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掌握二項式:帕斯卡三角形、定理與機率

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Erin Townley
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在這個為期三週的課程中,學生將學習二項式定理的結構和意義,並探索其與二項式展開式、帕斯卡三角形和二項機率的聯繫,
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課堂經歷

英語程度 - 未知
美國等級 9 - 12
Intermediate 等級
6 lessons//3 Weeks
 Week 1
Lesson 1
Intro to Binomial Expansion and Pascal's Triangle
In this lesson, students will explore the patterns that exist in binomial expansions and how those patterns relate to Pascal's Triangle.
Lesson 2
More with Binomial Expansion and Pascal's Triangle
In this lesson, we will expand on what was covered in the previous class and learn how to create full and partial expansions of binomials using Pascal's Triangle.
 Week 2
Lesson 3
The Binomial Theorem
In this lesson, we will define and analyze the Binomial Theorem, show how it connects to Pascal's Triangle and practice using it in a variety of problems.
Lesson 4
Challenge Problems with Binomial Theorem
In this lesson, we will work on solidifying and extending our understanding of the Binomial Theorem by tackling a variety of challenging, abstract problems related to the theorem and binomial expansion.
 Week 3
Lesson 5
The Binomial Theorem and Probability
In this lesson, we will make the connection between the terms of a binomial expansion and the outcomes of a binomial probability.
Lesson 6
Applications of Binomial Probability
In this lesson, we will expand on what was covered in the previous lesson and explore some of the applications of binomial probability, including coin flips, dice rolls, test taking, decision making, etc.
  • Students will understand how Pascal's Triangle can be used as a tool for binomial expansion.
  • Students will make connections among Pascal's Triangle, binomial expansion, and the Binomial Theorem.
  • Students will improve their understanding of the Binomial Theorem by applying it and its properties to binomial probability.
  • Students will solidify their understanding of the Binomial Theorem and binomial probability by exploring some of the many applications that exist in the real world.
Since learning about them in high school, Pascal's Triangle, the Binomial Theorem, and binomial probability have been one of my (many) favorite topics in math. As a student, I noticed that these topics seemed to appear in a wide variety of math courses and were often very challenging for students to understand and utilize effectively. As a teacher, I noticed that every year, this topic was listed as the most difficult by a majority of the students, so I've made it a goal to "demystify" this set of concepts.

In addition to my understanding of the importance of these topics and their value to a variety of areas of study, I have the following qualifications:
-B.A. in Mathematics from Rice University
-M.A in Mathematics from University of Houston
-Texas Teaching Certificate
-almost 15 years teaching and tutoring courses that teach and/or use these concepts
1 - 2 每週課外時間
Homework
頻率: 1-2 per week
回饋: 可根據要求提供
細節: Students will be given optional extra practice homework assignments after each class, so that they can check their own understanding of the topics prior to the next class period. Answer keys will be provided and questions will be addressed in the next class.
Students should have completed at least an Algebra 1 course and be familiar with basic probability and binomial expansion.
Paper
Pen or Pencil
a graphing calculator (I will be using the Numworks in class, but students can use what they have) 
已加入 June, 2024
5.0
1評論
Outschool 新內容
教師檔案
教師專業知識和證書
德州 教學證書 在 數學
碩士 in 數學 from University of Houston
Hi, I’m Erin! I graduated magna cum laude from Rice University in 2008 with a B.A. in both Mathematics and Psychology, as well as obtaining a teaching certificate for grades 7-12. I then went on to get a M.A. in Mathematics from the University of... 
團體課

US$40

每週或US$120 用於 6 課程
每週上課 x 2 次, 3 週
45 分鐘

即時視訊會議
年齡: 13-17
4-12 每班學員人數

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