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Introduction covering the lessons and goals of Unit 1.

Definition of Parallel, Perpendicular, and Transversal Lines will be covered. Angle relationships to lines and the angles formed by lines will be defined. Includes Vertical, Supplemental and complementary angles. An angle bi-sector will also be defined.

Worked solutions to Unit 1 Lesson 1 homework.

Defintion of corresponding angles, alternate exterior angles, and alternate interior angles.

Definition of corresponding angles, alternate exterior angles, and alternate interior angles.

Worked solutions to Unit 1 Lesson 2 homework

A basic intrduction to proofs and proof structure. Proofs of basic triangle relationships SAS, AAS, SSS.

A basic introduction to proofs and proof structure. Proofs of basic triangle relationships SAS, AAS, SSS.

Worked Solutions to Unit 1 Lesson 3

In this video students will learn to classify triangles by side and angle types.

Worked solutions for Unit 1 Lesson 4.

Part 1 Lesson 5: Application of material learned in Lessons 1 through 4 to a variety of problem types.

Part 2 Lesson 5: Application of material learned in Lessons 1 through 4 to a variety of problem types.

Worked solutions to Unit 1 Lesson 5 Homework.

Part 1 of Lesson 6: How to discuss angles in terms of circles using degrees.

Part 2 of Lesson 6: How to discuss angles formed inside a circle.

Worked Solutions for Unit 1 lesson 6 Homework

Intepretation of a circle graph using material learned in Unit 1 Lesson 6 on angles and percentages.

Worked solutions to Unit 1 Lesson 7 Homework

Overview of the lessons and material to be covered in Unit 2.

Definition of ratios and proportions, worked examples of applied proportions.

Worked solutions to Unit 2 Lesson 1.

Define similarity and congrence of two dimensional shapes.

Similarity and congruence of two-dimensional shapes.

Worked solutions to Unit 2 Lesson 2.

Introduction to the triangle property theorem and its use in proving similarity of triangles.

Worked solutions to Unit 2 Lesson 3.

Introduction to the triangle congruence theorems. Application to basic proofs.

Worked solutions to Unit 2 Lesson 4.

Introduction to basic congruence proofs of two dimensional shapes.

Worked solutions to Unit 2 Lesson 5.

Introduction to the use of ratios and similarity in applications from the Golden ratio to Fractals.

Worked solutions to Unit 2 Lesson 6.

Introduction to the content to be covered in Unit 3.

Definition of the coordinate plane, introduction to the transformations of trnaslation, reflection and rotation.

Introduction to the coordinate plane and basic definitions of translations, reflections, and rotations.

Worked solutions to Unit 3 Lesson 1.

How to graph two-dimensional translations in the coordinate plane.

How to graph translations and in the coordinate plane.

Worked solutions to Unit 3 Lesson 2

How to graph reflections in the coordinate plane.

How to graph relfections in the coordinate plane.

Worked solutions to Unit 3 Lesson 3

Identifying and classifying line and rotational symmetry of two dimensional shapes.

Identfying and classifying line adn rotational symmetry in two dimensions.

Worked solutions to Unit 3 Lesson 4

How to rotate two-dimensional shapes by degree, center, and direction.

Worked solutions to Unit 3 Lesson 5

Applications of transformations and symmetry in two-dimensional shapes.

Transformations and similarity in two-dimensional shapes.

Worked solutions to Unit 3 Lesson 6

How transformations and similarity create tessellations. Seeing tessellations and creating tessellations in the real-world.

How transformations and similarity create tessellations

Worked solutions to Unit 3 Lesson 7

Introduction and overview of Unit 4 material.

Introduction to the topics of squares, square roots and radicals.

Worked solutions to Unit 4 Lesson 1

Introduction to the pythagorean theorem. Application

Introduction to the Pythagorean Theorem.

Worked solutions to Unit 4 Lesson 2

Application of the Pythagorean Theorem to real-world word problems.

Word problems that use the Pythagorean Theorem

Worked solutions to Unit 4 Lesson 3

Using the converse of the Pythagorean Theorem and special types of right triangles.

Worked solutions to Unit 4 Lesson 4

Brief overview of the material covered in Unit 5.

Area and Volume of Cubes and rectangular solids.

Area and Volume of Cubes and rectangular solids.

Worked solutions to Unit 5 Lesson 1

Area and volume equations of cylinders and cones.

Area and volume equations of cylinders and cones.

Worked solutions to Unit 5 Lesson 2

Area and Volume of spheres

Worked solutions to Unit 5 Lesson 3

Area and volume of square pyramids and rectangular prisms.

Worked solutions to Unit 5 Lesson 4

Introduction to Euler's Theorem on the faces, edges and vertices of regular solids.

Worked solutions to Unit 5 Lesson 5

Introduction to taking cross sections of solids and deconstructing solids into nets.

Worked solutions to Unit 5 Lesson 6

**Course Description**

This course covers the major topics in 7th and 8th Grade Geometry. The course consists of 33 video-lessons with homeworks, homework review videos, tests, and discussion questions for parents. The goal of this course is to emphasis the link between geometry and the everyday world while creating a solid foundation for advancement to high school geometry.

Seeing geoemtry in the world around us is the emphasis of this course. Where applicable word problem are used to highlight how geometry can be used to solve "every-day" problems. Students are chellenged to find example of geometry in their daily lives adn to imagine how geometry could be used or is used in simple daily tasks, from how to slice a sandwich (rectangluar or square) to beidge design.

**Course Goals**

Upon course completion, students will be understand the relationships between angles and lines, similarity and congruence of two-dimensional shapes, the transformations of translation, rotation and reflection, the Pythagorean Theorem, the relationship between two-and three dimensional shapes, area, surface-area and volume, as well as the basic of proofs.

**Target Audience**

This video-course is primarily intended for Grades 7 and 8 students and Grade 9 students who may need to review previously taught concepts. The difficultly level of this course is medium.

**Course Requirements**

Students taking this course are expected to have satisfactorily understood and mastered the most important topics taught in a standard Grade 6 Math Course.

**Course Includes**

- 9 hours of video
- 33 Video-lessons
- 33 Worksheet review videos
- 33 Homework exercises
- Over 250 practice problems!
- 5 Quizzes
- 1 Comprehensive Exam
- Answer "keys" to all homeworks, quizzes and tests (Additional Resources For Parents)
- 10 additional discussion topics (Additional Resources For Parents)

**Course Topics **

- Introduction
- Line and Angle Types
- Angles formed by Transversals
- Intro to proofs: Proving Angles Relationships
- Classifying Triangles by Side or Angle
- Angles and Circles
- Circle Graphs
- Similar Figures
- Congruence
- Ratios and Proportions
- Proportions, Similarity and COngruence in Traingels
- Similarity adn COngruence in two-dimensional shapes
- Basic Triangle Proofs
- The Golden Ratio, Fractals, adn Fibbonnacci Sequence
- The Cooordinate Plane
- Translation, Reflection and Rotation
- Symmetry
- Tessellation
- Distance, square roots and radicals
- The Pythagorean Theorem
- Converses of the Pythagorean Theorem
- Perimeter, Area, Volume
- Three Dimensional Shapes
- Faces, Edges, Vertices
- Cross-sections
- Nets

- Teacher: Suzanne
- Areas of expertise: Mathematics
- Education: PhD in Mathematics, NMSU 2010
- Interests: Digital platform development for Math Education
- Skills: Word problems, interdisciplinary work
- Associations: AMATYC
- Issues I care about: Expanding Math Education, Integrating STEM and Art

Mathematics underlies the world around us, in the technology we use everyday to the patterns in a snail shell. I believe that everyone can understand and appreciate mathematics. While not everyone will be a mathematics major everyone can appreciate the role mathematics plays in how we see and shape our world.

Suggestions for best use of the course.

Answer Keys for Unit 1 homeworks

Answer Keys to Unit 2 Homework

Answer Keys to Unit 3 Homework

Answer Keys to Unit 4 Homework

Answer Keys to Unit 5 Homework

Quiz 1 covers material in Unit 1. The Solutions key is included.

Quiz covering Unit 2 material and Solution Key

Quiz covering Unit 3 Material and solution key

Quiz covering unit 4 material and solutions

Quiz covering Unit 5 material and solutions

Comprehensive exam covering material learned in Units 1-5. Solutions included

Discussion Questions to ask students to deepen their connection to the material.

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