Math 3 Table of Contents Revised 05/2015 Unit 1 – Inverse Functions and Logarithms Unit 2 – Circles and Trigonometry Unit 3 – Polynomial Functions Unit 4 – Rational and Radical Functions Unit 5 – Function Families Unit 6 – Inferences and Conclusions from Data Unit 7 – Arithmetic and Geometric Series Unit 8 – Mathematical Modeling/Geometric Constructions/Topics Not Covered Elsewhere Unit 1 – Inverse Functions and Logarithms 6-1 Inverse Functions I can demonstrate conditions that guarantee existence of an inverse function for a given function I can develop and use strategies for recognizing invertible functions from tables and graphs I can develop and use strategies for finding rules of inverse functions 6-2 Compound Interest and the Number e I can solve problems involving compound interest, including continuous compounding 6-3 Introduction to Logarithms I can recognize what is meant by “taking the logarithm” of a real number. I understand the connection between logarithmic functions and exponential functions and can use this understanding to solve problems. 6-4 Solving Exponential Equations I can solve for exponents using logarithms. 6-5 Properties of Logarithms I can use properties of logarithms and exponents to write algebraic expressions in equivalent forms and solve equations involving logs and exponents. Common Assessment Do we want to add function composition somewhere in here with inverse functions? It is not a standard for Math 1-3, but should we cover it anyway for ACT/SAT purposes? Or leave it until Math 4? Unit 2 – Circles and Trigonometry 5-1 Circles Algebraically I can identify/describe relationships among inscribed angles, arc measure, central angles, radii, chords and tangent lines. I can use knowledge of circles to solve problems 5-2 Writing Equations of a Circles I can write the equation of a circle given the center and a point on the circle I can determine the center and radius of a circle from an equation I can use knowledge of circles to solve problems 5-3 Unit Circle Exact Values (Degrees) I can use sine and cosine functions to describe rotations of circular functions I can use degree measures to measure angles and rotations I can evaluate exact values for sine, cosine, and tangent around the unit circle 5-4 Unit Circle Exact Values (Radians) I can use sine and cosine functions to describe rotations of circular functions I can use degree and radian measures to measure angles and rotations I can evaluate exact values for sine, cosine, and tangent around the unit circle 5-5 Solving for Primary Values and the Pythagorean Identity, 0 2 I can use the unit circle to solve for primary value solutions of simple trigonometric equations I can use the Pythagorean Identity to solve problems Common Assessment Unit 3 – Polynomial Functions 3-1 Quadratic Functions Revisited (SHORTEN!!) I can use my knowledge of quadratics from previous courses to solve problems 3-2 Zeroes, Factors, and End Behavior of Polynomials I understand the relationship between standard and factored forms of polynomials 3-3 Arithmetic with Polynomials I can use the definitions and important properties of arithmetic operations, including function composition, in order to combine functions 3-4 Polynomial Division & The Remainder Theorem I can extend the relationship between standard and factored forms of polynomials I can perform and interpret the results of polynomial division 3-5 Synthetic Division I can extend the relationship between standard and factored forms of polynomials I can perform and interpret the results of polynomial division and synthetic division 3-6 Complex Roots and Depressing Polynomials I can depress polynomials using polynomial division to find all zeroes (real and complex) Common Assessment Unit 4 – Rational and Radical Functions 4-1 Introduction to Rational Functions I can interpret expressions for rules of rational functions that model problem conditions 4-2 The Connection Between Polynomial Division and Rational Functions 4-3 Solving Rational Equations & Extraneous Solutions 4-4 Solving Radical Equations & Extraneous Solutions ** Honors add arithmetic with Rational Functions Common Assessment Unit 5 – Function Families 2-1 Function Family Review – Linear, Exponential, and Quadratic I can review and extend properties linear, exponential, and quadratic functions and their uses in mathematical modeling I can solve problems involving linear, exponential, and quadratic function families 2-2 Parent Functions I understand the basic function families and their important characteristics 5-6 Graphing Trigonometric Functions I can graph the parent functions for sine, cosine and tangent 2-3 Vertical Translations I can transform functions through vertical translations, both graphically and algebraically I can apply knowledge of vertical translations to problem situations 2-4 Reflections Across the X-Axis I can transform functions through vertical translation and vertical reflections both graphically and algebraically I can apply knowledge of vertical translations and vertical reflections to problem situations 2-5 Horizontal Translations I can transform functions through horizontal translations, vertical translation, and vertical reflections both graphically and algebraically I can apply knowledge of horizontal translations, vertical translations, and vertical reflections to problem situations 2-6 Vertical Stretches & Compressions I can transform functions through horizontal translations, vertical translation, vertical reflections, and vertical stretches/compressions both graphically and algebraically I can apply knowledge of horizontal translations, vertical translations, vertical reflections, and vertical stretches/compressions to problem situations 2-7 Horizontal Stretches and Compressions I can transform functions through horizontal translations, vertical translation, vertical reflections, and vertical and horizontal stretches/compressions both graphically and algebraically I can apply knowledge of horizontal translations, vertical translations, vertical reflections, and vertical and horizontal stretches/compressions to problem situations 5-7 Transformations of Trigonometric Functions I can define sine and cosine as functions of real numbers and analyze the resulting periodic graphs I can use the sine and cosine functions to model periodic patterns of change in various physical phenomena 2-8 Even and Odd Functions I can identify graphically and prove algebraically whether a function is even or odd Common Assessment Unit 6 – Inferences and Conclusions from Data 1-1 A Review of Data Analysis I can summarize, represent, and interpret data on a single variable 1-2 The Design of Experiments I can explain the characteristics of a well-designed experiment I can recognize and explain subject, evaluator, and double blind experiments 1-3 Simulations & Statistical Significance I can interpret a sampling distribution in order to decide if data provides statistically significant evidence to support the hypothesis Resources: http://serc.carleton.edu/sp/cause/datasim/examples/cokepepsi.html 1-4 Normal Distributions I can describe the characteristics of a normal distribution I can interpret the mean and standard deviation of a normal distribution 1-5 Standardized Values and Percentiles I can find and interpret standardized values I can use the standard normal distribution to find probabilities and percentiles 1-6 Estimating the Mean & Finding Confidence Intervals I can estimate the mean of a population from a simulation I understand the effect of sample size on how well a sample represents the population I can estimate a confidence interval for the mean of a population from a simulation Resources: http://serc.carleton.edu/sp/cause/datasim/examples/reeses.html http://www.rossmanchance.com/applets/Reeses/ReesesPieces.html http://www.rossmanchance.com/applets/JavaHelp.html http://learnzillion.com/lessons/3193-approximate-a-confidence-interval-for-a-population-proportion http://www.ixl.com/math/grade-6/identify-representative-random-and-biased-samples (use the last site for practice and/or quiz questions) 1-7 Statistical Studies & Sampling I can distinguish between the three types of studies - sample surveys, experiments, and observational studies - and understand what inference can be made from each I can identify random versus biased sampling and understand what inferences can be made based on how a sample was taken Resources: http://www.ck12.org/na/Random-and-Biased-Sampling-in-a-Population---7.SP.1,21/lesson/user%3Ac2ZveDJAb3N3ZWdvLm9yZw../Random-and-Biased-Sampling-in-a-Population---7.SP.1%252C2/ ** Honors could add “use probability to evaluate outcomes of decisions” (Math 3 text U4 L3) Common Project/Performance Assessment?? Common Assessment Unit 7 – Arithmetic and Geometric Series 7-1 Sequences revisited 7-2 Arithmetic Series Activity similar to U7 L1 I2 in Math 3 7-3 Geometric Series Activity similar to U7 L1 I2 in Math 3 Common Project/Performance Assessment?? Common Assessment Unit 8 – Mathematical Modeling/Geometric Constructions/Topics Not Covered Elsewhere Topics not covered elsewhere: Finding equations of parallel and perpendicular lines Linear Programming and Linear Programming-type problems involving non-linear functions – both by hand and using technology Modeling problems (both algebraic and geometric) involving all types of functions/shapes – for functions, include interpreting average rate when appropriate “Make formal geometric constructions with a variety of tools and methods” (M1 U5 G.CO.12 – see released sample task) “Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle” (M1 U5 G.CO.13) Comparing properties of two different functions represented in different ways (table vs. graph) “Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects” (U4 G.GMD.4) “Apply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTUs per cubic foot)” (U4 G.MG.2)

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