![[Why] 다각형의 무게중심이 오직 하나뿐인 이유는? : 삼각형의 다섯 가지 중심에 대해](https://i1.gguge.com/r/teacher/7cf03094-8130-48b7-9205-c9c5afc64fce.png.webp?w=1280)
[Why] 다각형의 무게중심이 오직 하나뿐인 이유는? : 삼각형의 다섯 가지 중심에 대해
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두께가 없는 삼각형이 무게를 가지고 있다니 이상하지 않은가요? 그리고 내심, 외심말고 삼각형에는 2가지 심이 더 있습니다. 이 각각은 나름대로 의미가 있습니다. 교과서에서 가르쳐주지 않는 삼각형의 오심 이야기를 들어보세요. 어려운 문제도 잘 풀 수 있습니다.
One Day
12-14
Max 5people
50min

구자익
Reviews
197
🧲 수업 후 아이는 이렇게 성장해요
삼각형 속 다섯 가지 중심을 직접 찾고 설명할 수 있어요
오심(五心)의 각각의 성질과 차이를 이해해요
교과서에서 배우지 못한 수학적 생각을 깊게 경험해요
✍️ 수업 내용 3줄 요약
삼각형에 숨겨진 다섯 가지 '심'의 의미와 성질을 알아봐요
무게중심이 오직 하나인 이유를 증명하며 논리적 사고를 키워요
실생활 속에서 오심이 어떻게 쓰이는지도 재미있게 찾아봐요
🎯 이런 아이에게 추천해요
단순한 계산에서 벗어나 수학 개념을 제대로 이해하고 싶은 아이
중등 과정의 도형 단원(특히 삼각형)을 미리 준비하거나 보충하려는 아이
깊이 있는 수학 이야기를 즐기거나 논리적 추론에 관심 있는 아이
직접 증명해보고 탐구하는 활동을 좋아하는 12~14세 학생
⚡ 수업은 어떻게 진행될까요?
기본적인 작도법(선분의 수직이등분선, 각의 이등분선 등)(5분)
내심·외심·무게중심 등 각각 다양한 심의 정의와 위치 탐구(15분)
각각의 심이 무엇을 의미하는가를 탐구(10분)
무게중심이 왜 오직 한 곳인지 증명 활동(15분)
Q&A 및 오늘 내용 정리(5분)
📐 교과서에서는 알려주지 않는 이야기
삼각형에서 내심, 외심, 무게중심이 익숙하게 느껴지지만, 사실 그 외에도 방심과 수심 등 신기한 중심들이 더 숨어 있어요. 이 수업에서는 단순히 형태만 보는 게 아니라, 수학적으로 '왜 그럴까?'라는 질문에 논리적으로 답해볼 거예요. 잘 모르거나 헷갈렸던 오심 개념이 확실하게 정리될 거예요.
궁금해했던 삼각형의 비밀, 이 수업에서 직접 증명하면서 풀어보세요! 부담 없이 질문하며, 무게중심의 의미부터 교과서 바깥의 신기한 수학까지 함께 탐구해요.

🎩선생님의 수업 특징은?
선생님의 수업 철학은 헝가리 수학자 폴리아의 문제해결기술(발견술)과
독일 수학자 프로이덴탈의 수학화에 근거하고 있습니다. 
G. Polya Hans Freudenthal
[선생님 수업 후기]










Great for These Kids
기하학에 대해 호기심이 많은 학생
삼각형의 외심, 내심, 무게중심의 의미가 궁금한 학생
삼각형의 오심에 대해 궁금한 학생
초등 저학년
One Day Class Information
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Teacher Info
Auto-translated to English.

구자익
Reviews
197
Graduated from Korea University (Seoul Campus) Served as the Director of a renowned academy in the Gangnam 3-gu district for over 15 years Personally produced over a dozen textbooks for elementary, middle, and high school students Taught a student who achieved a perfect score on the 2016 CSAT starting from their first year of high school. For 15 years, I taught middle school classes for medical school and top-tier students, as well as high school classes for Grade 1 students and Grade 1 CSAT students in the Gangnam 3-gu district of Seoul. As an academy director for 10 years, I gained diverse experience teaching students of various levels. In particular, the teacher has the strength of reading students' thoughts, quickly identifying their habits, and presenting appropriate countermeasures and methods. Through the teacher's diverse teaching experience and student observations, countless students have gained confidence in mathematics and improved their grades. Mathematics is a discipline that organizes complex thoughts and aids in problem-solving. In other words, it is a subject that is truly essential to us. However, nowadays, students view mathematics as a subject where they must memorize concepts and theories (without critical analysis) and repeatedly solve problems by type (without knowing why they are solved that way). Mathematics is based on operations, and as students advance through the grades, they must learn by connecting and expanding upon new concepts and theories with what they have already learned. However, students who strongly believe that mathematics is solely about operations face limitations because they view the subject through this single lens. Consequently, the better a student's calculation skills are, the more difficult middle school mathematics feels. This difficulty is experienced again when learning high school mathematics. Mathematical concepts and theories require students to develop a habit of proactively understanding them, while problem-solving requires problem analysis and solution strategies. Only by learning "the connection and expansion of mathematical concepts" and "problem analysis, understanding, and problem-solving strategies" will students realize that mathematics is simple and easy as time goes by. The teacher will help students come to this realization. The teacher's teaching method is somewhat unique. 1. The teacher explains "why" concepts and theories are necessary, "how" they are expressed in a particular way, and "what" they connect to among previously learned concepts. 2. The teacher provides students with the opportunity to express their own thoughts. This allows the teacher to distinguish between well-thought-out ideas and those that need correction. 3. Understand the student's thought process regarding 'how' they solved the problem. 4. Teach how to analyze and understand problems, and the starting point for solving them. 5. Do not teach by categorizing problems into types. Therefore, do not teach solution methods by categorizing them either. 6. Regularly check whether the student solved the problem correctly (logically), and encourage them to express their thoughts verbally (verbal expression helps them identify their weaknesses).
Experience & Activities
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Teaching middle and high school subjects to middle and high school students for approximately 20 years
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Coaching for various competitions such as KJMO, KMO, and AMC
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Producing numerous successful applicants to electronics high schools and specialized high schools
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Producing numerous students with Grade 1 high school GPA and CSAT scores in the Gangnam 3 districts for over a decade
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Produced perfect scorers on the CSAT (2016 academic year)
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Selling books personally created by the teacher at Kyobo Book Centre (search for JIK)
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International school IB classes or AP courses (Pre-Algebra, Algebra, Geometry, Combination, Number Theory, Pre-Calculus, Calculus)
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