Group Home School Math Tutorial Sessions

 

Thomas Jefferson said: I would advise you to make the Mathematics your principal and almost sole object.  Consider Natural philosophy as quite secondary, because the books will teach you that as well as any master can.  Whereas Mathematics requires absolutely the assistance of a teacher.

 

 

Complete Courses for Pre-Algebra, Algebra I, Algebra II, Algebra III, and Calculus For Groups of Students

Tutor: Danny Mills   Cary, Apex, Raleigh Area Phone: 919-460-3890 Email: tutor@tutorforallages.net Web: tfaa.net

 

Contents:

The Tutorial Sessions
The Goal

The Philosophy

The Tutor

Pre-requisites

The Scope and Sequence

Course Fees

Course Registration

Course Schedule

Supplies

Classwork and Evaluation

Course Outlines:

Pre-Algebra

Algebra I

Algebra II

Algebra III, Pre-Calculus, Trig., Geometry

Calculus

Supplemental Curriculum

Mathematics Placement Guide

Mathematics Placement Tests

 

 

The Tutorial Sessions

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These tutorial sessions are designed for homeschooled high school students and their parents who desire a comprehensive math tutorial program from 9^th grade to 12^th grade.  These sessions are based on the Saxon Math series of books.  Saxon has been chosen because it provides continuous review of all previously introduced topics which means lot of practice.  The instructor will be able to answer any questions about the math.

 

Note:

Parents may make other arrangements by meeting with the Instructor.  There may be a need to set up private tutorial sessions with the Instructor.  In these private tutorial sessions, any curriculum may be used to suit the parent and student.  For example, the student may want to concentrate on a specific area of math, such as Advanced Mathematics or AP Calculus; or perhaps concentrate on SAT, ACT, or CLEP Math Preparation.

 

                                                                                                                                               

The Goal

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The goal of these sessions is to give the homeschool parent and student the very best enrichment experience in math.

 

 

The Philosophy

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Mathematics is the language of commerce, finance, insurance planning, budgets, coupons, bargains, garage sales, technology, science, grade averages, sales quota, bonuses, taxes, and installment payments.  If you are going to do anything with other people, you will eventually use the language called Mathematics. 

 

It may be difficult for the homeschool parent to provide the fundamentals of problem solving techniques for algebra and advanced mathematics.  These tutorial sessions will provide the necessary demonstrations of those techniques so that the parents can execute their responsibilities to educate their students and to assess the students progress for success in the university environment.

 

 

The Tutor

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Danny Mills has a B.S in Physics from the U.S. Naval Academy.  While there, he conducted independent research in Solid State Physics as a Trident Scholar.  He attended the Navy Nuclear Power School and became qualified to operate Nuclear Powered Submarines. He has completed Graduate work in Advanced Engineering Mathematics from NCSU.  He has gained industry experience in Naval Computer Controlled Combat Systems working with the AEGIS Combat System at GE/RCA in Moorestown, New Jersey, and in Commercial Information Technology Systems working with IBM, Research Triangle Park, North Carolina.

 

Danny is a homeschool father of four children.  He has learned a lot about Homeschooling from his wife, Mary Susan, and from his homeschooled children.  He loves the Lord and has an appreciation for Gods Creation through math and science.

 

Danny has a thorough knowledge of math, a love for the subject, and an aptitude to teach math.  He is a tutor for algebra, calculus, and physics.  During the 2002-2003 school year, he tutored high school students, female and male, in Algebra I, Algebra II, and Pre-Calculus, and Chemistry; and college students in Calculus II and Physics, and substituted at Raleigh Charter High School for algebra and physics.  This year, he is tutoring students with SAT, ACT, and CLEP Math Prep studies, Pre-Algebra, Algebra I, and Pre-Calculus.

 

Dannys education and experience enables him to explain concepts and give real world examples to students.  It is important to him to be able to give his students more than just the procedures of math.  He teaches his students the skills of critical thinking.  As the students progress through the tutorial sessions, they are able to ask questions like why?, what does that mean?,  when would I ever use that?; or make statements like I dont get it, or that doesnt make sense and expect to get a reasonable response from the instructor.  This is kind of Homeschool experience parents want for their children.

 

 

Pre-requisites

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Each parent should give the students a placement test provided by the Instructor.  The results are used to give the student and the parent the best possible experience with math.   There is a placement test for

 

Pre-Algebra:

Pass the Pre-Algebra (Algebra 1/2) placement test.

Algebra I:

Students need to have completed the Pre-Algebra (Algebra ½) level and pass the Algebra I placement test.

Algebra II:

Students need to have completed the Algebra I level and pass the Algebra II placement test.

Advanced Math:  Pre-Calculus, Algebra III, Trig., Geometry

Students need to have completed an equivalent of Algebra II.

Calculus

            Students need to have completed an equivalent of Advanced Math.

 

The Scope and Sequence

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Saxon Publishers provides a comprehensive Scope and Sequence document for:

1.      Comparison of Algebra ½ (3^rd Edition), Algebra 1 (3^rd Edition), Algebra 2 (3^rd Edition),

2.      Advanced Mathematics (Pre-Calculus, Algebra III, Trig., Geometry), and

3.      Calculus. 

 

The parent can obtain a copy of this document from

 http://www.saxonpublishers.com/pdf/school/math/Algebra_SS.pdf ,

or the Instructor can provide a copy, 44 pages, $6.00, upon request.

 

 

Course Fees (tentative)

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Contacts Danny Mills for details about fees.

 

The sessions are held twice a week, Monday and Wednesday, for one hour each day at a cost of  $320/semester. (equivalent to $80/month or $10/hour: over 4 months there are 32 one hour sessions).  Each course is 2 semesters long.

 

Course Registration

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There are 5 seats available in each class.  Contact Danny Mills hold your seat.

 

 

Course Schedule (date and times are tentative)

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Sessions start Monday, January 5, 2004.  Contact Danny Mills for Course Schedule details.

 

Twice a week: Monday and Wednesday.  Arrangements can be made for session times starting at 9:00, 10:10 11:20, 1:00, and 2:00.

 

  9:00   Algebra II

10:10   Pre-Algebra

11:20   Algebra I

  1:00   Algebra III Advanced Math/Trig/Geometry/Pre-Calculus

  2:00   Calculus

 

If necessary, additional classes will be made available on Tuesdays and Thursdays.

 

If necessary, additional tutorial sessions will be scheduled.

 

The sessions will meet every week except these days:

 

1. Spring Break                 March 15 - 19
2. Easter Break                 April 12 16
3. Memorial Day                May 24

 

Last session is May 26

 

 

Supplies

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1. Textbook:  Textbooks will be provided at a rental fee of $10 per semester.  If necessary, handouts will be provided until additional textbooks are ordered and become available to the student.

 

2. Notebook:  Students will need a 3 inch notebook for course work and homework.

3. Paper, Pencils, erasers.

4. Calculator: Students will need a scientific graphing calculator.  The TI-83+ is standard.

 

 

Classwork and Evaluation

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Proficiency in math takes practice. Saxon Math provides for plenty of practice.

 

At each session, some or all of following will occur as appropriate:

1.       The Instructor will go over the quiz/test or test from the previous session.

2.       The Instructor will go over any problems from homework for the students.

3.       A quiz/test on the previous homework material will be given.  

4.       The Instructor will introduce the new chapter in the session book (Saxon), work sample problems, and assign reading and problems to be completed by next session.

 

A student, under the supervision of the parent, will be expected to read the introductory text for each lesson and complete assigned problems at home as preparation for each session.  Each chapter in the book has a test. Take home quizzes and tests will be given in order for parents to have feedback on their childs progress.

 

A written evaluation will be provided, at the end of the course, to the parents as a suggested performance rating for the student and for the purpose of college applications.

 

 

 

Course Outlines:  Pre-Algebra : Algebra ½

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In Algebra 1/2, students will learn:
fractions and their arithmetic operations decimals and their arithmetic operations mixed numbers and their arithmetic operations signed numbers and their arithmetic operations translating from words to algebraic expressions order of operations percents proportions ratios divisibility rounding place value unit conversions	scientific notation data representation evaluation of algebraic expressions the simplification of algebraic expressions the solution of linear equations in one unknown word problems involving pre-algebraic concepts perimeter area surface area volume classification of geometric figures and solids geometric constructions symmetry

 

Detailed Curriculum

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The parent can obtain a copy of this document from

http://www.saxonpublishers.com/pdf/resources/math/algebra_one-half_3e_toc.pdf

or the Instructor can provide a copy, at cost, upon request.

 

Course Outlines:  Algebra I

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Algebra 1 includes such topics as:

arithmetic and evaluation of expressions involving signed numbers, exponents, and roots properties of real numbers absolute value equations and inequalities involving absolute value scientific notation unit conversions solution of equations in one unknown solution of simultaneous equations the algebra of polynomials and rational expressions word problems requiring algebra for the solution (such as uniform motion and coin problems) graphical solution of simultaneous equations graphs of a variety of functions: linear, quadratic, cubic, square root, absolute value, etc.

translations and reflections of graphs factoring Pythagorean theorem algebraic proofs functional notation and functions solution of quadratic equations by factoring, completing the square, and quadratic formula direct and inverse variation exponential growth computation of the perimeter and area of two-dimensional regions computation of the surface area and volume of a wide variety of geometric solids statistics probability

 

 

 

Detailed Curriculum

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The parent can obtain a copy of this document from

http://www.saxonpu http://www.saxonpublishers.com/school/math/item.do?item_toc=1-56577-135-4 or the Instructor can provide a copy, at cost, upon request.

 

 

Course Outlines:  Algebra II

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Algebra 2 includes such topics as:

·         graphical solution of simultaneous equations

·         basic trigonometric functions

·         scientific notation

·         radicals

·         conic sections

·         roots of quadratic equations, including complex roots

·         properties of real numbers

·         geometric proofs

·         factoring

·         inequalities and systems of inequalities

·         logarithms and antilogarithms

·         exponential equations

·         algebra of polynomials

·         vectors

·         algebraic word problems

·         gas law

·         set theory

·         probability

 

Detailed Curriculum

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The parent can obtain a copy of this document from

http://www.saxonpublishers.com/pdf/resources/math/alg_2_3e_TOC.pdf

or the Instructor can provide a copy, at cost, upon request.

 

 

Course Outlines:  Algebra III, Advanced Mathematics

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Advanced Mathematics consists of Trigonometry, Geometry, and Pre-Calculus.

Advanced Mathematics is made up of five instructional components: Introduction of the New Increment, Examples with complete Solutions, Practice of the Increment, Daily Problem Set, and Cumulative Tests. In Advanced Mathematics, topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis are interwoven to form a fully integrated text. A rigorous treatment of Euclidean geometry is also presented. Word problems are developed throughout the problem sets and become progressively more elaborate. With this practice, students will be able to solve challenging problems such as rate problems and work problems involving abstract quantities. The graphing calculator is used to graph functions and perform data analysis. Conceptually-oriented problems that prepare students for college entrance exams (such as the SAT, ACT, or CLEP) are included in the problem sets.

Advanced Mathematics includes such topics as:
permutations and combinations trigonometric identities inverse trigonometric functions conic sections graphs of sinusoids	rectangular and polar representation of complex numbers De Moivre's theorem matrices and determinants the binomial theorem the rational roots theorem

 

Detailed Curriculum

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The parent can obtain a copy of this document from

 http://www.saxonpublishers.com/school/math/item.do?item_toc=1-56577-040-4

or the Instructor can provide a copy, at cost, upon request.

 

 

Course Outlines:  Calculus

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Calculus is AP Calculus.

Calculus is made up of four instructional components: Introduction of the New Increment, Examples With Complete Solutions, Daily Problem Set, and Cumulative Tests. Calculus covers all topics in the Advanced Placement Calculus AB and Calculus BC syllabi. The instruction takes full advantage of graphing calculators, using them for visual demonstrations of concepts and confirming calculations.

Calculus includes such topics as:
review of functions review of trigonometry limits graphing calculators derivatives integrals optimization problems techniques of integration polar functions area between two curves inverse functions motion analysis applications of integrals solids of revolution	continuity L'Hôpital's rule logarithmic differentiation parametric functions Mean Value Theorem Newton's method trapezoidal rule series tests of convergence slope fields Euler's method logistic growth arc length

 

 

Detailed Curriculum

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The parent can obtain a copy of this document from

 http://www.saxonpublishers.com/pdf/resources/math/calc_2e_toc.pdf

or the Instructor can provide a copy, at cost, upon request.

 

 

Supplemental Curriculum

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The curriculum will be enhanced as appropriate by guidance available in 

1.      The Noah Plan, Mathematics Curriculum Guide, by Arthur Paul Ricciardi, published by Foundation for American Christian Education, Chesapeake, Virginia, 2001.

2.      Mathematics: Is God Silent?, Nickel, 2001.

3.      Men of Mathematics, Bell, 1965.

4.      An appropriate book on Women of Mathematics.

 

 

Mathematics Placement Guide

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1.      The curriculum that I will present is structured for the Normal Track.

2.      If the student has difficulty with the material, then provisions can be made to follow the Support Track.  It is perfectly normal for a student to show gifting in one subject such as English or History and need extra help in Math.

3.      On the other hand, if the student needs more of a challenge in math, then provisions can be made to follow the Acclerated Track.

 

 

 

 

*

Suggested course titles. Accelerated students will finish Advanced Mathematics in the first semester of eleventh grade and begin Calculus in the second semester.  Pre-Calculus I consists of the first 70-90 lessons in Advanced Mathematics.  Pre-Calculus II comprises the remaining lessons.

 

**

Suggested course titles. The content in Geometry-Trigonometry-Algebra 3 is identical to that in Pre-Calculus I but is presented at a slower pace. Likewise, Geometry-Trigonometry-Algebra 4 is the same as Pre-Calculus II. Using these course titles allows accelerated students who are not successful in Advanced Mathematics during the tenth grade to try again and still receive credit. Students who complete Advanced Mathematics will have taken the equivalent of two semesters of geometry, one semester of trigonometry, and one semester of advanced algebra. ("Geometry" in the course title ensures credit for geometry.)

 

***

These students may find the material in Advanced Mathematics difficult. Consider placing them in a less rigorous mathematics course.

 

 

Mathematics Placement Tests

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Saxon books are skill-level books, not grade-level books. It is essential that each student be placed in the text that meets his or her skill level. Success with one Saxon book strongly suggests success with the next Saxon book. The following placement guide may be used to estimate which book a student should use. A placement test will provide a more accurate measure, however.

 

1.      The placement tests are used to give the student the best possible experience with math.

2.      The placements tests will be provided by the Instructor, and administered by the parent to continue the Homeschool bond between the student and the parent.

3.      The parent should give the student time to complete as much of the test as possible.

4.      The parent should note, on the test, which problems the student got right but were a difficult challenge in completing. 

 

The parent and the Instructor are now able to decide the best course of Math study for the student.