weekly
or for 15 classes
Class

High School Geometry : Right Triangle Trigonomoetry for Exceptional Learners

Completed by 7 learners
Ages 12-15
Live Group Course
In this rigorous math course, learners will continue geometry by developing their understanding of right triangles and encountering trigonometric ratios.
Average rating:
5.0
Number of reviews:
(346 reviews)
Popular

Live video meetings
5x per week, 3 weeks
2-6 learners per class
50 min

What's included

15 live meetings
12 hrs 30 mins in-class hours
Projects
1 hour per week. Students will complete a modeling project in which they create a mathematical model to understand and propose a solution to a real world problem.
Assessment
We will end the unit with a mastery assessment.

Class Experience

US Grade 9 - 10
Intermediate Level
This is the second course in a year-long sequence which covers standards and ideas in Geometry. These courses are taught in small-groups to provide individual instruction and social-learning opportunities aligned with a social constructionist or situated cognition view of learning. 

The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs and students will construct their own models or proofs of real-world scenarios in project based assignments. This process prepares students well who may seek advanced mathematics in high-school or beyond. 

In this unit, we build on our prior knowledge of right triangles, starting with what we learned in grade 4 and expanding on concepts from grade 8 like the Pythagorean Theorem and slope. Now, we use that foundation to introduce trigonometric ratios in familiar contexts.

We begin by exploring special cases of similar right triangles, focusing on how right triangles with one congruent acute angle are similar. Though not required by the standards, these lessons offer valuable practice, especially for college exams. We then gather data on side length ratios, organizing it into a table to help us understand relationships before learning trigonometric terms like cosine, sine, and tangent.

After practicing with a calculator to find these ratios, we apply them to real-world problems, learning to check if our answers are reasonable and how precise they need to be. By the end of the unit, we also explore how mathematicians have historically refined the value of π using polygons.

Throughout the unit, we’ll notice patterns, such as the relationship between cosine and sine, before formally learning the concepts. Later, we use these patterns to prove that the ratios for complementary angles are equal. We’ll also estimate angles using our reference table before calculating them with inverse trigonometric functions like arcsine, arccosine, and arctangent.

As we progress, we’ll continue adding to our reference charts, which help us track key concepts and calculations

Learning Goals

HSG.SRT.A.1: Understand similarity in terms of similarity transformations.
SG.SRT.A.2: Use similarity transformations to explain the meaning of similarity for triangles as the equality of corresponding angles and proportionality of corresponding sides.

Syllabus

Standards
Aligned with Common Core State Standards (CCSS)
15 Lessons
over 3 Weeks
Lesson 1:
Readiness Assessment
 We will complete a quick readiness check to introduce unit topics and allow for increased individualization with catered support and enrichment activities throughout the unit 
50 mins online live lesson
Lesson 2:
Angles and Steepness
 We will recognize the fixed ratios in right triangles given a specific angle and understand practical applications through the context of the Americans with Disabilities Act guidelines. 
50 mins online live lesson
Lesson 3:
Half a Square
 We will begin our exploration of special triangle relationships with right triangles as half a square understanding the 45-45-90 triangle and reasoning about diagonals. 
50 mins online live lesson
Lesson 4:
Half an Equilateral Triangle
 We will build on our work with special triangles and explore 30-60-90 triangles. 
50 mins online live lesson

Other Details

Learning Needs
This class is designed by an AUDHD/Dyspraxic Educator - slides and fonts designed to support dyslexia and visual processing - ability to type and use virtual drawing tools - communication aids including chat - ND Affirming classroom
Parental Guidance
Students will need to use Nearpod. They will need to click a link and enter their first name or initial. No other identifying information will be collected. Students will also need to use a compass.
Pre-Requisites
Learners should have completed Algebra 1 and be familiar with the basic ideas of geometry.
Supply List
Learners will need a way to write/draw to solve problems. This class is best taken using a computer and mouse, but learners might benefit from having a secondary touch screen device in order to be able to screen share math work.  

Learners will need a teacher provided printable workbook.
Language of Instruction
English (Level: B1)
External Resources
In addition to the Outschool classroom, this class uses:
Sources
The scope and sequence of this course is based on the open source Illustrative Mathematics curriculum and has been adapted for 2e, neurodiverse, and home-based learners. Illustrated Mathematics is licensed under a creative commons attribution license: https://creativecommons.org/licenses/by/4.0/ Pedagological Resources: Gravemeijer, K. (2020). A socio-constructivist elaboration of realistic mathematics education. In National reflections on the Netherlands didactics of mathematics (pp. 217-233). Springer, Cham. Vintere, A. (2018). A constructivist approach to the teaching of mathematics to boost competences needed for sustainable development. Rural Sustainability Research, 39(334), 1-7. Briscoe, L., & Van Kesteren, J. (2018). THE ART OF MATH. Gazette-Ontario Association for Mathematics, 57(2), 21-24.

Meet the teacher

Joined April, 2021
5.0
346reviews
Popular
Profile
Teacher expertise and credentials
Professional Experience:
I have been a math tutor for over 12 years and have worked with students from ages 5-25 in small group and academic settings including serving as a primary teacher for home educated learners. I have received training and tutoring certification/awards from nationally recognized organizations. I was a group supplemental instruction leader for math at the collegiate level for four years at ETSU including working with dual enrolled and accelerated learners. I have taught and tutored math up to a graduate level in algebra, geometry, probability, and quantitative reasoning. 
Academic Experience: 
Constructivism and Mathematics, Science, and Technology Education
	This graduate level online course for educators used practical examples and empirical research to connect the educational philosophy of constructivism to best practices in STEM education and demonstrated online teaching strategies for this endeavor. It highlighted the power of solving problems through building and applying understandings rather than rote processes which influences the problem-centered curriculum This class also addressed common misconceptions or alternative schemas students develop for math and science prior to instruction and provided ideas for experiments and explorations to adjust these conceptions. 
Math 1410 Numbers, Concepts, and Algebra for Math Teachers
      This in-person semester long coursed prepared students to teach common core mathematics to students in grades kindergarten through eight including early access to algebra. It included practical teaching experience, ensuring the personal math conceptual fluency of each educator, and demonstrating expertise on the Praxis math exam for educators. 
Math 1420: Logic, Problems, and Geometry for Math Teachers
      This in-person semester long course prepared teacher candidates to teach common core mathematics to students in grades kindergarten through eighth including advanced ideas of logic, problem solving, and geometry using a constructivist lens. 


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