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Hello! Thank you for visiting my profile page! My name is Ellsworth and I would LOVE to help you overcome any difficulties you may be facing with math or related subjects.

First of all, who better to learn math from than … an actual math teacher? That’s right! I taught high school math for the last eight (8) years. Here’s a quick read of my qualifications:

•Bachelor’s degree in Electrical Engineering (from MIT!)

•Master’s degree in Computer Science

•Eight years of high school classroom math teaching experience in TWO states (Texas and California)

•Currently certified to teach math in Texas

•Extensive prior tutoring (math) experience both as a school teacher and with tutoring firms

•Prior college teaching experience in various math courses

WHAT CAN YOU HELP ME WITH?

Probably just about any math area you’re likely to face in high school or college. This includes, but is not limited to:

•Pre-Algebra*

•Algebra 1*

•Geometry*

•Math Models*

•Algebra 2*

•Pre-Calculus*

•Calculus (intro)

•Developmental Math

•College Algebra

(* = “I’ve taught this class at least once, in an actual school classroom, with real live students!”)

Also, I can help you prepare for tests:

•SAT (especially math!)

•ACT (especially math!)

•GRE (especially… well, you get the idea…)

•GMAT

•GED

I also like to do what I call “math literacy”, which is basically everyday math that most schools have now abandoned because it’s not a college-prep course. I think this is a terrible mistake! I’m talking about general math skills that you encounter in daily life, like scaling up a recipe to make multiple batches of cookies, calculating how much that sale discount takes off the price of a sweater, or how to (fairly) split up the cost of a meal with friends (including tax!).

If you need something not on this list, just ask. I’ll give you some information and/or point you in the right direction.

SO, HOW DO WORK WITH STUDENTS TO KNOW WHAT THEY NEED?

Well, there are at least three approaches, and I use one or more depending on the situation:

1) Interview the student and family to get a sense of strengths and areas for improvement

2) Perform a general assessment (that’s teacher-speak for “give a test”) to spot trouble areas. I made my own Algebra skills test just for this purpose!

3) Ask them if there is some area they are specifically having trouble with (e.g. word problems, solving quadratic equations, reducing rational expressions…)

GREAT. SO THEN WHAT?

Based on what we find, we develop customized tutoring plans. I recommend several possible courses of tutoring, the same way a doctor writes you a prescription when you’re sick. The difference here, though, is I can give you a range of options to consider, depending on the results you want to achieve and the time frame in which you want them.

Using your preferences and requirements, we can fine-tune a plan to fit your budget and schedule.

WHAT’S YOUR TEACHING STYLE LIKE?

I have developed an approach that I call “I do / we do / you do”:

•I Do: I explain and demonstrate the concept by solving sample problems

•We Do: We do a couple more problems, but I put more of the load on your shoulders

•You Do: Still more problems which I let you work completely on your own while I watch

In this way, you are assured that you can do the problems because… well, you just did them! If you run into trouble we can repeat the above process, or, alternatively, step back and work on a supporting concept.

HOW DO I KNOW WE’LL ALL GET ALONG? I DON’T WANNA RISK MONEY TO FIND OUT…

Well, you can certainly “try before you buy”! The first session is free, where we discuss your needs and maybe do a little light problem-solving to see how things go. That way everyone can assess their comfort level and act accordingly.

SOUNDS WONDERFUL! WHAT DO I DO NOW?

You can send me an e-mail with specific questions that you may have. Or you can just contact the folks at Wyzant to help you set something up. Either way, we can start the process of getting you the help you need.

ANY LAST WORDS?

Math is hard for people for many different reasons. Perhaps it’s because it wasn’t taught well the first time. Maybe you just weren’t ready to receive the information, or connections weren’t made between one math topic and another.

Whatever the cause, it’s 100% fixable, but with a catch: you have to BE WILLING TO DO THE WORK to become proficient. No one who has seriously applied themselves has ever failed my math class, and, conversely, the single leading cause of failure is “not doing the work”.

So if you’re looking to improve your math proficiency, come with the right attitude. I LOVE TEACHING MATH, and nothing gives me more satisfaction than helping a deserving student succeed where they struggled before, demonstrating first-hand that doing well in math IS possible if you put in the effort.

I’m ready to start our math adventure. Are you?

Corporate Training:

Microsoft Word

Test Preparation:

ACT Math, GRE, SAT Math

Homeschool:

Business:

GRE, Microsoft Word

Science:

Physical Science

Computer:

Microsoft Word

Math:

ACT Math, Algebra 1, Algebra 2, Calculus, Differential Equations, Geometry, Logic, Prealgebra, Precalculus, Probability, SAT Math, Trigonometry

Algebra 1 is the “gateway” course to high school math. You must master the concepts learned in this course to be successful in Geometry, Algebra 2 and beyond, since your continuing in the math curriculum assumes as much.

QUALIFICATIONS TO TUTOR THIS COURSE

• Taught this course in a high school setting in varied formats

• Tutored this subject both in school and online

• Degrees in Electrical Engineering and Computer Science

• plus… I’m pretty good at it!

WHAT *IS* ALGEBRA, ANYWAY?

Oh, *so* many answers to that question. Here are a few:

• A branch of mathematics that substitutes letters for numbers (think: Captain Crunch Super Decoder Ring!)

• A language for expressing abstract concepts (think: French, Latin, Urdu or Esperanto)

• A mathematical model of a real-life situation (think: word problems)

• A system of mathematical rules for calculating unknown numerical values which meet specified conditions (think: solving equations)

I like this last definition most, since it is closest to how we actually use it in this course, and elsewhere.

Algebra is a * -- system of rules -- * by which we get stuff done. The rules are consistent (always work the same way), no matter how simple or complex the problem; learn these rules, and how to use them productively, and they will take you far! To quote that great mathematician Buzz Lightyear, “To Infinity, And Beyond!”

MY TOP FIVE MATH “TROUBLE TOPICS”

I’ve been a high school math teacher for eight years, and in that time the same handful of topics hold students back year after year because they didn’t take the time to master them. ALL OF THEM are found in Algebra 1:

1) solving equations

2) word problems

3) systems of linear equations (2 equations, 2 unknowns)

4) equations of lines, and their graphs

5) adding and subtracting negative numbers (this one’s easily fixed – ask me how!)

I can help you become more confident in these areas, because they are so important for your mathematical success! Later courses build on them (and trust me: they lean VERY heavily on this foundation), so it’s best to master them now.

ALGEBRA 1 TOPIC LIST

Here’s a list of what most Algebra 1 courses cover:

Introduction

• variables

• order of operations

• equations

• expressions

Real Numbers and Integers

• number line

• basic four operations (add, subtract, multiply, divide )

Solving Linear Equations (this is CRUCIAL!)

• one-step and two-step equations

• multi-step equations (terms in parentheses, like terms)

• variables on both sides

• formulas and functions

Graphing Linear Equations

• what is slope?

• slope-intercept form

• solving linear equations using graphs

Writing Linear Equations

• point-slope form: y – y1 = m(x – x1)

• slope-intercept form: y = mx + b

• standard form: ax + by = c

[ ==> ??? Do these last three topics tell you that LINEAR EQUATIONS ARE IMPORTANT ??? <===]

Solving and Graphing Linear Inequalities

• (parallels section on solving linear equations, above)

Systems of Linear Equations and Inequalities

• solving by graphing

• solving by substitution

• solving by linear combination

Exponents and Exponential Functions

• multiplication and division properties of exponents

• zero and negative exponents

• scientific notation

• exponential growth/decay functions

Quadratic Equations and Functions

• simplifying radicals

• solving by finding square root

• solving by graphing

• solving by the Quadratic Formula

Polynomials and Factoring

• adding, subtracting and multiplying polynomials

• special products of polynomials

• solving polynomial equations in factored form (THIS is COOL!)

• factoring x^2 + bx + c and ax^2 + bx +c (THIS is even COOLER! I’ll show you the EASIEST WAY EVER to do this!)

• factoring using the Distributive Property (Factor By Grouping)

BUT WAIT… THERE’S MORE!

This is as far as most high school Algebra 1 courses dare go… and it’s quite a challenge for most students. But if you’re still with us, and it’s not yet June, here are some “Scenes From Upcoming Math Courses” included in the last two or three chapters of most textbooks for the more advanced student:

Rational Equations and Functions (I really pound this home in Algebra 2!)

• ratio and proportion

• direct and inverse variation

• simplifying rational expressions

• multiplying and dividing rational expressions

• adding and subtracting rational expressions

• dividing polynomials

Radicals and Connections to Geometry

• functions involving square roots

• radical expressions

• solving radical equations

• Completing The Square (this is where the Quadratic Formula comes from!)

• the Pythagorean Theorem and its converse

• the distance and midpoint formulas

• investigating similar triangles

• trigonometric ratios

You can see that Algebra 1 is a very broad course, and to be held responsible for so much varied material is a pretty tall order! As your tutor, I can help you in areas where you may need assistance.

At the high school I taught at, I designed this Algebra 2 curriculum for our department, and we used it as the scope and sequence for teaching the actual course:

===============================

REVIEW SOLVING EQUATIONS AND SYSTEMS

* 1 equation, 1 unknown and

* 2 equations, 2 unknowns

QUADRATIC EQUATIONS: We became EXPERTS at solving ax^2 + bx + c = 0. using three different methods:

1) Quadratic Formula (of course!)

2) Factoring (the NEATEST and SIMPLEST trick I EVER saw makes this EASY and FOOLPROOF!)

3) Completing the Square (for those who need/want the extra rigor)

FACTORING HIGHER ORDER EXPRESSIONS: After mastering quadratics, we expanded our factoring repetoire to higher-order functions (x^3, x^4 and beyond) by building up our "bag of tricks" for reducing these big-boys to products of first- and second-order expressions. Some of the tools we developed:

* Synthetic Division

* Factor by Grouping

* Greatest Common Factor (GCF)

* Difference of Squares

* Sum/Difference of Cubes

And all of this was to prepare you for...

RATIONAL EXPRESSIONS AND EQUATIONS: Around the end of the first semester we finally arrive at the mountain top -- being able to:

* find least-common denominator (LCD) and greatest common factor (GCF) of two rational expressions

* simplify rational expressions (using our factoring methods developed above!)

* solve rational equations (including identifying extraneous solutions)

RADICAL EQUATIONS AND EXPRESSIONS: The same "simplify expression/solve equation" duality we used for quadratics and rational expressions is harnessed to tame equations containing radicals.

* Eliminating Radicals (where possible)

* Rationalizing the Denominator

* Simplifying Radical Expressions

* Solving Radical Equations

COMPLEX NUMBERS: Remember the "lie" you were told in second grade about how you can't evaluate 3 - 7, since 7 is bigger than 3? Well, one day you suddenly *could*, and "negative numbers" were born!

Similarly, the statement "you can't take the square root of negative numbers" is also going into the dust bin, because we are again expanding our numbering system, this time to include "i", the square root of -1.

* Using Complex Conjugates

* Getting "i" out of the Denominator (or, as I pithily put it, "Keeping It Real"... nyuk nyuk...)

* Simplifying Complex Expressions

* Solving Complex Equations

* Solving Quadratic Equations with Complex Roots (you know... the ones you "couldn't" solve before, because the quantity under the radical was negative)

LOGARITHMS AND EXPONENTIALS: Finally, after losing a month to state testing, we got to end the year in a subject which was long neglected at my school: logarithms and exponentials. Besides learning each of these topics inside and out, I also emphasize their dual nature, namely how every logarithmic equation can be written in an exponential form (and vice versa), and how to exploit the fact that logs and exponentials are inverse functions of each other.

Specifics:

* What is a logarithm -- REALLY?

* Simplifying log equations

* Log identities

* Exponential equations (solving)

* Applications (e.g. population)

ALL THE OTHER STUFF: Sadly, everything we'd like to see in every Algebra 2 course won't fit... which is why I can also tutor on many of the things we were forced to leave out:

* Conic Sections

* Sequences and Series

* Using a Calculator to Characterize Functions

If you don't see what you need listed, please ask. If I can, I'll give you some ideas or point you in the right direction.

Geometry can be a difficult class for many students. Lodged in most high school curricula between Algebra 1 and Algebra 2, geometry is different from those classes because it calls upon more than just the pure mathematical aptitude the others require.

But make no mistake: you DO need solid algebra skills to succeed in geometry, but in my experience you also need to be creative, logical and be able to “think” logically, and visualize in 2 and 3 dimensions. I’ve taught this class twice, mostly to 10th graders, and it’s been a challenge for many of them to make that leap from just using formulas.

When you get to “Pre-Cal”, you’re getting SERIOUS about math! Most students bail after Algebra 2, because that’s the last math class they are required to take, so if you’re still around for Pre-Cal, it’s because you WANT to be here, and my hat is certainly off to you!

QUALIFICATIONS TO TUTOR THIS COURSE:

• Taught this course in a high school setting

• Tutored this subject both in school and online

• Degrees in Electrical Engineering and Computer Science

• plus… I’m pretty good at it!

USEFUL PREREQUISITES:

Before you jump in to pre-calculus, I’d recommend brushing up on some prerequisites you’ll need from earlier courses:

• Solving Equations Algebraically (Algebra 1 and 2) -- you NEED to MASTER this!

• Graphical Representation of Data (Algebra 1)

• Graphs of Equations (Algebra 1, Geometry)

• Lines in the Plane (Algebra 1, Geometry)

• Solving Equations Algebraically and Graphically (Algebra 1 and 2)

• Solving Inequalities Algebraically and Graphically (Algebra 1 and 2)

THE COURSE ITSELF:

Here’s a subject list for a typical modern pre-calculus class.

The first topics (1-5) are a review of material covered in Algebra 2 (or before), but also given a more advanced in-depth treatment.

Starting with 6) you’re largely into new concepts.

This is roughly how the class is typically broken up between two semesters in high school.

Review/Advanced Treatment:

1) Functions and Their Graphs

• Function Basics

• Graphs of Functions

• Shifting, Reflecting, and Stretching Graphs

• Combinations of Functions

• Inverse Functions

2) Polynomial and Rational Functions

• Quadratic Functions

• Polynomial Functions of Higher Degree

• Real Zeros of Polynomial Functions

• Complex Numbers

• The Fundamental Theorem of Algebra (polynomials with complex coefficients)

• Rational Functions and Asymptotes

• Graphs of Rational Functions

3) Exponential and Logarithmic Functions

• Exponential and Logarithmic Functions (and their graphs!)

• Properties of Logarithms

• Solving Exponential and Logarithmic Equations

3) Trigonometric Functions

• Radian and Degree Measurement

• Trigonometric Functions: The Unit Circle

• Right Triangle Trigonometry

• Trigonometric Functions of Any Angle

• Graphs of Sine and Cosine Functions

• Inverse Trigonometric Functions

4) Analytic Trigonometry

• Using Fundamental Identities

• Verifying Trigonometric Identities (VERY algebra-intensive!)

• Solving Trigonometric Equations (gotta be creative here!)

• Sum and Difference Formulas

• Multiple-Angle and Product-Sum Formulas

5) Systems of Equations and Inequalities

• Solving Systems of Equations

• Systems of Linear Equations in Two Variables

• Multivariable Linear Systems

• Systems of Inequalities

• Linear Programming (constraint optimization, using a system of linear inequalities)

New Stuff:

6) Advanced Topics in Trigonometry

• Law of Sines (and Cosines)

• Vectors and Dot Products

• Trigonometric Form of a Complex Number (believe it or not, they ARE related!)

7) Matrices and Determinants

• Matrices and Systems of Equations

• Operations with Matrices

• Inverse of a Square Matrix

• Determinant of a Square Matrix

• Applications of Matrices and Determinants (e.g. Cramer’s Rule for solving linear systems)

8) Sequences and Series

• Arithmetic Sequences and Partial Sums

• Geometric Sequences and Series

• Mathematical Induction

9) Probability (This is a whole course in itself! But we’re just introducing it here)

• Introductory Concepts (counting, experiments, outcomes, sample spaces, …)

• Counting Principles

• The Binomial Theorem

10) Advanced Topics In Pre-Calculus

• Conic Sections (parabolas, ellipses and hyperbolas)

• Systems of Quadratic Equations

• Parametric Equations

• Polar Coordinates (and their graphs)

11) Three-Dimensional Analytic Geometry

• The Three-Dimensional Coordinate System

• Vectors in Space

• Cross Product of Two Vectors

• Lines and Planes in Space

12) Limits and an Introduction to Calculus

• What ARE Limits, anyway?

• Techniques for Evaluating Limits

• The Tangent Line Problem

• Limits at Infinity

• Limits of Sequences

• The Area Problem (you’re actually doing calculus here, but you’re not supposed to know that yet! Shhhh…)

Trigonometry (sine, cosine, tangent, etc.) is usually first encountered in Geometry, and then amplified in either Algebra 2 or Pre-Calculus. It is typically used in the context of the angles of triangles, and how they are related to the lengths of the triangle’s sides.

Wherever you encounter it, I can help you understand this material from the ground up.

QUALIFICATIONS TO TUTOR THIS COURSE:

• Taught this course in a high school setting

• Tutored this subject both in school and online

• Degrees in Electrical Engineering and Computer Science

• plus… I’m pretty good at it!

I can start out, if needed, by illustrating how sine, cosine and tangent are the ratios of certain pairs of triangle sides (opposite, adjacent and hypotenuse). From there we can use the following road-map to develop our understanding. We can jump in at an appropriate point if you are an advanced student, or need specific help:

BASIC TRIGONOMETRY (Geometry)

• Using Trigonometric Functions: Find angles, given side lengths

• Solving Right Triangles: You can find all the missing angles and sides when you are given two sides, or one side and one angle

• Inverse Trigonometric Functions (arcsin, arccos, arctan): Given the side lengths in a right triangle, find the angles!

• Special Right Triangles: The triangles 45-45-90 and 30-60-90 have special properties which make finding missing side lengths a snap, even if you are given only one side!

• Sum and Difference Formulas (including Double Angle): Find, for example, cos(2x) or tan(a – b)

INTERMEDIATE TRIGONOMETRY (Geometry, Algebra 2)

• Using Fundamental Identities: your “survival kit” of basic trig identities

• Radian and Degree Measurement: Angles may be measured in either degrees or radians. Learn to do both.

• The Unit Circle: A circle of radius 1, centered at the origin, can tell us so much about trigonometry…

• Graphs of Sine and Cosine Functions: Everything you wanted to know about amplitude, phase shift, period, offset… and how to get from graphs to equations, and vice versa

ADVANCED TRIGONOMETRY (Algebra 2, Pre-Calculus)

• Law of Sines (And Cosines): Now we’re not restricted to right triangles! Use these rules to relate angles and side lengths in a more general way.

• Verifying Trigonometric Identities: VERY algebra-intensive! Only “Algebra Ninjas” need apply… but I’ll help you out…

• Solving Trigonometric Equations

As usual, if you don’t see what you need… ask!

Great improvement with each lesson — My son is really starting to feel confident with his algebra. He said last night was the best lesson yet, so he and Ellsworth are building a great rapport ...

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