eMathInstruction

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United States - New York - Red Hook
eMathInstruction
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Tools for Teaching Math in the 21st Century
 
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Linear functions are reviewed from Common Core Algebra I in this 7 lesson unit. The slope-intercept and point-slope forms of a line are both used and applied in linear modeling problems. Inverse and piecewise linear functions are developed. Finally,
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Polynomial functions are explored in the beginning of this 14 lesson unit. Students use factors of polynomials as well as their long-run behavior to sketch graphs of polynomial functions. Polynomial identities are used to justify algebraic and
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Exponential and logarithmic functions are both thoroughly explored in this 14 lesson unit. The unit begins with a development of rational exponents. Exponential functions are then introduced and their equations are found from any two arbitrary
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Arithmetic, geometric, and recursively defined sequences are all reviewed from Common Core Algebra I in this 6 lesson unit. Series are then introduced, with the help of summation (sigma) notation. The structure of both arithmetic and geometric
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This 13 lesson unit explores one of the most important types of functions, linear. It builds from proportional relationships and equations of lines to linear modeling. The fundamental concept of a graph showing solutions to equations is emphasized.
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The 7 lessons in this unit lay the groundwork for using functions to explore Algebra II throughout the course. Functions are explored, using standard notation, in algebraic, graphical, and tabular forms. Function composition, domain and range, and
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The major transformations of functions are explored in this 5 lesson unit, using algebraic and graphical examples. In each case the affect on the graph of f(x) by the transformations f(x)+k, f(x+k), kf(x), and f(kx) is investigated for various
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We start this 9 lesson unit with review of major descriptive statistics. The normal distribution and normally distributed populations are explored and probabilities are explored using graphs, tables, and the calculator. Inferential statistics are
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This 8 lesson unit concentrates on the solution to linear systems of equations. The fundamental notion of solution to a system is introduced by solving the systems graphically. A review of solving systems of substitution is included. The method
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Quadratic functions and their ties to polynomial algebra are thoroughly explored in this 11 lesson unit. All major types of factoring techniques are developed, including factoring by grouping. The Zero Product Law is reviewed and used to solve
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This 13 lesson unit builds a basis for linear equation and inequality solving. The basic concept of solutions to equations and inequalities is stressed along with fluency exercises in solving linear equations and inequalities. Modeling with linear
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Quadratic functions and their graphs are extensively developed in the early portion of this 7 lesson unit. The shifting of functions is then introduced and gives a perfect vehicle for introducing the process of Completing the Square. The zeroes of a
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Functions serve as the cornerstone of this course. In this 7 lesson unit, the basic notion of a function is introduced in algebraic, graphical, and tabular forms. Various functions and modeling problems are explored and the concepts of domain and
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Fundamental exponent laws are developed early in this 9 lesson unit and give rise to an exploration of basic exponential functions. Percent calculations are then used to develop increasing and decreasing exponential models. A comparison between
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Square root functions and their graphs are introduced in this 8 lesson unit and allow for an exploration of the properties of rational versus irrational numbers. Students then solve quadratic equations using inverse operations and completing the
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Standard statistical displays of data are reviewed at the beginning of the 10 lesson unit. Box plots are used to compare data sets and emphasize use of the quartiles and interquartile range. Measures of central tendency and dispersion, such as mean
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In this 8 lesson unit, the square root function is explored along with the algebra of solving square root equations, including those with extraneous roots. Rational exponents are covered and the properties of exponents are used to help rewrite
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In this 11 lesson unit the sine and cosine functions are extended from right triangle trigonometry by the use of the unit circle. Angles are specified in both degrees and radians throughout the unit. The transformations of the sine and cosine
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Probability is developed in this 6 lesson unit by using sets, their intersections, and their unions. Two way frequency charts are extensively used to introduce the concept of conditional probabilities. The multiplication of probabilities is used to
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Eleven lessons that introduce the fundamental concepts needed for Common Core Algebra I. Lesson include variables, expressions, order of operations, real number properties, and equivalence. Great lessons to start the year in Common Core Algebra
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TEACHING EXPERIENCE

16 years as a teacher in a public high school in New York State. Taught courses as varied as 2-year Algebra, Geometry, Algebra 2 with Trigonometry, precalculus, and Calculus. Has served as department coordinator since 2011.

MY TEACHING STYLE

Mostly the Socratic direct instruction method.

HONORS/AWARDS/SHINING TEACHER MOMENT

National Board Certified in 7-12 Math

MY OWN EDUCATIONAL HISTORY

BS in Engineering, University of Illinois, MS in Engineering, Cornell University, MS in Math Education, Syracuse University

ADDITIONAL BIOGRAPHICAL INFORMATION

Kirk Weiler is a teacher and the department chair of the mathematics department at Arlington High School in New York's Hudson Valley. He is the founder of eMathInstruction and lives with his wife and two children in Red Hook, NY

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