Back to Learning Catalog

Status

Open

Estimated Completion Time

2 segments/36 weeks

Overview

One day in 2580 B.C.E., a very serious architect stood in a dusty desert with a set of plans. His plans called for creating a structure 480 feet tall, with a square base and triangular sides, using stone blocks weighing two tons each. The Pharaoh wanted the job done right. The better this architect understood geometry, the better his chances were for staying alive.

Geometry is everywhere, not just in pyramids. Engineers use geometry to build highways and bridges. Artists use geometry to create perspective in their paintings, and mapmakers help travelers find things using the points located on a geometric grid. Throughout this course, students travel a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem-solving.

 

Note: content varies depending on the course version. For currently enrolled students, please refer to the syllabus located in the course information area for curriculum specifics.

Course Requirements

Besides engaging students in challenging curriculum, VLACS guides students to reflect on their learning and to evaluate their progress through a variety of assessments. Assessments can be in the form of self-checks, practice lessons, multiple choice questions, projects, oral assessments and discussions. Instructors evaluate progress and provide interventions through the variety of assessments built into a course, as well as through contact with the student in other venues.

Major Topics and Concepts

Segment I

Module 01 Basics of Geometry

  • Basics of Geometry
  • Basic Constructions
  • Constructing with Parallel and Perpendicular Lines
  • Constructions with Technology
  • Introduction to Proofs

 

Module 02 Transformations and Congruence

  • Translations
  • Reflections
  • Rotations
  • Rigid Motion and Congruence

 

Module 03 Proofs of Theorems

  • Line and Angle Proofs
  • Triangle Proofs
  • Parallelogram Proofs

 

Module 04 Dilations and Similarity

  • Dilations
  • Similar Polygons
  • Similar Triangles

 

Module 05 Triangle Similarity Proofs

  • Triangle Congruence and Similarity
  • Applications of Congruence and Similarity

 

Segment 2

Module 06 Coordinate Geometry

  • Using the Coordinates
  • Slope
  • Coordinate Applications

 

Module 07 Right Triangles and Trigonometry

  • 07.01 Solving Right Triangles
  • 07.02 Trigonometric Ratios
  • 07.04 Applying Trigonometric Ratios

 

Module 08 Volume and Figures

  • Formulas
  • Applications of Volume
  • Density
  • 3-D Figures

 

Module 09 Circles

  • Properties of a Circle
  • Inscribed and Circumscribed Circles
  • Applications of Circles

 

 

Career

Gemologist

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Students will demonstrate an understanding of transformations and congruence by describing transformations of rigid motion, describing congruence by rigid motion, solving geometric theorems, and creating logical arguments.

Project

You are a gemologist at a jewelry firm. You are responsible for appraising diamonds. A customer has brought a diamond to you for an appraisal. The cut of a diamond is useful in performing an appraisal. Unfortunately, the diamond is not cut to the standard that the customer expected, and therefore is not worth as much money as she originally thought. Your task is to create a report that suggests how the customer’s diamond should be cut to one with ideal proportions and symmetry.

Career

Textile Designer

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Students will demonstrate an understanding of dilations and similarity by explaining dilation of a geometric figure and dilation rules, describing similar triangles, and solving proofs and real-world problems involving congruence and similarity.

Project

You are a textile designer who creates appealing patterns and prints for various fabrics, clothing, and non-clothing material. A clothing designer has hired you to create a frieze pattern that can be enlarged or reduced depending on the clothing. This pattern will create a strong geometric theme for an upcoming fashion show. The designs will preserve angles and keep lengths in proportion for all dilations of your patterns. You will present the pattern designs in a portfolio.

Career

Transportation Planner

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Students will demonstrate an understanding of coordinate geometry by comparing geometric properties, proving geometric relationships, and describing algebraic models.

Project

You are a Transportation Planner. You were hired by a company which makes daily deliveries to various businesses throughout the city. The company wants to save money by planning out a route for their drivers that will cut both driving time and gas expenses. Your task is to plan the most efficient transportation route for their deliveries.

Along with your project, you will complete the Skills and Practice Problem Set Work to practice the skills necessary to develop a thorough understanding of statistics. You may complete these problems at any time.

Career

Irrigation Design Engineer

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Students will demonstrate an understanding of circles by describing circle properties, solving circle theorems, and applying circle applications.

Project

You are an irrigation design engineer. You have been hired by a farmer to design an irrigation system for his crop field. The farmer owns circular sprinklers and would like to use the equipment she already has. It is your job to design a system using circular sprinklers that waters the most amount of land without double watering or leaving un-watered areas, as these areas are considered unsuitable for planting.

Career

Package Designer

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Students will demonstrate an understanding of volume and figures by explaining calculations for volume, explaining calculations for area, explaining calculations for density, and analyzing two and three dimensional figures.

Project

You are a Package Designer hired by a new sports company. Your task is to design packaging for their different sports lines – pucks or golf items. The company would like the packaging to be as efficient as possible. They would like you to use the least amount of material and have the least amount of wasted space in the package. They would also like their design to be unusual enough to be noticed on a shelf with other manufacturers’ products. Your job is to design two packaging options for two of their products in one of the sports lines (golf or hockey) and to create a presentation comparing the options.

Career

Land Surveyor

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Students will demonstrate an understanding of right triangles and trigonometry by explaining the Pythagorean Theorem, solving problems using trigonometric ratios, and comparing special right triangle properties.

Project

You are a land surveyor working for a surveying company. You need to settle a land dispute between a town tax collection office and a landowner. The landowner is claiming that they are being taxed on too much acreage; whereas the town claims that the figures for the area of the land the taxpayer owns is correct. To help settle the dispute, you will use the landowner’s land deed to diagram the land, compute the acreage of the land, and then create a report with your survey conclusions.

Credits 1

Competency Group Overview

If you wish to take Algebra 1 and Geometry concurrently, please contact [email protected]

Meets mathematics graduation requirement.

Competencies

  • Transformations and Congruence
    Students will demonstrate an understanding of transformations and congruence by describing transformations of rigid motion, describing congruence by rigid motion, solving geometric theorems, and creating logical arguments.
  • Dilations and Similarity
    Students will demonstrate an understanding of dilations and similarity by explaining dilation of a geometric figure and dilation rules, describing similar triangles, and solving proofs and real-world problems involving congruence and similarity.
  • Coordinate Geometry
    Students will demonstrate an understanding of coordinate geometry by comparing geometric properties, proving geometric relationships, and describing algebraic models.
  • Right Triangles and Trigonometry
    Students will demonstrate an understanding of right triangles and trigonometry by explaining the Pythagorean Theorem, solving problems using trigonometric ratios, and comparing special right triangle properties.
  • Volume and Figures
    Students will demonstrate an understanding of volume and figures by explaining calculations for volume, explaining calculations for area, explaining calculations for density, and analyzing two and three dimensional figures.
  • Circles
    Students will demonstrate an understanding of circles by describing circle properties, solving circle theorems, and applying circle applications.

Pre-Requisites

Algebra 1 Segment 1, or the following Algebra Competencies: Linear Equations, Linear Inequalities, Graphs and Linear Functions.

Honors

Course: To complete the honors version of this offering, you must discuss this with your instructor during your welcome call.

Project/Experience: Honors is awarded by earning "Exceeds" on all rubric assessments.

Attend a virtual open house

We offer regular online open house webinars where VLACS staff members provide parents and students with an overview of our programs and answer questions about online learning.