Advanced Mathematics II

1. Advanced Mathematics II Rebecca Runnels Morrison Runnels School

2. The Power of Teaching • Or… be careful who you teach… • 24 participants x 100 students/year = 2400 lives touched yearly

3. What is Advanced Math II?

4. Vertical Sequences • Traditional sequence ending in Calculus: Algebra II  Advanced Math Calculus AB • Sequence ending in Statistics AP: Algebra II Advanced Math II  Statistics AP

5. Questions and Answers about Advanced Math I and Advanced Math II • All answers are IMHO.

6. Concerns • Do students take either Advanced Math I or Advanced Math II or can they take both? • Typically, students would take only one of these two courses.

7. Concerns (continued) • Upon completion of Advanced Math I or Advanced Math II, what courses should a student be prepared to take? • A student who successfully completes either Advanced Math I or Advanced Math II should be ready for either AP Calculus or AP Statistics, but Advanced Math I is the ideal preparation for Calculus and Advanced Math II is the ideal preparation for statistics.

8. Concerns (continued) • OK, but can a student take both Advanced Math I and Advanced Math II, and when would be appropriate to do so? • Taking an AP class in high school really helps prepare a student for college. Any student who completes Algebra I/ Algebra II/ Geometry/ Advanced Math, and still has time to take another math should be preparing for college. However, if the student is not ready for AP level work, taking the other Advanced Math class can help develop and reinforce mathematical skills. Some topics will be reinforced, but no topics will be taught in exactly the same way.

9. Concerns (continued) • So why are they called Advanced Math I and Advanced Math II? • Only to distinguish them from each other. They are NOT sequential. • Other names: Advanced Math Trig and Advanced Math Stats; Advanced Math Science focus and Advanced Math Social Science focus • The focus of Advanced Math II is the exploration of data.

10. Who needs Statistics? • Information Systems and Decision Sciences • Psychology • Education • And, of course, everybody

11. Advanced Math II Units • Unit 1:Single Variable Statistics and Data Collection • Unit 2: Bivariate Statistics, Regression, and Correlation • Unit 3: Probability and Probability Distributions • Unit 4: Functions • Unit 5: Triangle Trigonometry • Unit 6: Modeling Data with Trigonometric Functions • Unit 7: Modeling Data with Exponential and Logarithmic Functions • Unit 8: Graphs and Paths

12. Unit I Single Variable Statistics and Data Collection • This unit includes methods of collecting, analyzing, and displaying univariate (single-variable) data. Sampling and other collection techniques are discussed since appropriate methods of data collection are necessary in order to obtain any meaningful information. The concepts of sampling, randomization, and bias are introduced and discussed. Both graphical and numerical methods will be used to analyze information. These concepts will be employed to design experiments

13. Unit I (continued) Material in Units I – III and Unit VIII are described in greater detail since many of these topics may not be included in a traditional Advanced Math text book.

15. Unit II Bivariate Statistics, Regression, and Correlation • This unit covers the statistics of two related variables. The topics include displaying and analyzing paired data and formalizing relationships which have been introduced in previous years. In particular, techniques for quantitatively describing the relationship between independent and dependent variables will be presented.

16. Unit III Probability and Probability Distributions • This unit further develops the notions of probability introduced in earlier math classes. The relationship between probability and statistics is introduced, and the term “random variable” is defined. Probability distributions, such as the binomial and normal distributions, are presented.

17. Unit IV Functions • This unit will continue the study of functions begun in Algebra I with an approach centered on data collection. The major topics include a more thorough study of the graphs of functions and the different ways to express functions (rules, descriptions, tables of data, and algebraic expressions). Functions that model physical phenomena will be used as examples for a study of the concepts of domain, range and function composition. A special emphasis will be placed on data that can be modeled by power functions and polynomial functions. A further topic for study includes using transformations of functions (including using matrices) to improve or adapt a mathematical model.

18. Unit VTriangle Trigonometry • This unit covers all aspects of triangle trigonometry. It begins with a review of the right triangle ratios. The Laws of Sine and Cosine are introduced so that problems involving oblique triangles can be solved. The unit ends with some real-life applications of triangle trigonometry.

19. Unit VIModeling Data with Trigonometric Functions • This unit covers the trigonometric functions and the material needed for students to be successful in working with applications of those functions. Exploration of the trigonometric identities using a graphing calculator is also included.

20. Unit VII Modeling Data with Exponential and Logarithmic Functions • This unit focuses on modeling data using the exponential and logarithmic functions. The unit expands on the properties of exponents and logarithms taught in earlier courses as well as provides a review of essential mathematical skills needed in this course and in future courses. Applications include many types of consumer problems.

21. Unit VIIIGraphs and Paths • In this unit students will receive an introduction to the study of graph theory. Graph theory is a topic that is not often taught in high schools, but it has remarkable uses in some fields such as computer networking. In addition, graph theory can be a lot of fun, and students can experience something a little different.