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高校幾何学、第 1 学期

より伝統的で詳細な幾何学コースを希望する人のための幾何学。人生で成功するために必要な思考スキルも学べます。思考スキルは世界で非常に求められています。
Michael Gold
平均評価:
4.8
レビュー数:
(166)
クラス

含まれるもの

42 ライブミーティング
42 授業時間
宿題:
週あたり 2-4 時間. 含まれる
テスト
If parents would like to make a course in which tests and quizzes are given and graded, we could arrange that.
評価
If parents would like to make a course in which tests and quizzes are given and graded, we could arrange that.
この文章は自動翻訳されています

このクラスで学べること

英語レベル - 不明
米国の学年 9 - 12
We will learn concepts of geometry that are important in themselves and everyday life, but that are also an important foundation for later mathematics and for physics, chemistry, and biology. And from what we do in class we will learn important thinking skills (like proof) you will use in school, later at work, and all through life.  You will learn some life-altering logic and reasoning.  A course not to miss. 

We will use a combination of lecture, interactive discussion, Q&A, and in-class work.  

Homework will be assigned, but not required. We can find you some optional quizzes and tests, if you'd like. 

If parents would like to make a course in which homework is required and tests and quizzes are given and graded, we could arrange that. 

Be prepared to work in this course -- and be prepared to profit immensely from it in later math, science, work, and life. 

Prerequisite: algebra 1. 

Topics include:
1. Points, lines, planes, and angles
2. Angles and perpendicular lines
3. Parallel lines and planes
4. Congruent triangles
5. Quadrilaterals. 

Tentative schedule:
Week 1:  introduction; what geometry is about; why study it; deriving some area formulas
Week 2:  points, lines, planes, and more; measurement and congruence; collinearity and betweenness; proof
Week 3:  division of segments and angles; proof; perpendiculars; complements and supplements
Week 4:  more proof; congruent complements and supplements; adding/subtracting segments and angles

Week 5: "multiplying" and "dividing" segments and angles; transitive and substitution properties of congruence; vertical angles
Week 6:  congruent figures; proving triangles congruent
Week 7:  using congruent triangles; segments in triangles; more complex proofs
Week 8:  isosceles triangle theorems; right triangle theorems

Week 9:  more complex proofs
Week 10:  right angles; equidistance; parallel lines
Week 11:  indirect proof; proving lines parallel; angles around parallel lines
Week 12:  quadrilaterals; properties of quadrilaterals

Week 13:  proving that a figure is a special quadrilateral
Week 14:  lines in planes; perpendiculars to planes; parallel planes

And more good stuff, time permitting. 


Here are some testimonials from other classes but representative of what we will do in class:

“My son has enjoyed this class and made friends as well as broadened his understanding of Calculus. I recommend this class.” –Xaidie C., parent, “Calculus, Semester 1,” 14 Jan 2022

“This class was excellent! My daughter said 'He is the best teacher ever! He actually explains why things work so you understand what’s going on instead of just memorizing it.' She took Calc 1 a year ago and wanted to review. She feels she understands it so much better now. She said they covered an entire semester in two weeks more in depth than her original college level class. She can’t wait to take the next level.” –Danielle L., parent, “Summer Calculus Review/Preview, Session 1,” 7 Aug 2021

"Michael Gold’s 'Summer Geometry Preview/Review' was a in-depth yet efficient way (8-classes over a two-week period @ 1.5 hours per class) to get a preview of what to expect in the fall. My daughter wants to stay sharp over the summer (around the fun and relaxation that all kids need) and the structure of a class that meets live is the only option for us. Also, the class was comprised of like-minded students and a nice group of kids.

"We first came to know Mr. Gold through his 'Logic Essentials: How to Think Well' class. I highly recommend this class because logic and deductive reasoning are the cornerstones of thinking well. We need our kids to flag poor arguments and discern the truth. Unless you are attending an elite prep school, I don’t know where you would find exposure to a class like this. I am so grateful that Mr. Gold makes this class offering available. So when I shared Mr. Gold’s Geometry offering with my daughter, she wanted to sign up knowing he is a wonderful teacher.

"What was most telling – my daughter never forgot about the class date or time. I know Mr. Gold is engaging because if I walked past her room, she was never distracted. He connected with kids on all fronts using lecture, illustrating problems on the board and showing YouTube videos. He has a warm personality, inflection in his voice and good sense humor. After each class ended, my daughter wanted to show me her notes and explain a problem set she learned. Also, I received a detailed email from Mr. Gold outlining everything that was covered in each class, along with links to videos, books, geometry worksheets and more. I also appreciate that homework was optional – your child can leisurely gain exposure or go all out on mastering the subject matter – there’s no pressure.

"Michael Gold has high standards for teaching and truly cares about his students. My family joins his long list of five star reviews because he’s that good. My daughter and I highly recommend Mr. Gold’s ‘Summer Geometry Preview/Review’ and ‘Logic Essentials: How to Think Well’. We enthusiastically encourage you to sign up for any class he teaches!"
–Mary B, parent, “Summer Geometry Preview/Review, Session 1,” 19 Aug 2020

“For the past 2 years, my son has taken a different math class over the summer with Michael Gold just to sharpen up before the upcoming school year, and the payoff has been tremendous. He loves this teacher’s style, is surprisingly riveted during the class, always on time, and absorbs the equivalent of an entire years worth of work in 2 weeks, helping him to breeze through the academic school year with great grades and a real sense of satisfaction. You’re kids might roll their eyes at you at first, but they will thank you if you are lucky enough to grab a spot in one of Michael Gold’s classes. He is fast, clear, to the point and gives real life application examples to make math make sense. 10 stars if I could.” –Lia J., parent, “Summer Algebra 2 Review/Preview, Session 1,” 10 Jul 2021

(Image from https://commons.wikimedia.org/wiki/File:Aristarchus_working.jpg)

その他の情報

受講に必要なもの
We will use the classic text Plane Geometry by Welchons and Krickeberger, which is available free on The Internet Archive:  https://archive.org/details/planegeometry00welc

A different edition for free if you register (does not require credit card or anything like that) with the Internet Archive is https://archive.org/details/newplanegeometry0000amwe

You could purchase a copy of Plane Geometry by Welchons and Krickenberger (maybe a different edition than on The Internet Archive) at  https://www.amazon.com/Plane-Geometry-M-Welchons/dp/B000UCH4G6/

I recommend getting a graphing calculator like the TI-84 or the HP Prime -- or you could use some online calculator like Desmos or WolframAlpha.


If you want more exercises and material to do on your own, you could buy
1. Geometry by Jurgensen, Brown, & Jurgensen (ISBN-13: 978-0395977279, ISBN-10: 9780395977279).
Or see it for free: https://archive.org/details/jbj-geometry/mode/2up

2. Geometry for Enjoyment and Challenge by Rhoad, Milauskas, & Whipple (ISBN-13: 978-0866099653; ISBN-10: 9780866099653). 
Or see it for free:  https://ia803106.us.archive.org/24/items/geometrytextbook/Geometry%20Textbook.pdf
外部リソース
学習者は、Outschoolが提供する基本ツール以外のアプリやウェブサイトを使用する必要はありません。
参加しました June, 2019
4.8
166レビュー
プロフィール
教師の専門知識と資格
テキサス州 教員免許 数学で
学士号 University of Texas at Austinから 数学 へ
I have a degree in mathematics, and have taught geometry  (and all math from pre-algebra through calculus and statistics) for decades.  But having a degree in philosophy, having studied physics, chemistry, and biology, and having some knowledge of history and of life, I know how geometry and its study is useful beyond measure.  You will learn geometry -- I will help you connect it, help you start relating it to everything else you know, and help you draw important lessons from it: wisdom you just cannot buy. 

What matters is not so much my personal credentials (which, yes, I have, as you can see in my profile bio), but the success of my students. 

Those student successes are my real credentials: what my students achieve, not what I have achieved. Here are some examples:

“My 13 yo son got a lot out of this class. The teacher is funny. I wasn’t around much but when I was there was some hilarious things going on. But not all the kids got his humor. That was so funny because they didn’t realize some of his humor. He makes class interesting and fun but also serious and talks about how things will help them in the future. We would do another class in the future but it’s just a little expensive for us to do classes all the time. Not a bad price it’s just hard to do that all the time.” –Lindsay W., parent, “Geometry Essentials, Semester 1,” 10 Mar 2021

"My 14 year old appreciated the feel of a real class – we even signed up for Part 2. There were a lot of practice problems and then he would review how to walk through it.” –An Outschool parent, “Summer Geometry Preview/Review, Session 1,” 25 Jul 2020

“Great overview of what geometry class will be like in the upcoming school year. It teaches you how to think about geometry, and the importance of logic and systematic thinking in general.” –Gita S., parent, “Summer Geometry Preview/Review, Session 1,” 28 Jun 2020

“This class helped my son prepare for 9th grade Geometry Honors. He felt the teacher was very prepared, extremely knowledgeable, worked at a good pace for understanding and was thorough. There was time for questions and help if needed. He enjoyed taking this class.” –Laura S., parent, “Summer Geometry Preview/Review, Session 1,” 22 Aug 2021

“Great class! The teacher is very knowledgeable. My son learned a lot. The teacher is very good in explaining details as well as the bigger picture, why it is important, how it is used. I wish math was always taught this way.” –Anna, parent, “Math Lab: Sine, Cosine, and Tangent Basics,” 28 May 2020

“My son knew a little about these (self-taught, because he’s interested) before, but he liked the class a lot and it’s pretty clear that what he he learned here made them “stick” better than they were before. I looked at his notes, and, honestly, I wish I’d had this type of explanation of this material when I was in trig. My son has taken several classes from this teacher and enjoyed all of them, likes this teacher’s style.” –Julie M., parent, “Math Lab: Sine, Cosine, and Tangent Basics,” 9 Jun 2020

“Very useful and informative class. Just what we needed. Very good teacher.” –Aleksandra K., parent, “Math Lab: Sine, Cosine, and Tangent Basics,” 27 Apr 2020

“My son loved this course. He said that the teacher was really funny. I have never seen my son so excited about math. Thank you, Mr. Gold!” –Rosa L., parent, “Math Lab: Sine, Cosine, and Tangent Basics,” 26 Mar 2020

Dylan T, ex-high school student now in his 20s: "I really did learn more than geometry and math taking classes with you. I learned to reason and use logic to start solving things in everyday life. It’s pretty useful at work when I use reasoning to find root causes, and to find and fix problems. You teach people how to THINK!"

Mr. M, high school teacher of Madison S; quote from emailed note from teacher to parent "I agree with you 100%. [Madison] has gone from a D/C student to a B/A student. She is knocking it out of the park right now, not just by getting the work done but by also doing it correctly. It is nice to have her as a student I can rely on to do her work and know how to do it. I know that she has tried to share her story with others to encourage them to just try and do their work, that Algebra is not as hard as they are making it out to be and I appreciate that. I hope she finishes up the year strong."

Joe S, ex-high school student: "I tutored with Michael for physics and calculus at the end of my senior year of high school in order to prepare myself for my first semester of engineering at Texas A&M University. Not only was I prepared enough to feel comfortable and excel in the coursework my 1st semester but Michael introduced me to thinking about problems as a whole and inductively (a thought process which has helped in every form of learning). To this day, 7 years later, I still use this method to help me solve problems and learn, in work and in life, more effectively. I highly recommend Michael to anyone looking to not only improve their grades but also to improve their ability to problem-solve and appreciate learning."

Rajiv R, ex-junior high and high school student:  "Michael sets the standard for excellence among tutoring services. I was a student of Michael Gold for around 7 years, and the education I received has had an immeasurably positive impact on my life.

"I originally only sought out tutoring for Geometry & Algebra, during middle school, in order to place into higher level math classes. I found the tutoring to be so valuable that I continued my lessons even after placing into and acing my desired courses -- I received tutoring in math through high school and some of college (all the way up to 3D Calculus). Additionally, I received tutoring for English and Grammar, Physics, SAT prep and more.

"Gold's tutoring helped me achieve A's in my classes and great scores on standardized tests, but this was just the 'tip of the iceberg.' With each lesson I also learned how to better think logically, carefully, and reasonably. These skills are essential to life and have helped me immensely - I still use the learning/study methods I developed through Gold's lessons to earn top scores in many college courses and to do well in my work and hobbies.

"I will forever be grateful to Gold Academy, and highly recommend the service to any student who is looking to start learning, thinking and living."

レビュー

ライブグループクラス
共有

$490

42 クラス分
週に3回、 14 週間
60 分

6 人がクラスを受けました
オンラインライブ授業
年齢: 12-17
クラス人数: 4 人-12 人

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