Pre-DP Precalculus: Scope And Sequence (Units & Topics)
Pre-AP Geometry Overview (Units & Topics)
Unit 0: Algebra 1 Review (Aug. 27-30; Quiz Sept. 4-5)
Solving Linear Equations
Solving Quadratic Equations
Factoring Quadratics
Using the Quadratic Formula
Unit 1: Essential Elements of Geometry (Sept. 3-12; Test Sept. 17)
Textbook: Chapter 1
Unit Question: How do we construct figures to represent problem situations?
Points, Lines, Planes, Segments, & Rays
Congruence
Postulates & Axioms
Bisectors & Midpoints
The Distance Formula
Measuring & Classifying Angles
Complementary, Supplementary, & Vertical Angles
Classifying Polygons
Perimeter & Area of Polygons
Circumference & Area of Circles
Unit 2: Logic, Reasoning, & Proof (Sept. 12 – Sept. 26; Test Oct. 1)
Textbook: Chapter 2
Unit Question: How do we draw valid conclusions from our observations?
Patterns & Inductive Reasoning
Conditional (if-then) Statements
Deductive Reasoning
Using Deductive Reasoning on Postulates & Diagrams
Using Deductive Reasoning on Algebraic Properties
Proving Statements Using Flow Proofs
Proving Statements Using Two-Column Proofs
Proofs of Angle Pair Relationships
Unit 3: Parallel & Perpendicular Lines (Sept. 27 – Oct. 8; Test Oct. 15)
Textbook: Chapter 3
Unit Question: What are the possible relationships between lines in the plane?
Identifying Line Pairs & Their Angles
Parallel Lines & Transversals
Proving Lines Are Parallel
Slopes of Lines in the Coordinate Plane
Linear Functions & Their Graphs
Proving Lines are Perpendicular
Unit 4: Triangle Congruence (Oct. 10-24; Test Oct. 29)
Textbook: Chapter 4
Unit Question: How can we tell when two things are exactly the same?
Triangle Sum Properties
Properties of Congruent Triangles
The Side-Side-Side Postulate
The Side-Angle-Side Postulate & the HL Theorem
The Angle-Side-Angle Postulate
The Angle-Angle-Side Theorem
Proving Triangles Congruent
Solving Problems Using Congruent Triangles
Isosceles & Equilateral Triangles
Translating, Reflecting, & Rotating Polygons
Unit 5: Triangle Properties & Relationships (Oct. 25 – Nov. 11; Test Nov. 12)
Textbook: Chapter 5
Unit Question: Where are the most important parts of a structure?
Midsegments & Coordinate Proofs
Perpendicular Bisectors
Angle Bisectors of Triangles & the Incenter
Medians of Triangles & the Centroid
Altitudes of Triangles & the Orthocenter
Inequalities in One Triangle
Inequalities in Two Triangles
Indirect Proof
Unit 6: Similar Polygons (Nov. 13 – Dec. 3; Test Dec. 10)
Textbook: Chapter 6
Unit Question: How can we measure things that are too far away to touch?
Ratios, Proportions, & Geometric Means
Proportional Reasoning & Problem-Solving
Properties of Similar Polygons & Scale Factors
The Angle-Angle Postulate
The Side-Side-Side Similarity Theorem
The Side-Angle-Side Similarity Theorem
Triangle Proportionality
Dilating Polygons
Unit 7 Part 1: Right Triangles (Dec. 4 – Dec. 9; unit will be continued in January)
Textbook: Chapter 7 Sections 1-3
Unit Question: Why do we use right angles in architecture & engineering?
The Pythagorean Theorem & Its Converse
Classifying Triangles
Similar Right Triangles
Semester Review (Dec. 11-13)
Semester Exams (Dec. 16-19)
Unit 7 Part 2: Special Right Triangles and Trigonometry (Jan. 6 – 17; Test Jan. 21)
Textbook: Chapter 7 Sections 4-7 & Extension
Unit Question: How can we measure lengths and angles we can’t reach?
Special Right Triangles (45-45-90 and 30-60-90)
The Trigonometric Ratios
Using the Tangent Ratio
Using the Sine and Cosine Ratios
Using Inverse Trigonometric Functions
Solving Right Triangles
The Law of Sines
The Ambiguous Case
The Law of Cosines
Unit 8: Quadrilaterals (Jan. 25 – Feb. 3; Test Feb. 4)
Textbook: Chapter 8
Unit Question: How do we construct parts of stable structures?
Angle Measures in Polygons
Properties of Parallelograms
Parallelogram Proofs
Properties of Rhombi, Rectangles, and Squares
Properties of Trapezoids and Kites
Identifying Types of Quadrilaterals
Unit 9: Circles (Feb. 5-17; Test Feb. 25)
Textbook: Chapter 10
Unit Question: How do we measure distances and angles without straight lines?
Circles, Tangent Lines, & Their Properties
Arc Measures
Properties of Chords
Inscribed Angles & Inscribed Polygons
Relationships of Angles, Chords, and Secants
Segment Lengths in Circles
Equations of Circles & Their Graphs
Unit 10: Measuring Lengths and Areas (Feb. 28 – Mar. 3; Test Mar. 10)
Textbook: Chapter 11
Unit Question: How are side lengths and areas related for different shapes?
Areas of Triangles & Parallelograms
Areas of Other Quadrilaterals
Perimeters & Areas of Similar Figures
Circumference & Arc Length
Areas of Circles & Sector Areas
Areas of Regular Polygons
Geometric Probability
The Sine-Area Rule & Heron’s Formula
Areas of Irregular Polygons
Finding Areas of Triangles Using Trigonometric Ratios
Spring Break (March 11-15)
Unit 11: Solids, Surface Area, and Volume (Mar. 4 – Apr. 2; Test Apr. 14)
Textbook: Chapter 12
Unit Question: How are the edge lengths, side areas, and volumes of solids related?
Types of Solids & Their Properties
Surface Areas of Prisms & Cylinders
Surface Areas of Pyramids & Cones
Volumes of Prisms & Cylinders
Volumes of Pyramids & Cones
Surface Areas & Volumes of Spheres
Properties of Similar Solids
Unit 12: Transformations & Vectors (Apr. 3 – 23; Test Apr. 28)
Textbook: Chapter 9
Unit Question: How do we represent changes of a figure in a coordinate plane?
Defining a Vector
Translations Using Vectors
Decomposing a Vector
Matrices & Their Properties
Reflections
Rotations
Compositions of Transformations
Identifying Symmetry
Dilations
Unit 13: Probability & Volumes of Revolution (Apr. 24 – May 18; Test May 19)
Textbook: Supplemental handouts
Unit Question: How can we determine how likely an event is?
Permutations & Combinations
Experimental & Theoretical Probability
Independent & Dependent Events
Probabilities With and Without Replacement
Conditional Probabilities & Two-Way Tables
The Side-Angle-Side Similarity Theorem
Defining Solids of Revolution
Finding Volumes of Revolution
Semester Review (May 20-22)
Semester Exams (May 26-29)
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