幾何：優秀學習者的同餘與證明
在這門嚴格的數學課程中，學習者將透過使用嚴格的變換和膨脹來證明三角形的相似定理並擴展畢達哥拉斯定理的工作，從而繼續幾何學。
Malikai Bass M.A
平均評分：
5.0
評論數量：(329)
熱門課程
包含什麼
20 現場會議
16 小時 40 分鐘 上課時間作業
每週 1 小時. We will end the unit with a mastery assessment.項目
Students will complete a modeling project in which they create a mathematical model to understand and propose a solution to a real world problem.進度報告
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課堂經歷
英語程度 - B2+
美國 8 - 10 年級
Intermediate 等級
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.
學習目標
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.
教學大綱
課程
遵循 Teacher-Created 課程標準
與 Common Core State Standards (CCSS)對齊20 課程
超過 4 週課 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 分鐘線上直播課
課 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 分鐘線上直播課
課 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 分鐘線上直播課
課 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 分鐘線上直播課
其他詳情
學習需求
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
父母的引導和規範
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.
先決條件
Learners should have completed Algebra 1.
供應清單
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, a compass, straight edge, and tracing paper.
教學語言
英語 （等級： B2+）
外部資源
除了 Outschool 教室外，本課程也使用：
來源
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.
已加入 April, 2021
5.0
329評論
熱門課程
教師專業知識和證書
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.
評論
現場團體課程
US$90
每週每週5次，共 4 週
50 分鐘
有6 位學習者完成此課程
即時視訊會議
年齡: 12-15
2-6 每班學員人數
