TI-83 Programming Exercises
Pythagorean Theorem Proof

Pre-calculus, 2005-2006 Syllabus

Christ Preparatory Academy

Mr. Rives

Phone: 816-223-5565

Email: steve.rives@gmail.com

Web Site: www.Math.MrRives.com

Course Description:

This course is the study of patterns in nature and patters invented.  The patterns in nature that concern us are not to be confused with the system of symbols on the paper – that system is just a way to discuss the patterns. It is the patterns that concern us most, and that is math!  The patterns we will explore are geometric shapes as they are added and subtracted (polynomial math), the square-edged wedges we call triangles and the math symbols that go with those (also called trigonometry), the idea of coordinate systems representing objects as housed on grids, the idea of storing information in a table of rows and columns (matrix math), programming the TI-83 to play math games, and finally, at the end of the course, Statistics and Data Analysis. All of this is lumped under the title of Precalculus; in many schools it is called Advanced Math, Trigonometry and Discrete Mathematics.

Subjects Covered:

1^st Semester

· Number Math (Integer Math, [the kind computers use!])

o Kinds of numbers

o Counting, Counting Systems, Different Bases

o Modular Arithmetic

· Algebra Math (Algebra III)

o Polynomials

o Linear and non-linear functions

o Complex Numbers

o Graphing Equations

2^nd Semester

· Geometry Math (Trigonometry)

· Math for Thinking (Discrete Mathematics/Computer Math)

o Statistics

o Data Modeling

o Matrix Math

Special Skills to be Learned:

Excel Spreadsheet Math

TI-83 programming in BASIC

Writing a paper using LaTeX

Getting formulas into computers

Textbook

The main text is Advanced Math with Discrete Mathematics. See http://www.christprep.com/SiteResources/data/files/curriculum.pdf,

The textbook listed in that PDF is right, though the author is mistakenly listed as Larson.

Our textbook is set up to allow for the teaching of a discrete mathematics track – that is the course I will be teaching.   This will become especially evident in the second semester (in the first semester, we will cover chapters 1-6).

In addition to the required text, we will be reading extra materials.  There is a world of mathematical literature that is recreational, informative, and entertaining.   To that end, we will start with a classic in the field: Flatland, by Edwin Abbott.    You may purchase any edition.

Course Materials:

• Three-ring binder with four sections.  I am going to hand out a collection of material that they will want properly stored and saved – this notebook will be essential.   I will also be testing from material that I distribute, so they will want to keep it all in once easy to find place.
• Red grading pen.  When we grade in class, I want the student to grade in a red pen.
• TI-83 calculator.  If you already own a TI-89, I will try to work with you, but it makes the class run better if we all have the TI-83 (which includes the regular TI-83, the silver edition, or the TI-83 plus).
• Graph paper.
• Loose leaf paper.  I like assignments, quizzes and tests to be handed in with loose leaf.
• (optional): Solutions Manual
• Protractor.  Please buy a protractor that has a swing-arm attached.
• A drafting compass for drawing arcs and circles.
• An orienteering compass for outdoor use.  The more expensive models (around $15.00) will enhance the learning experience, but that is not required.   Those compasses that are less than $4.00 are generally not useful, so avoid those.  If you want, you can wait for the second semester to buy this item.
• Flatland, by Edwin Abbott
• The main text, Advanced Math See http://www.christprep.com/SiteResources/data/files/curriculum.pdf The textbook listed in that PDF is right, though the author is mistakenly listed as Larson.

Final Grade

There is one test per chapter and we will cover six chapters in the first semester, and four to six in the second semester. Each test is equally weighted, and the final grade is based on the percentage of points earned across all tests. There is no curve.

Homework

Homework is assigned and discussed, but does not contribute to the final grade.

Grading Philosophy

Each student's grade is based solely on what is learned over-and-against what was taught.  A student has from the start of the semester to the end to master any or all of the material.  I give every chance to get an A.  Thus, a misstep at the start of the course will be erased if the material missed is later learned.   For example, if on the first test a person does not know the meaning of complex numbers, they can still learn that at a later time and demonstrate it to me (I will offer times of retesting).  

This means that each student has every opportunity to do well.  It also means they have the latitude to fail.  This course requires discipline.  I assign homework, and we discuss and review it in class, yet no one will do well on a test if they opt out of home studies.   If I find a student not doing the homework and then not doing well on the tests, I will be contacting the parents.  As an Advanced Math course, I want to give the students the chance to decide how much preparation they need for each exam.  

One advantage of this system is that it accounts for those students who can do less homework (fewer instances of certain kinds of problems), and still perform well on the exams.   At this level of secondary math, there are some people who grasp certain concepts with great ease; they should spend their time preparing for classes more difficult.  

Another advantage to this system is that it does not penalize a student who needs more time.  I have had students who missed an idea (either for bad teaching or for a failure on their part), but weeks later—or sometimes only days later—overcame the mental roadblock.   All of us relate to that experience, and I want to acknowledge that different people take different routes to learning mathematical concepts.

Outline of Course

Day 1: Number Bases and Modular Math (Not in Book)

I. What is Math

II. Base Numbers

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Handouts on Modular Math

Read Flatland Section 1-2

Read Chapter 1.1-1.2

Day 2: Linear Equations

Linear and Quadratic Functions

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