Unit 0 – Algebra and Geometry Review

The students will review basic algebra and geometry skills commonly seen on the TSIA and ACT exams and will practice solving math problems without the use of a calculator

Unit 1 – Tools of Geometry

The students will begin exploring geometry and learn basic vocabulary, thought processes, and theorems to be used throughout the rest of the course, including segments, angles, and angle pair relationships

Pearson’s Lessons:

1-1 Points, Lines, and Planes

1-2 Measuring Line Segments

1-3 Measuring Angles

1-4 Exploring Angle Pairs

1-5 Basic Constructions

Unit 2 – Parallel and Perpendicular Lines

Students will determine if lines are parallel and perpendicular or neither based on their slopes and equations and use this information to make conjectures regarding various angles.

Pearson’s Lessons:

3-1 Lines and Angles

3-2 Properties of Parallel Lines

3-3 Proving Lines Parallel

3-4 Parallel and Perpendicular Lines

3-5 Parallel Lines and Triangles

3-6 Constructing Parallel and Perpendicular Lines [Pre-AP only]

3-7 Equations of Lines In the Coordinate Plane

3-8 Slopes of Parallel and Perpendicular Lines

3-9 Comparing Spherical and Euclidean Geometry

Unit 3 – Congruent Triangles

The students will determine if triangles are congruent using triangle congruence postulates while making conjectures using a variety of approaches.

Pearson’s Lessons:

4-1 Congruent Figures

4-2 Triangle Congruence by SSS and SAS

4-3 Triangle Congruence by ASA and AAS

4-4 Using Corresponding Parts of Congruent Triangles

4-5 Isosceles and Equilateral Triangles

4-6 Congruence in Right Triangles

4-7 Congruence in Overlapping Triangles

Unit 4 – Relationships Within Triangles

The student will understand, justify, and apply CPCTC to prove triangles are congruent. Students will also prove and use Isosceles Triangle Theorem to solve problems

Pearson’s Lessons:

5-1 Midpoint and Distance in the Coordinate Plane

5-2 Midsegments of Triangles

5-3 Perpendicular and Angle Bisectors

5-4 Bisectors in Triangles

5-5 Medians and Altitudes

5-6 Indirect Proof [Pre-AP only]

5-7 Inequalities in One Triangle

5-8 Inequalities in Two Triangles

Unit 5 – Coordinate Geometry

Students will construct, classify, and make conjectures regarding various polygons on the coordinate plane.

Pearson’s Lessons:

7-1 Polygons in the Coordinate Plane

7-2 Applying Coordinate Geometry

7-3 Proofs Using Coordinate Geometry [Pre-AP only]

Unit 6 – Transformational Geometry

The student is able to transform geometric figures using translations, rotations, and reflections and identify symmetries that allow for tessellations of geometric figures in the plane.

Pearson’s Lessons:

8-1 Translations

8-2 Reflections

8-3 Rotations

8-4 Symmetry

8-5 Composition of Rigid Transformations

8-6 Congruence Transformations (Pre-AP only)

8-7 Dilations

8-8 Other Non-Rigid Transformations (Pre-AP only)

Unit 7 – Probability

Students will calculate various types of probabilities, explore permutations and combinations, and relate probability back to geometric concepts.

Pearson’s Lessons:

15-1 Experimental and Theoretical Probability

15-2 Geometric Probability

15-3 Permutations and Combinations

15-4 Compound Probability

15-5 Conditional Probability with Frequency Tables

15-6 Conditional Probability Formulas

Unit 8 – Polygons & Quadrilaterals

Students will explore properties of various quadrilaterals to compare and contrast, make conjectures, and to solve problems.

Pearson’s Lessons:

6-1 The Polygon Angle-Sum Theorems

6-2 Properties of Parallelograms

6-3 Proving That a Quadrilateral Is a Parallelogram

6-4 Properties of Rhombuses, Rectangles, and Squares

6-5 Conditions for Rhombuses, Rectangles, and Squares

6-6 Trapezoids and Kites

Unit 9 – Similarity

The students will learn to use proportions to solve for variables and missing parts of polygons

Pearson’s Lessons:

9-1 Similar Polygons

9-2 Similarity Transformations

9-3 Proving Triangles Similar

9-4 Similarity in Right Triangles

9-5 Proportions in Triangles

Unit 10 – Right Triangles & Trigonometry

The students will identify and apply patterns from special right triangles to solve meaningful problems. Students will use trigonometric ratios to calculate the side lengths and angle measures of right triangles and apply trigonometric ratios when solving real life situations.

Pearson’s Lessons:

10-1 The Pythagorean Theorem and Its Converse

10-2 Special Right Triangles

10-3 Trigonometry

10-4 Angles of Elevation and Depression

Unit 11 – Circle Measurement

Students will demonstrate an understanding of circle properties and how to use them to solve problems

Pearson’s Lessons:

11-1 Circles and Arcs

11-2 Radian Measure

11-3 Areas of Circles and Sectors

11-4 Circles in the Coordinate Plane

Unit 12 – Theorems About Circles

The students will demonstrate an understanding of circle properties such as tangents, secants, and arcs and use them to solve problems

Pearson’s Lessons:

12-1 Tangent Lines

12-2 Chords and Arcs

12-3 Inscribed Angles

12-4 Angle Measures and Segment Lengths

Unit 13 – Area

Students will be able to find areas of different polygons and circles. Students will apply knowledge of finding areas of polygons to finding areas of composite figures.

Pearson’s Lessons:

13-1 Areas of Parallelograms and Triangles

13 -2 Areas of Trapezoids, Rhombuses, and Kites

13-3 Areas of Regular Polygons

13-4 Perimeters and Areas of Similar Figures

13-5 Trigonometry and Area

Unit 14 – Surface Area & Volume

The student is able to calculate the surface area of simple and composite three-dimensional geometric figures and uses these skills to solve application and real-world problems involving surface area.

Pearson’s Lessons:

14-1 Three-Dimensional Figures and Cross Sections

14-2 Surface Areas of Prisms and Cylinders

14-3 Surface Areas of Pyramids and Cones

14-4 Volumes of Prisms and Cylinders

14-5 Volumes of Pyramids and Cones

14-6 Surface Areas and Volumes of Spheres

14-7 Surface Areas and Volumes of Related Solids

Unit 15 – Reasoning and Proof

Students will use deductive reasoning, write conditional statements, and use logical reasoning to prove statements and theorems

Pearson’s Lessons:

2-1 Patterns and Conjectures

2-2 Conditional Statements

2-3 Biconditionals and Definitions

2-4 Deductive Reasoning

2-5 Reasoning in Algebra and Geometry

2-6 Proving Angles Congruent