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얼마나 가파른지!!! 기울기와 방정식 시스템을 풀어보세요.

기울기와 방정식 시스템 풀기, 학생들이 기울기 개념을 탐구하고 방정식 시스템을 단계별로 푸는 법을 배우는 대화형 수학 수업입니다. 실제 세계 응용 프로그램과 흥미로운 활동을 통해.
BIlly Edward Bush B.A, M.Ed.
평균 평점:
4.8
수강 후기 수:
(463)
인기 선생님
수업
재생

무엇이 포함되어 있나요?

4개의 라이브 미팅
수업 4 시간
숙제
주당 1-2시간. Worksheets will be provided ( pending on students skill sets during the lessons)
학습 평가
Via an exciting online program that will introduce a topic, review and reinforce knowledge, and run a formative assessment.
보고계신 지문은 자동 번역 되었습니다

수업 소개

영어레벨 - B1
미국 8학년 - 11학년 학년
레벨 Beginner - Advanced
How will students learn? 

There will be several ways to interact with me in an online class: through synchronous interaction and asynchronous interactions.

Here are some examples of ways I will engage in synchronous interactions:
Live course orientation. 

Synchronous online meeting. 

How will they interact with myself and each other?

I will use the gradual release method of teaching: " I do, we do, you do" 
- First, I demonstrate how to do it (using several examples).  
- Next, the students do some problems along with me.
- Finally, they complete some problems on their own that I will check for accuracy and give more guidance if needed. 

How is class time structured?

The material taught in an online course follows a structure. Just like a traditional course, students start at the beginning of the education objectives and progress through the coursework. They move from the most introductory topics the class covers to the most advanced.

What topics will be covered?

1. Find the slope of a line given two points. 
2. Find the slope of vertical and horizontal lines. 
3. Graph a line using its slope and a point on the line. 
4. Work with applications of slope.
5. Be able to solve a system of equations from graphing the equations Determine.
6. Solve systems of linear equations by substitution.
7. Solve systems of linear equations by elimination.
8. Solve systems of linear equations by graphing.
9. Students are able to determine if a system of linear equations has no solution, one solution, or infinitely many solutions.
10. Students are able to determine which method is best to solve a system of linear equations.
11. Students are able to set up equations based off of real life situations to solve a system of linear equations.12. 
12. Students are able to solve equations base off of real life situations.

The keys for this lesson is going to be precision (mathematical practice 7), perseverance (mathematical practice 1) and reasonableness (mathematical practice 3).  Students will need to be precise when completing the steps - being careful to remember to flip the sign when dividing by a negative.  Students will also be encouraged to check answers from their solution sets - is your answer reasonable? If I choose a random number from your shaded region will it work?  Finally, students will need to persevere! Getting inequalities right takes time!  The negative rule is tricky, and frustrating - practice practice practice!

학습 목표

Students are able to substitute values in for variables
Students are able to graph linear equations.
Students are able to solve equations for a specific variable.
Students are able to add and subtract equations by combining like terms.
학습 목표

강의 계획서

커리큘럼
Teacher-Created 커리큘럼 기반
표준
Common Core State Standards (CCSS)에 맞춰짐
4 레슨
1 주 이상
레슨1:
Mastering Slope
 Learning Objective: Understand the concept of slope and how to calculate it in various forms.
	•	Session Outline:
	•	Review & Connection:
	•	Connect slope to real-life scenarios (e.g., ramps, roads, graphs).
	•	Recap: Rise over Run, slope from two points.
	•	Guided Practice:
	•	Calculate slopes from graphs and coordinate pairs using online tools (e.g., Desmos).
	•	Problem-Solving Session:
	•	Analyze slopes in different contexts: positive, negative, zero, and undefined.
	•	Wrap-Up Activity: 
60 분 온라인 라이브 레슨
레슨2:
Slope-Intercept Form (y = mx + b)
 Learning Objective: Interpret and graph linear equations in slope-intercept form.
	•	Session Outline:
	•	Concept Introduction:
	•	Breakdown of slope (m) and y-intercept (b) with practical examples.
	•	Interactive Graphing:
	•	Use a graphing tool to input equations and identify slopes and intercepts.
	•	Real-World Applications:
	•	Analyze and create equations from real-world data (e.g., distance vs. time graphs).
	•	Independent Practice: 
60 분 온라인 라이브 레슨
레슨3:
Introduction to Systems of Equations
 Learning Objective: Understand systems of equations and solve them graphically.
	•	Session Outline:
	•	Mini-Lesson:
	•	Define systems of equations and explain their real-world significance (e.g., budgeting, intersection points).
	•	Graphing Practice:
	•	Solve systems graphically to find points of intersection.
	•	Real-world problem examples where systems are applied.
	•	Student-Led Graphing:
	•	Graph and solve systems of equations with live support.
	•	Wrap-Up Activity 
60 분 온라인 라이브 레슨
레슨4:
Solving Systems Algebraically
 •	Learning Objective: Solve systems of equations using substitution and elimination methods.
	•	Session Outline:
	•	Step-by-Step Introduction:
	•	Substitution method: Solving for one variable and substituting.
	•	Elimination method: Adding or subtracting equations to eliminate a variable.
	•	Guided Examples:
	•	Solve systems using both methods with detailed explanation.
	•	Student Practice:
	•	Solve problems using substitution and elimination, with real-time feedback.
	•	Wrap-Up Quiz: 
60 분 온라인 라이브 레슨

그 외 세부 사항

수업 자료
To ensure their success in this course, here is a list of materials that your student will need to participate fully:

Required Supplies:
	1.	Notebook or Graph Paper
	•	For solving problems and graphing equations.
	2.	Pencil and Eraser
	•	To work through calculations neatly and make corrections easily.
	3.	Ruler or Straightedge
	•	Useful for drawing accurate graphs and straight lines.
	4.	Graphing Calculator (or a Scientific Calculator with Graphing Features)
	•	If your child does not already have one, free online graphing tools like Desmos 
               (www.desmos.com) can be used.

Optional Supplies (for hands-on learners):
	•	Colored Pencils/Markers
	•	To color-code different graphs or systems of equations for better visual 
                understanding.
	•	A fun, reusable way to practice graphing and solving equations.
수업 진행 언어
영어 (레벨: B1)
Outschool 외 필요 앱/웹사이트
이 수업에서는 아웃스쿨 교실 외에도 다음의 툴을 사용합니다:
출처
가입일: March, 2020
4.8
463수강 후기
인기 선생님
프로필
교사 전문성 및 자격증
캘리포니아 교직증명서 초등 교육에
캘리포니아 교직증명서 수학에
석사 학위 교육 Claremont Graduate University에서
"I can’t recommend this class enough! The instructor was super interactive and really encouraging when working with my child. We’re definitely planning to have him as our Math tutor again! Thanks again. !"
Tahesa N. on Nov 4, 2024

"This dude rocks!!!!. Easy to talk to. Very flexible." 
Juby J. on Oct 13

I am a California certified teacher with multiple degrees and certifications  (B.A., M.Ed, Ed.D in Educational leadership, ESOL, GLAD, and AVID) who has taught Middle school and Upper Elementary school for 26 years and I have been teaching mathematics to homeschoolers from grades k-12, both in-person and online for over 6 years.  I always wanted to be a teacher, and I am living the dream!  Also, I cater to students who struggle with or do not care for math. I say this because Algebra is critically important because it is often viewed as a gatekeeper to higher-level mathematics and it's a required course for virtually every postsecondary school program.  I have 6 basic reasons why I think offering this class is so important.  

1)Algebra is Faster And Better Than “Basic” Math
Just as multiplying two by twelve is faster than counting to 24 or adding 2 twelve times, algebra helps us solve problems more quickly and easily than we could otherwise. Algebra also opens up whole new areas of life problems, such as graphing curves that cannot be solved with only foundational math skills.

2) Algebra is Necessary to Master Statistics and Calculus

While learning one kind of math to learn more kinds of math may not be an immediately satisfying concept, statistics and calculus are used by many people in their jobs. For example, on my other side job as a research person for a local non-profit organization, I use statistics every day. I help departments identify ways to measure their success. In general, statistics are used in certain jobs within businesses, the media, health and wellness, politics, social sciences, and many other fields. Understanding statistics makes us wiser consumers of information and better employees and citizens.

Calculus helps us describe many complex processes, such as how the speed of an object changes over time. Scientists and engineers use calculus in research and in designing new technology, medical treatments, and consumer products. Learning calculus is a must for anyone interested in pursuing a career in science, medicine, computer modeling, or engineering.

3) Algebra May Be a Job Skill Later

A student may be confident they are not going into any career needing statistics or calculus, but many people change jobs and entire careers multiple times in their working life. Possessing a firm knowledge and understanding of algebra will make career-related changes smoother.

4) Algebra Can Be Useful in Life Outside of the Workplace

I have found algebra helpful in making financial decisions. For example, I use algebra every year to pick a health care plan for my family using two-variable equations to find the break-even point for each option. I have used it in choosing cell phone plans. I even used it when custom-ordering bookshelves for our home. 

5) Algebra Reinforces Logical Thinking

I would not use algebra as the only means of teaching logic. There are more direct and effective means of doing so, but it is a nice side-benefit that the two subject areas reinforce one another.

6) Algebra is Beautiful

The beauty of algebra is an optional benefit because one has to truly choose to enjoy it, but algebra provides us with a basic language to describe so many types of real-world phenomena from gravity to the population growth of rabbits. That five letters can be used to describe how an entire category of matter, namely ideal gases, behaves is amazing and beautiful in its simplicity.

There is also a beauty when we start with a complex-looking problem and combine and simplify over and over until we have one value for each variable. The process can be enjoyable and the result immensely satisfying.

Algebra is an important life skill worth understanding well. It moves us beyond basic math and prepares us for statistics and calculus. It is useful for many jobs some of which a student may enter as a second career. Algebra is useful around the house and in analyzing information in the news. It also reinforces logical thinking and is beautiful.

So, keep an open mind about why we learn algebra and look for ways to share its applications with students. Dispel the stigma that it is a boring list of rules and procedures to memorize. Instead, consider algebra as a gateway to exploring the world around us. Those are our top reasons why we learn algebra, and there are plenty more. 

리뷰

실시간 그룹 수업
공유
4 회 수업에

US$140


1주 동안 주당 4회
60분
7 명의 학생이 수업을 완료함
실시간 화상 수업
연령: 13-16
수업당 학습자 1-12 명

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