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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

Rigid Motions: Students will demonstrate an understanding of rigid motions by analyzing various types of rigid motions and congruence in terms of rigid motion.

Project

You are a Gemologist responsible appraising diamonds for your jewelry firm. You have a customer who has brought her diamond in for an appraisal and believes her diamond is a 1A grade cut. Unfortunately, the diamond is not cut to that standard and therefore is not worth as much money as she originally thought.

To demonstrate your jewelry store’s exceptional services and keep the customer coming back to your jewelry store for future purchases and appraisals, your task is to create a report to give the customer in which you describe and diagram the cut of her diamond and compare her diamond’s cut to one with ideal proportions and symmetry.

Career

Building Inspector

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Congruence: Students will demonstrate an understanding of rigid motions by analyzing various types of rigid motions and congruence in terms of rigid motion.

Project

You are a Building Inspector working for a small town in northern New England recently experiencing budget cuts. Your department is especially hit hard by these cuts, and you know you will no longer be able to spend as much time as you previously had at each building site. Your task is to convince your board of selectmen that you can adequately inspect buildings with less time at each site by using the theorems of geometry.

Career

Textile Designer

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Similarity: Students will demonstrate an understanding of similarity through working with dilations, similar polygons, similar triangles, and proofs of similarity and using the concepts of congruence and similarity to solve real-world problems.

Project

You are a Textile Designer who creates appealing patterns and prints for a variety of fabrics, clothing, and non-clothing material. You have been hired by a clothing designer to create a frieze pattern that can be enlarged or reduced depending on the clothing. This pattern will be integrated into a variety of clothing to maintain a strong geometric theme for an upcoming fashion show. In a portfolio, you will present your pattern designs and prove to the designer that you were able to preserve angles and keep lengths in proportion for all dilations of your creations!

Career

Land Surveyor

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Right Angles and Trig: Students will demonstrate an understanding of right triangles by reasoning to solve right triangles using various techniques including Pythagorean Theorem, trigonometric ratios, and special right triangle properties.

Project

You are a Land Surveyor that surveys land to help the landowners establish the correct boundaries of their land and settle land boundary disputes between neighbors. You also diagram land plots, a process called platting, and compute the acreage of land.

Your task is to settle a land dispute between a town tax collection office and a landowner. The landowner is claiming they are being taxed on too much acreage, whereas the town claims their 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.

Career

Irrigation Engineer

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Circles: Students will demonstrate an understanding of circles by reasoning with and applying theorems about circles.

Project

You are an Irrigation Engineer 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

Solid Geometry: Students will demonstrate an understanding of solid geometry by calculating volume of various solid figures, problem-solving, and visualizing the relationship between two and three-dimensional figures.

Project

You are a Package Designer, just hired by a new sports company to design packaging for their different sports lines. While the company would like the packaging to be as efficient as possible, using the least amount of material and having 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 each product in one of the sports lines and to create a presentation comparing the options.

Career

Transportation Planner

Status

Open

Estimated Completion Time

3-4 weeks

Competency

Expressing Geometric Properties with Equations: Students will demonstrate an understanding of geometric properties by using coordinates and applying algebraic models to express and prove geometric relationships.

Project

You are a Transportation Planner 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.

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.