Geometry: Congruence and Proofs for Exceptional Learners
In this rigorous math course, learners will continue geometry by using rigid transformations and dilations to prove similarity theorems about triangles and extend their work with the Pythagorean theorem.
Malikai Bass M.A
Average rating:
5.0
Number of reviews:(316)
Popular
What's included
20 live meetings
16 hrs 40 mins in-class hoursAssignments
1 hour per week. We will end the unit with a mastery assessment.Projects
Students will complete a modeling project in which they create a mathematical model to understand and propose a solution to a real world problem.Progress Report
includedClass Experience
US Grade 8 - 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 will focus on the relationships between congruent parts of figures and congruent figures themselves. We will utilize transformations as tools for reasoning and making generalizations. Through these transformations, we will prove three theorems about triangle congruence: Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Side-Side-Side (SSS). As we establish these theorems, we will apply them to demonstrate properties of quadrilaterals, isosceles triangles, and other shapes. Finally, we will employ our skills to conjecture and investigate congruences and properties of quadrilaterals.
Learning Goals
CCSS.Math.Content.HSG.CO.B.6: Students will be able to use geometric descriptions of rigid motions to transform figures and predict the effects on these figures, and determine if two figures are congruent by analyzing their transformations.CCSS.Math.Content.HSG.CO.B.7: Students will be able to demonstrate that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent, using the definition of congruence in terms of rigid motions.
Syllabus
Curriculum
Follows Teacher-Created CurriculumStandards
Aligned with Common Core State Standards (CCSS)20 Lessons
over 4 WeeksLesson 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:
Congruent Parts, Part 1
We will explore congruent figures and corresponding parts and use them to make conjectures about quadrilaterals based on transforming triangles. 50 mins online live lesson
Lesson 3:
Congruent Parts, Part 2
We will continue to work with corresponding parts and explore using this to disprove congruence between figures. We will also begin our work on establishing congruence shortcuts for triangles. 50 mins online live lesson
Lesson 4:
Congruent Triangles, Part 1
We will work on proofing triangle congruence using transformations based on work in unit one and use this to write proofs. 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.
Joined April, 2021
5.0
316reviews
Popular
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:
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Reviews
Live Group Course
$90
weekly or $360 for 20 classes5x per week, 4 weeks
50 min
Completed by 6 learners
Live video meetings
Ages: 12-15
2-6 learners per class
