and AAS Conruence Criteria; Congruence in Right Triangles; Congruent Triangles Review/Test; Solving Multi-step Equations Review (7 days)Prove triangle congruence given special congruence criteria; Prove the Hypotenuse-Leg Theorem; Assessments/Review: Congruent Triangles Review/Test; Solving Multi-step Equations Review
11
Weeks 13–14Unit 4: Proportions and Similar PolygonsRatios and Proportions Review; Similar Polygons; Similar Triangles; Midterm Review (7 days)How can the ratio of a scale factor be used to prove similar polygons and find a line segment is bigger or smaller; Prove Similar Triangles and use proportions to solve for the sides; Prepare for the midterm exam; Assessments/Review: Ratios and Proportions Review; Midterm Review
12
Weeks 15–16Unit 4: Proportions and Similar PolygonsMidterm Exams; Parallel Lines and Portional Parts in Triangles (7 days)Prove parallel sides of triangles using the proportional lengths of the other two sides of the triangles
13
Weeks 17–18Unit 4: Proportions and Similar Polygons / Unit 5: Right TrianglesPrportions in Triangles; Similarity Assessment; Similarity in Right Triangles (9 days)How can the ratio of a scale factor be used to find the perimeter/area of similar triangles; How can Geometric Mean be used to solve right triangles; Assessments/Review: Similarity Assessment
14
Weeks 19–20Unit 5: Right TrianglesPythagorean Theorem; Special Right Triangles (9 days)Use Pythagorean Thm to solve right triangles and identify Pythagorean Triples; What a the properties of a 45-45-90 and 30-60-90 triangle
15
Weeks 21–22Unit 5: Right TrianglesTrigonometric Ratios (8 days)How can Trig Ratios be used to solve right triangles
16
Weeks 23–24Unit 5: Right TrianglesTrigonometric Applications; Trigonometric Assessment (7 days)Assessments/Review: Trigonometric Assessment
17
Weeks 25–26Unit 5: Right TrianglesLaw of Sines (6 days)Given a ratio of the side of a triangle and the angle opposite, how can Law of Sines be used to solve oblique triangles
18
Weeks 27–28Unit 5: Right TrianglesLaw of Cosines (6 days)How can Law of Cosines be used to solve oblique triangles
19
Weeks 29–30Unit 5: Right TrianglesSolving Oblique Triangles; Oblique Triangle Assessment (7 days)How can Law of Sines and Cosines be used to solve for the missing parts of an oblique triangle; Assessments/Review: Oblique Triangle Assessment
20
Weeks 31–32Unit 6: CirclesArcs and Sectors of Circles; Lines Tangent to a Circle (8 days)How are arc lengths and sector area found; Identify lines that are tangent to a circle using angle measures and segment lengths
21
Weeks 33–34Unit 6: CirclesChords of a Circle; Intro to Parts of Circles Assessment; Inscribed Angles (8 days)Prove and apply relationships between chords, arcs, and central angles; Identify and apply relationships between the measures of inscribed angles, arcs, and central angles; Assessments/Review: Intro to Parts of Circles Assessment
22
Weeks 35–36Unit 6: CirclesSecant Lines and Segments; Equations of Circles; Circle Assessment (9 days)Recognize and apply angle relationships formed by secant and tagents intersecting inside and outside a circle; Identify the equation of a Circle, and graph the equation of a Circle; Assessments/Review: Circle Assessment
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100