Willsboro Central School
PO Box 180
29 School Lane
Willsboro, NY  12996
(518) 963-4456
Stephen Broadwell,
Superintendent

Board of Education
Andrea Robare, President
Craig Jackson, Vice President
Phyllis Klein
Scott Sayward
Bruce Hale
Brandy Sweatt, District Clerk

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Mr. Vanderhoff
Math Teacher & Discipline

Teaching three advanced Regents level math classes and being the Disciplinarian/Dean of Students has been my role since 2001.  It makes for hectic and unpredictable days that consist of correcting any conflicts among the people in our K - 12 building.  However, the influence I have on the students, parents, and staff makes me feel that I am making a strong contribution to the progress of our school and community.  My philosophy for motivating anyone is to find the right “button” to push that spurs them on and the right “button” for the group they are involved with.  Sometimes that button is not a pleasant one to push, but it is the one I feel is necessary to not only get them on the right track, but to advance them as far as possible academically and socially.     

I graduated from college certified to teach grades K – 12 (math) with a strong minor in counseling & psychology.  Prior to teaching in the North Country I had substitute teaching and assistive counseling experiences in Florida and at an orphanage/reform school in Peekskill , New York .  Returning to the Champlain Valley led to substitute teaching at Plattsburgh High, Beekmantown Central, and Peru Central while I completed my Masters Degree.  

 I began my teaching and coaching career in 1980 at Northeastern Clinton Central at the junior high level.  Willsboro Central School was my next experience where I began teaching grades 9 – 12 math and coaching varsity basketball and baseball in 1983.

Coaching elite travel teams in baseball and fast pitch softball for over a decade have also been experiences that I enjoyed tremendously.  Other interests of mine are music, boating, camping, and travel.  My favorite destinations over the years have been London , Paris , Montreal , New York City, Jekyll Island , Barbados , Florida , and Alaska .

I try to learn as much as possible about people’s tendencies whether it is in a formal or informal setting.  The former students, parents, and professionals (most of them are retired now) at the institutions and schools where I have worked have made me who I am.  I am grateful for their insight, advice, and guidance as I grew up in this profession.  I would like to hear from them and learn about their life at this point because they have not been forgotten. 

 Feel free to contact me for any type of assistance.

Mr. V during a past
School Spirit Week.
 

INTEGRATED ALGEBRA I TOPICS

 

Number Systems

               Identify Integers

                        Identify Rationals

                        Identify Irrationals

                        Identify Reals

                        Measurement

 

Operations & Properties

                 Order of Operations

                        Operation Properties

                        Add, Subtract, Multiply, and Divide Signed Numbers

                        Operations with Sets

                        Graph Numbered Pairs

 

Algebraic Expressions & Open Sentences

                 Use Letters to Represent Numbers

                        Translate Verbal Phrases Into Symbols

                        Algebraic Terms & Vocabulary

                        Write Algebraic Expressions Into Words

                        Evaluate Algebraic Expressions

                        Open Sentences & Solution Sets                      

                 Writing Formulas

 

First Degree Equations & Inequalities w/One Variable

                 Solve Equations Using More Than One Operation

                        Simplify Equations

                        Solve Multiple Step Equations

                        Use Formulas to Solve Equations

                        Solve for a Variable in Terms of Another Variable

                        Transform Formulas

                        Properties of Inequalities

                        Find & Graph Solution Set of Inequalities

                        Use Inequalities to Solve Word Problems

 

Operations w/Algebraic Expressions

                 Add & Subtract Algebraic Expressions

                        Multiply Monomials & Polynomials

                        Divide Polynomials

    Multiply & Divide Powers w/Same Base

                        Zero Exponents & Negative Exponents

                        Basic Scientific Notation

                 Divide Binomials

 

Ratio & Proportion

                 Writing & Simplifying Ratios

                 Express a Rate Using Ratios

                        Solve Word Problems w/Ratios

                        Proportions

                        Direct Variation

                        Percent & Word Problems

                        Convert Units of Measure

 

Geometric Figures, Area, & Volume

                        Points, Lines, & Planes

                        Angles

                        Parallel Lines & Angle Characteristics

                        Triangles

                        Quadrilaterals

                        Area of Polygons & Irregular Objects

                        Surface Area of Solids

                        Volume of Solids

 

Trigonometry of the Right Triangle

                 Pythagorean Theorem

                        Sine, Cosine, & Tangent Ratios & Applications

                        Solve Word Problems Using Trigonometric Ratios

 

Graphing Linear Functions & Relations

                 Sets, Relations, and Functions

                        Graph Linear Functions

                        Graph Lines Parallel to an Axis

                        Slope of a Line

                        Intercepts of a Line

                        Graph Linear Functions Using Slopes

                        Graph Direct Variation

                        Graph 1st Degree Inequalities w/Two Variables

                        Graph Absolute Value

                        Graph Exponential Functions

 

Writing & Solving Systems of Linear Functions

                 Write Equations Using Slope & Given Point

                        Write Equations Using Two Points

                        Write Equations Using Two Intercepts

                        Solve Systems of Linear Equations Graphically

                        Solve Systems of Linear Equations Algebraically

                        Solve Word Problems Using Systems of Linear Equations

                        Graph Solutions of Inequalities on a Number Line

 

Special Products & Factoring

                 Remove Greatest Common Factor from an Expression

                        Common Monomial Factors

                        Square a Monomial

                        Multiply Binomials

                        Factor Trinomials

                        Factor Polynomials

 

Operations w/Radicals

                        Rational Radicals & Irrational Radicals

                        Simplify Radicals

                        Add, Subtract, Multiply, and Divide Radicals

 

Quadratic Relations & Functions

                 Solve Quadratic Equations

                        Graph Quadratic Equations

                        Find Roots from the X-Intercepts of a Graph

                        Solve Quadratic-Linear Systems of Equations Graphically

                        Solve Quadratic-Linear Systems of Equations Algebraically

 

Algebraic Fractions, Equations, and Inequalities

             The Meaning of an Algebraic Fraction

Reducing Algebraic Fractions to Lowest Terms

Multiply & Divide Algebraic Fractions

Add & Subtract algebraic Fractions

Solve Equations & Inequalities w/Fractional Coefficients

Solve Fractional Equations

 

Probability

                   Empirical Probability

                   Theoretical Probability

                   Evaluate Simple Probabilities

                   Evaluate Probabilities w/Overlapping Conditions

Evaluate Complex Probabilities w/Two or More Activities

                    Counting Principle, Sample Spaces, and Probability

                    Permutations & Permutations w/Repetition

                    Combinations & Combinations w/Probability

 

Statistics

                 Collect & Organize Data

                        Create Histograms

                        Mean, Median, Mode, & Range

                        Quartiles, Percentiles, and Cumulative Frequency                     

                       

                      

 

Math  A Topics

The Real Numbers

The Whole Numbers

The Integers

The Rational Numbers

The Irrational Numbers

The Real Numbers

Number Lines and Rulers

Number Lines and Graphs

 

Operations and Properties

Operations in Arithmetic

Bases, Exponents, and Powers

Order of Operations

Properties of Operations

Properties of a Field

 

Problem Solving

General Technique for Solving Problems

Guessing and Checking

Using a Simpler Related Problem

Working Backward

Discovering Patterns

Drawing Pictures and Diagrams

Making Lists and Charts

Choosing and Combining Strategies

 

Algebraic Expressions, Geometric Formulas, and Open Sentences

Translating Verbal Phrases Into Algebraic Language

Using Letters to Represent Variables

Algebraic Terms and Vocabulary

Evaluating Algebraic Expressions

Translating Verbal Sentences Into Formulas

Formulas for Perimeter and Area of Polygons

Formulas for Circumferences and Area of a Circle

Reasoning with Perimeter, Area, and Shaded Regions

Formulas for Volume of a Solid

Open Sentences and Solution Sets

 

Signed Numbers

The Opposite of a Directed Number

The Absolute Value of a Number

Addition of Signed Numbers

Subtraction of Signed Numbers

Multiplication of Signed Numbers

Division of Signed Numbers

Evaluation Algebraic Expressions Using Signed Numbers

Number Lines and Graphs Using Signed Numbers

 

 

Introduction to Solving Equations

Preparing to Solve an Equation

Solving Equations Using Addition

Solving Equations Using Multiplication

Solving Equations Using More Than One Operation

Writing Verbal Sentences as Equations

Using Equations to Solve Problems

Solving Percent Problems

More Practice in Solving Equations

 

Mathematical Reasoning

Sentences, Statements, and Truth Values

Negations and Symbols

Conjunctions

Disjunctions

Conditionals

Biconditionals

Inverses, Converses, and Contra positives

Drawing Conclusions

 

Operations With Algebraic Expressions

Adding Algebraic Expressions

Subtracting Algebraic Expressions

Multiplying Powers That Have the Same Base

Multiplying By a Monomial

Multiplying Polynomials

Dividing Powers That Have the Same Base

Powers With Zero and negative Exponents

Using Scientific Notation

Dividing By a Monomial

 

First-Degree Equations and Inequalities in One Variable

Simplifying Each Side of an Equation Before Solving

Solving Equations That Have the Variable in Both Members

Consecutive-Integer problems

Solving for a Variable in a Formula

Perimeter Problems

Solving for a Variable in Terms of Another Variable

Transforming Formulas

Motion Problems

Coin Problems

Age Problems

Properties of Inequalities

Finding and Graphing the Solution Set of an Inequality

Using Inequalities to Solve Problems

   

Angle Measure in Geometry

Points, Lines, and Planes

Angles, Angle Measures, and Perpendicularity

Pairs of Angles

Angles and Parallel Lines

Triangles and Angles

Triangles with Congruent Angles

 

Congruence and Transformations

Geometric Figures

Congruent Triangles

Quadrilaterals

Line Reflections and Line Symmetry

Point Reflections and Point Symmetry

Translations

Rotations

Compositions of Transformations

 

Ratio and Proportion

Ratio

Using a Ratio to Express a Rate

Using Ratio in Dimensional Analysis

Verbal Problems Involving Ratio

Proportion

Direct Variation

Percent and Percentage Problems

Error in Measurement

Similar Polygons

Similar Triangles

Dilations

Scale Drawing

Ratio of Perimeters and Ratio of Areas of Similar Polygons

 

Probability

Empirical Probability

Theoretical Probability

Evaluating Simple Probabilities

The Probability of (A and B)

The Probability of (A or B)

The Probability of (not A); Probability as a Sum

 

The Counting Principle, Permutations, and Combinations

The Counting Principle and Sample Spaces

Probabilities and the Counting Principle; Predicting Outcomes

Probabilities with Two or More Activities

Permutations

More about Permutations

Probability Without Replacement; Probability with Replacement

Combinations

Probability and Combinations

A Mixture of Probability Problems

 

 

.

 

Math B Topics

*Graphing calculator used throughout the course

 

Rational Numbers

                          Number Line & Sets of Numbers

                                    Quantifiers & Negated Statements

                                    Math Systems & Groups

                                    Rational Number Properties

                                    First Degree Equations & Inequalitites

                                    Ratio & Proportion

                                    Operations w/Polynomials

 

Rational Expressions

                          Reduce Rational Expressions

                                    Add, Subtract, Mult., & Divide Expressions

                                    Operations w/Complex Numbers                                 

                                    Solve Fractional Equations

 

Real Numbers

                          Graph Solution Sets

                                    Absolute-Value Equations & Inequalities

                                    Roots & Radicals

                                    Simplifying Radicals

                                    Add, Subtract, Mult., & Divide Radicals

                                    Rationalize Denominators w/Radicals

                                    Quadratic Formula & Quadratic Equations

                                    Solving Radical Equations

 

Circle Geometry

                          Arcs, Angles, & Chords

                                    Central & Inscribed Angles

                                    Tangents & Secants

                                   

Relations & F unctions

                          Differentiate Relations & Functions

                                    Relate Graphs to Real Life Situations

                                    Function Notation

                                    Types of Functions

                                    Parabola, Circle, Ellipse, Hyperbola

                                    Direct Variation and Inverse Variation

 

Transformation Geometry & Functions

                          Line Reflection

                                    Translation

                                    Dilation

                                    Rotation

                                    Point & Line Symmetry

                                    Compositions

                                    Direct and Indirect Isometries

 

Trigonometric Functions

                          Right Triangle Characteristics

                                    Angles as Rotations

                                    Unit Circle and Degree-Radian Conversion

                                    Sine, Cosine, Tangent, & Reciprocal Functions

                                    Find Angles From Given Trig. Value

                                    Find Reference Angles & Coterminal Angles

                                    Pythagorean Identities & Proofs

                                    Find Other Trig. Functions From Given Info.

 

Trigonometric Graphs

                          Identify and Sketch Sin, Cos , & Tangent Graphs

                                    Amplitude, Frequency, and Period

                                    Maximums & Minimums

                                    Line Reflections and Translations of Graphs

 

Exponential Functions

                          Laws of Exponents

                                    Scientific Notation

                                    Fractional, Negative, and Zero Exponents

                                    Graph Exponential Functions

                                    Solve Word Problems

                                    Solve Exponential Equations

 

Logarithmic Functions

                          Rewrite Log Form Into Exponential Form

                                    Logarithmic Form of an Equation

                                    Exponent/Power Rule of Logarithms

                                    Solve Logarithmic Equations

 

Trigonometric Applications

                         Use Law of Sines & Law of Cosines in Word Problems

                                    Find Components of Triangles

                                    Area of a Triangle

                                    Ambiguous Case

                                    Forces & Vectors

 

Complex Numbers

                          Simplify Complex Numbers Using Imaginary Unit

                                    Add, Subt., Mult., & Divide Complex Numbers

                                    Solve Quad. Equations w/Imaginary Roots

                                  &n