여름 기하학 미리보기/리뷰, 세션 1
1학기에는 기하학의 핵심 개념과 방법을 배워 앞으로의 재미있는 학습을 준비하거나 지금까지의 재미있는 학습을 복습해 보겠습니다.
Michael Gold
평균 평점:
4.8
수강 후기 수:(166)
무엇이 포함되어 있나요?
10개의 라이브 미팅
수업 15 시간숙제
주당 2-4시간. Optional assignments for each day's work will be provided. The homework is optional, but will allow you to retain and grasp the material better in the course and in the long run, and to better build your knowledge day by day.보고계신 지문은 자동 번역 되었습니다
수업 소개
영어 수준 - 알 수 없음
미국 7학년 - 10학년 학년
“Never before was my son as motivated and interested in a course. It was a delight to see and fun to hear him share about the lessons without prodding 😄” –Paula L., parent, “High School Geometry, Semester 1,” 2 Jan 2022
Get ready for high school geometry by getting a head start and giving yourself more time to assimilate concepts and techniques that some students find difficult. Or review some important geometric concepts and ideas (like that of proof). Good for SAT/ACT prep. Good for getting ready for calculus. Good for making sure you learned some essentials of high school geometry.
We will learn how proofs work, take a look at what geometry studies, get some geometry concepts under our belts, and develop some strategies for learning geometry. We cannot cover everything in here that is covered in a year-long geometry course, of course, but we can learn some geometric concepts and some geometric methods.
Which we should do, as geometry has had a profound impact for the better on our culture and world. We will dig into some of that impact so we know why geometry is important, so we know exactly how it helps in thought and in life, and so we know what logic and proof really are. The point of education is to develop the ability to reason independently, the point is not do destroy it, so I teach multidisciplinary thinking, understanding, and logic as I work. I do not do the blind memorization, the compartmentalized "thinking," or the homework-problems-in-isolation thing. I do not teach math-in-a-box, I teach what real people in the real world need to know to survive and thrive (and get good grades with understanding, not parroting).
We will have some lecture, some interactive work, and some independent work that we will check in class. Everyone will get a chance to ask and answer questions, get feedback, and check their understanding.
You will get some class notes posted everyday on Outschool (you will need to take some of your own notes!), some optional extra reading for understanding, and lots of optional practice work. All classes on Outschool are recorded, so you can watch ones you might have to miss and watch class over again to take notes or review.
Note: this course is preparation for a high school geometry course. It is preparation for a semester 1 (and some semester 2).
“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
Topics:
1. Geometry, what it is and why it is important
2 Derivation of some area and volume formulas
3. Parallel lines and angles around a transversal
4. Theorems about triangles and congruent triangles
5. Quadrilaterals and diagonals
6. Proof, what it is and why it matters
More (e.g., internal and external angles in a polygon; induction vs. deductions; similarity) if time permits
Tentative schedule (subject to some change to fit the class needs and interests)
Week 1
Day 1
-what geometry is and why it is important; what you should aim to get out of it; how to study it; the idea of proof
-basic terms of geometry; naming geometric figures
-parallel lines, transversals, and angles
Day 2
-parallel lines, transversals, and angles
Day 3
-proof that the angles of a triangle actually do add to 180º
-the exterior angle theorem
Day 4
-types of triangles; their characteristics
-definiton congruence; congruent triangles
-triangle congruence theorems and practice proofs
Day 5
-triangle congruence theorems and practice proofs
Week 2
Day 1
-triangle congruence theorems and practice proofs
Day 2
-types of quadrilaterals; diagonals of quadrilaterals
-theorems about quadrilaterals (parallelograms, trapezoids, rectangle, rhombus)
Day 3
-theorems about quadrilaterals (parallelograms, trapezoids, rectangle, rhombus)
Day 4
-derivation of some the common area formulas (so we understand, not merely memorize)
-area exercises
Day 5
-review
-derivation of other common area formulas
-derivation of some volume formulas (so, again, we understand, not merely memorize)
-area and volume exercises
-wrap up, review, and conclude
Taking this particular course over would also help retain the material in the long run -- we need it for algebra 2, precalculus, calculus, the SAT, the ACT, and for many situations in real life.
I agree with Martin Luther King, Jr., and teach accordingly: "Education must also train one for quick, resolute and effective thinking. To think incisively and to think for one’s self is very difficult. We are prone to let our mental life become invaded by legions of half truths, prejudices, and propaganda. At this point, I often wonder whether or not education is fulfilling its purpose. A great majority of the so-called educated people do not think logically and scientifically. Even the press, the classroom, the platform, and the pulpit in many instances do not give us objective and unbiased truths. To save man from the morass of propaganda, in my opinion, is one of the chief aims of education. Education must enable one to sift and weigh evidence, to discern the true from the false, the real from the unreal, and the facts from the fiction.” --Martin Luther King, Jr. (From MLK’s 1947 article “The Purpose of Education,” published in the Morehouse College campus newspaper The Maroon Tiger. See: https://kinginstitute.stanford.edu/king-papers/documents/purpose-education)
“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
“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://en.wikipedia.org/wiki/Triangle#/media/File:Remint3.svg)학습 목표
To learn what geometry is about and why it is important.
To learn basic and important geometric concepts.
To learn how to do proofs.
To learn how human knowledge is developed.
그 외 세부 사항
수업 자료
In the course, I will provide links to (free) supplementary materials on the Internet. But, to better follow along, you might get, if you want, Geometry by Jurgensen, Brown, & Jurgensen (ISBN-13: 978-0395977279, ISBN-10: 9780395977279).
Outschool 외 필요 앱/웹사이트
아웃스쿨 사이트의 기능 외 별도의 앱이나 웹 사이트를 사용할 필요가 없습니다.
가입일: June, 2019
4.8
166수강 후기
교사 전문성 및 자격증
텍사스 교직증명서 수학에
학사 학위 수학 University of Texas at Austin에서
I have a degree in mathematics, and have taught geometry (and all math from pre-algebra through calculus and statistics) for decades. Because I have studied philosophy, physics, chemistry, and biology, I can help you see how and where geometry is useful in life, help you see how it developed in history, and will help you draw life lessons from it.
What matters is not so much my credentials (which, yes!, I have, as you can see in my profile bio), but the success of my students. Those successes are my real credentials. Here are some:
“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
"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
“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 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 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
"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
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."리뷰
실시간 그룹 수업
10 회 수업에
US$249
2주 동안 주당 5회
90분
179 명의 학생이 수업을 완료함
실시간 화상 수업
연령: 12-17
수업당 학습자 5-18 명
