Transcript Advanced Mathematics II

Advanced Mathematics II
Rebecca Runnels Morrison
Runnels School
The Power of Teaching
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Or… be careful who you teach…
24 participants x 100 students/year =
2400 lives touched yearly
What is Advanced Math II?
Vertical Sequences
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Traditional sequence ending in Calculus:
Algebra II  Advanced Math Calculus
AB
Sequence ending in Statistics AP: Algebra
II Advanced Math II  Statistics AP
Questions and Answers about
Advanced Math I and Advanced
Math II
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All answers are IMHO.
Concerns
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Do students take either Advanced Math I
or Advanced Math II or can they take
both?
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Typically, students would take only one of
these two courses.
Concerns (continued)
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Upon completion of Advanced Math I or
Advanced Math II, what courses should a
student be prepared to take?
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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.
Concerns (continued)
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OK, but can a student take both Advanced Math
I and Advanced Math II, and when would be
appropriate to do so?
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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.
Concerns (continued)
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So why are they called Advanced Math I
and Advanced Math II?
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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.
Who needs Statistics?
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Information Systems and Decision
Sciences
Psychology
Education
And, of course, everybody
Advanced Math II Units
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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
Unit I
Single Variable Statistics and Data
Collection
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This unit includes methods of collecting,
analyzing, and displaying univariate (singlevariable) 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
Unit I (continued)
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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.
Unit II
Bivariate Statistics, Regression,
and Correlation
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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.
Unit III
Probability and Probability
Distributions
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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.
Unit IV
Functions
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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.
Unit V
Triangle Trigonometry
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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 reallife applications of triangle trigonometry.
Unit VI
Modeling Data with Trigonometric
Functions
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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.
Unit VII
Modeling Data with Exponential
and Logarithmic Functions
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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.
Unit VIII
Graphs and Paths
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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.