## Geometry

This course aligns with the learning outcomes for:

## United States

This course aligns with the learning outcomes for:

## United States

From the times of Ancient Greece and earlier, to 17th century Europe and beyond, humanity’s understanding of geometric principles and relationships has developed into something powerful, beautiful, and applicable. Indeed, this branch of mathematics called Geometry has become fundamental and even essential to everyday life! Students of this course will experience both the development and application of geometry as they explore and interact with topics such as angles, lines, triangles, circles, transformations, and more. Along the way, students will perform constructions in a variety of mediums, analyze and complete deductions and proofs, and apply the geometric principles and theorems that have been discovered over the centuries. Students will also have fun meeting geometry-loving siblings who get into all sorts of adventures and predicaments, which — you guessed it — require geometry to solve.

From beginning to end, the StudyForge Geometry course is set up for student success. Each unit contains numerous interactive explorations that encourage students to discover geometric principles and relationships. Each lesson involves interactive videos that allow students to proceed at their own pace, with the ability to pause and rewind at any point. Additionally, each video is accompanied by a student-friendly note package to encourage deeper engagement and retention. To help students avoid getting stuck and to learn how to solve even the most challenging of geometric problems, all practice questions have detailed solution. Furthermore, students are well prepared for the wide variety of assessments they will encounter, and every quiz and test is randomized to allow retakes and encourage students to strive for mastery. Teachers of the course are equally well resourced, with detailed answer keys to all assessments, a customized dashboard, and supportive analytics to enable them to help all of their students succeed, whatever their skill levels are.

*Each lesson is designed to take 60 – 90 minutes to complete with the exception of major projects and assignments.

Lesson 1: Some Terminology and the Coordinate Plane
Lesson 2: Slope
Lesson 3: The Equation of a Line Part 1: Slope-Intercept Form
Quiz: Review & Warm-up Quiz #1: Lessons 1-3
Lesson 4: The Equation of a Line Part 2: General and Point-Slope Form
Lesson 5: Parallel and Perpendicular Lines
Lesson 6: Distance and Midpoint Formulas
Quiz: Review & Warm-up Quiz #2: Lessons 4-6

Lesson 1: Geometric Constructions
Lesson 2: Bisecting and Other Constructions
Lesson 3: Introduction to Angle Relationships and Terminology
Quiz: Lines and Angles Quiz #1: Lessons 1-3
Lesson 4: Parallel Lines and Transversals – Solving and Reasoning
Lesson 5: Parallel Lines and Transversals – Applications
Quiz: Lines and Angles Quiz #2: Lessons 4 & 5
Quiz: Lines and Angles Practice Test
Quiz: Lines and Angles Test
Quiz: Lines and Angles Test – No Written Work

Lesson 1: Triangle Properties
Lesson 2: Triangle Inequalities
Lesson 3: Triangle Congruence Part I
Quiz: Triangles Quiz #1: Lessons 1-3
Lesson 4: Triangle Congruence Part II
Lesson 5: Triangle Bisectors
Lesson 6: Triangle Medians and Altitudes
Quiz: Triangles Quiz #2: Lessons 4-6
Quiz: Triangles Practice Test
Quiz: Triangles Test
Quiz: Triangles Test – No Written Work

Lesson 2: Parallelograms
Lesson 3: Similarity in Polygons
Quiz: Polygons and Transformations Quiz #1: Lessons 1-3
Lesson 4: Reflections
Lesson 5: Rotations
Lesson 6: Translations
Lesson 7: Dilations
Quiz: Polygons and Transformations Quiz #2: Lessons 4-7
Lesson 8: (Enrichment) Fractals
Quiz: Polygons and Transformations Practice Test
Quiz: Polygons and Transformations Test
Quiz: Polygons and Transformations Test – No Written Work

Lesson 1: Introduction to Trigonometry
Lesson 2: The Three Ratios
Lesson 3: Application of Trigonometric Ratios
Quiz: Trigonometry Quiz #1: Lessons 1-3
Lesson 4: Special Angles and Triangles
Lesson 5: The Sine Law
Lesson 6: The Cosine Law
Quiz: Trigonometry Quiz #2: Lessons 4-6
Quiz: Trigonometry Practice Test
Quiz: Trigonometry Test
Quiz: Trigonometry Test – No Written Work

Lesson 1: Circle Basics and Sectors
Lesson 2: Circle Arcs and Angles
Lesson 3: Circle Intersections
Lesson 4: Circles and Polygons
Lesson 5: Other Circle Geometry Relationships
Lesson 6: Conics: Circles
Lesson 7: (Enrichment) Conics: Parabolas
Lesson 8: (Enrichment) Conics: Ellipses and Hyperbolas
Quiz: Circles Practice Test
Quiz: Circles Test – No Written Work
Quiz: Circles Test
Quiz: Circles Quiz #1: Lessons 1-3
Quiz: Circles Quiz #2: Lessons 4-6

Lesson 1: Perimeter and Area of 2D Shapes – Introduction
Lesson 3: Area and Perimeter in Composite Figures and the Coordinate Plane
Quiz: Measurement Quiz #1: Lessons 1-3
Lesson 4: Surface Area of Prisms and Pyramids
Lesson 5: Surface Area of Cylinders, Cones, and Spheres
Lesson 6: Volume of 3D Shapes
Lesson 7: Scaling and Proportions
Quiz: Measurement Quiz #2: Lessons 4-7
Lesson 8: (Optional) 3D Representations
Quiz: Measurement Practice Test
Quiz: Measurement Test
Quiz: Measurement Test – No Written Work

Lesson 1: Introduction to Reasoning (Logic)
Lesson 2: Conditional Statements
Lesson 3: Deductive Reasoning
Quiz: Reasoning and Proofs Quiz #1: Lesson 1-3
Lesson 4: Geometric Proofs Part I
Lesson 5: Geometric Proofs Part II
Quiz: Reasoning and Proofs Quiz #2: Lessons 4 and 5
Lesson 6: Circle Property Proofs
Lesson 7: Putting it All Together
Quiz: Reasoning and Proofs Quiz #3: Lessons 6 and 7

Lesson 1: Exploring Data
Lesson 2: More Ways to Represent Data
Lesson 3: Standard Deviation
Lesson 4: The Normal Distribution
Quiz: Statistics Quiz #1: Lessons 1-4
Lesson 5: Simulations
Lesson 6: Statistical Studies
Lesson 7: Estimations and Predictions
Quiz: Statistics Quiz #2: Lessons 5-7
Lesson 8: (Enrichment) Misuse of Statistics
Lesson 9: (Enrichment) Modeling Situations Using Regression
Quiz: Statistics Practice Test
Quiz: Statistics Test
Quiz: Statistics Test – No Written Work

Lesson 1: Sample Space
Lesson 2: Classifying Events
Lesson 3: Classifying Events (Dependent or Independent)
Quiz: Probability Quiz #1: Lessons 1-3
Lesson 4: Conditional Probability
Lesson 5: Expected Value
Quiz: Probability Quiz #2: Lessons 4 and 5
Lesson 6: (Enrichment) The Fundamental Counting Principle
Lesson 7: (Enrichment) Permutations
Lesson 8: (Enrichment) Combinations
Quiz: Probability Practice Test
Quiz: Probability Test
Quiz: Probability Test – No Written Work

Lesson 1: Welcome to your course!
Lesson 2: Teacher Orientation

Lesson 1: START HERE: Welcome to your Course
Lesson 2: Teacher Orientation

## See What Others Have to Say:

StudyForge has been an effective instructional program for students who are learning math. There are many visual representations as well as audio explanations on all the topics. Most of the practice questions provide both an answer and a solution to help students understand the procedures. From the teacher’s perspective, the course instruction can be easily rearranged for students who need a review of concepts from a previous grade.

## Online Teacher at EBUS Academy

I have been using the StudyForge math videos for a year now. The benefits were immediate as I was able to free up the time spent with my students to better track their progress and construct personalized learning goals. My students love the ease of use of the system and most of all, the increase in their test scores! I can’t ever imagine going back to a traditional classroom!

## Blended Teacher at Brampton Christian School

I think the videos are excellent. Unlike lectures, I can actually rewind back and forth as much as I want. In class, students kind of miss important information because they are busy writing notes.

## StudyForge Student

I love the reporting tool. In my distributed learning context, seeing student’s work habits in a helpful format has become invaluable to me. I wouldn’t ever want to give one on one help to students again without the course overview report handy!

## Course Features

• Engaging interactives to encourage discovery of principles and theorems
• Intentional elements to increase engagement and enhance interest in topics, such as a narrative storyline, games, historical figure vignettes, emphasis on real-life applications, and more
• Proofs are carefully introduced and scaffolded to enhance accessibility and avoid overwhelming students