中學數學、邏輯和問題解決：相似的形狀、比例和斜率
在為期五週的預代數和中學數學課程中，學習者將識別相似的形狀，創建比例圖，並透過以問題為中心的探索將現有的幾何知識與坡度的概念聯繫起來。
Malikai Bass M.A
平均評分：
5.0
評論數量：(316)
熱門課程
包含什麼
25 現場會議
20 小時 50 分鐘 上課時間掌握程度評估
包括評估
Students will receive weekly written progress reports.我們無法翻譯此文，請刷新頁面並再試一次。
課堂經歷
英語程度 - A2
美國 7 - 8 年級
Beginner 等級
This is the second course in year two of a series of middle school mathematics courses. 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. This series is based on an accelerated math curriculum that covers three years of content, aligned to Common Core Math Standards, over the course of two school years. It is perfect for students preparing to begin Algebra ahead of time, or those who need review and remedial support. 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. This process prepares students well who may seek advanced mathematics in high-school or beyond. Students will complete a math notebook In the style of a main lesson book to help with recall and long-term retention. In this unit, students gain a conceptual understanding of scale and learn to recognize when pictures and plane figures aren't in scale. They will reason about measurements in scaled copies, interpret and reason with scale drawings, and create their own with and without units. Students will also learn about dilation as they discuss center and scale factor while exploring circles and lines on and off the coordinate plane. They learn what is preserved in a a dilation and compare it to their existing concept of rigid transformations. We then use the developed geometric understanding to explore slope and slope triangles allowing us to generate the equation of a line and reason with equations representing lines.
學習目標
Students will understand and use the terms " scaled copy", "to scale", "scale factor", "scale drawing", and "scale".
Students will recognize when two pictures or plane figures are not scale copies of each other.
Students will use tables to reason about measurements in scaled copies.
Students will make, interpret, and reason with scale drawings.
Students will understand dilation and recognize center and scale in this context.
Students will understand how dilation impacts different polygons including line and angle measures.
Students will understand similarity of plan figures using rigid transformations and dilations.
They will use the properties of similarity to make, prove, and disprove claims.
They will learn the terms "slope" and "slope triangle".
They will use similarity to prove they can sue any two distinct points on a straight line to determine the slope.
教學大綱
標準
與 Common Core State Standards (CCSS)對齊5 單位
25 課程
超過 5 週單位 1: Scaled Copies
課 1:
Readiness Assessment
We will begin with a readiness check to understand students existing conception of geometry and algebra ideas that may need to be addressed and inform instruction throughout the unit. 50 分鐘線上直播課
課 2:
What are scaled copies?
We will explore the idea of a scaled copy and learn to distinguish scaled copies both formally and informally using length and articulate the characteristics of scaled copies quantitatively. 50 分鐘線上直播課
課 3:
What is a scale factor?
We will focus on developing vocabulary and understanding how to formalize the concepts developed about scaled copies. We will work on describing scaled copies using a scaled factor. We will create scaled copies of simple shapes off a grid and understand the relationship as multiplicative. 50 分鐘線上直播課
課 4:
How does scale impact the relationship between shapes
We will work on understanding corresponding distances between non-connected points in scaled copies. We will use virtual protractors to explore what happens to angles in scaled copies and reason as to why they are preserved. We will use arguments about angles and lengths to identify scaled copies. We will also work with fractional scale factors to understand how factors greater or smaller than one impact scaled copies. 50 分鐘線上直播課
其他詳情
學習需求
This class is designed by an AUDHD/Dysgraphic 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.
先決條件
Students should have good content mastery over elementary math standards and sixth grade math standards. Students should have proficiency (with or without aid) of keyboard and mouse or touch screen devices.
已加入 April, 2021
5.0
316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$80
每週或US$400 用於 25 課程每週5次，共 5 週
50 分鐘
有9 位學習者完成此課程
即時視訊會議
年齡: 11-14
3-6 每班學員人數
