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High School
Geometry/Geometry Honors
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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.
Major Topics and Concepts
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
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
Competencies
Geometric Constructions
Students will demonstrate an understanding of geometric constructions by creating constructions, explaining the logic underlying constructions, and creating regular polygons using construction techniques.
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.
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Projects allow students to demonstrate competence and understanding of concepts and skills by completing a career-related task. For example, the assignment might be to create a mural, a package design, a speech, a film review, or a movie set – you name it! These creative projects are about applying your learning acquired through in-depth research to real-world career tasks.
Each competency will be addressed through a project that is based on a real-life career task. Here are the careers you will explore: Gemologist, Building Inspector, Textile Designer, Transportation Planner, Irrigation Design Engineer, Package Designer, Surveyor, and Carpenter.
Please also review the competency statements to learn more about the major topics and concepts covered in this offering.
Projects
Gemologist
You will take on the role of a gemologist at a jewelry firm, tasked with creating a diamond appraisal report for a customer, describing the grade and cuts.
Textile Designer
You will take on the role of a textile designer working for a fashion designer, tasked with creating a portfolio with frieze patterns that preserve angles and keep lengths in proportion for all dilations.
Transportation Planner
You will take on the role of a transportation planner for a delivery company, tasked with creating a plan for delivery routes.
Irrigation Design Engineer
You will take on the role of an irrigation design engineer hired by a farmer to design an irrigation system for his crop field. 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.
Package Designer
You will take on the role of a package designer working for a sports company, tasked with creating a presentation of your package designs.
Surveyor
You will take on the role of a surveyor, tasked with creating a report to settle a dispute. Using the landowner’s land deed to diagram the land, you will compute the acreage of the land and write a conclusion.
Carpenter
You will take on the role of an apprentice for a carpenter, tasked with creating a design for a customer’s new kitchen cabinet.
Competencies
Geometric Constructions
Students will demonstrate an understanding of geometric constructions by creating constructions, explaining the logic underlying constructions, and creating regular polygons using construction techniques.
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.
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Experiences allow you to explore a career field you’re curious about while mastering competencies for school credit. Through experiential learning, you will learn skills and apply them to tasks you would complete as part of a career rather than completing traditional assessments like essays or tests. During your Experience, you’ll work with a professional in the field to support your learning whom we call a “mentor.” You’ll earn a badge for your accomplishments to share on social media and higher education platforms, or with colleges, potential employers, peers, and colleagues to display your qualifications.
Here’s how Experiences work:
- Each competency you work on is addressed through a separate deliverable predetermined by you and your instructor.
- Guided learning for each module consists of research and/or work with a professional in the field. Your instructor will coach you through this process.
- Each module culminates in a final demonstration of understanding, which includes a deliverable and a discussion-based assessment with your instructor.
- Here’s an example:
Let’s say you’re curious about a career in healthcare. You decide you’d like to learn about this career area, make a professional connection, earn a badge, and meet competencies for your 9th-grade English requirement. While enrolled in English 1 Experiences, you conduct research to better understand language and structure in writing. Then you may work with an Occupational Therapist to help apply your writing skills to the creation of an informational video about adaptive equipment for patients. The video aims to advise family members of patients regarding the use of accommodations and equipment to help patients perform daily tasks. Now you’ve earned the Language and Structure in Writing competency! This is just one example of the many ways Experiences can bridge competencies to careers.
Obtaining a Mentor: Prior to enrollment, please have an idea for a mentor in mind. We have partnered with hundreds of mentors you can work with during your Experience, who you can find in our Career Mentor Catalog here. Or, you may consult with our counseling department by emailing [email protected] for help in identifying one.
*A parent/guardian permission form and background check of the mentor are both required to work with mentors without parental supervision.
Competencies
Geometric Constructions
Students will demonstrate an understanding of geometric constructions by creating constructions, explaining the logic underlying constructions, and creating regular polygons using construction techniques.
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.
