Math III Pacing Guide

Transcription

1 Unit 1 - Geometry Days CCSS Pearson Alignment Objective 1 G-CO.1 G-CO.9 2 G-CO.9 G-CO.12 1 G-CO.10 G-SRT.4 G.1.2 Points, lines and planes G.1.3 Measuring segments G.1.4 Measuring angles G.1.6 Basic constructions G.2.6 Proving Angles Congruent G.3.1 Lines and angles G.3.2 Properties of Parallel Lines G.3.5 Parallel Lines and Triangles G.5.1 Midsegments of Triangles G.5.2 Perpendicular and Angle Bisectors G.5.4 Medians and Altitudes Students will learn the correct notation for points, segments, sides of polygons and angles. Students will learn how to identify angle pair relationships and parallel/perpendicular lines. Students will examine relationships between angles when two parallel lines are cut by a transversal and construct simple proofs of these angle pair relationships using definitions of vertical angles and linear pairs. [include constructions of two parallel lines] Students will find missing angles and sides of triangles using definitions of isosceles triangles, perpendicular bisectors, triangle sum theorem, midsegments and medians 2 G-CO.11 G.6.1 The Polygon Angle-Sum Theorems G.6.2 Properties of Parallelograms G.6.3 Proving that a Quadrilateral is a Parallelogram G.6.4 Properties of Rhombuses, Rectangles and Squares G.6.5 Conditions for Rhombuses, Rectangles and Squares Students will use properties of parallelograms to find missing sides and angles of figures. Students will use the Pythagorean Theorem to prove diagonals of rectangles are congruent 3 G-SRT.5 G.4.2 Triangle Congruence SSS and SAS G.4.3 Triangle Congruence ASA and AAS Students will find missing sides and angles of congruent figures.

2 G.4.5 Isosceles and Equilateral Triangles G.4.6 Congruence in Right Triangles G.4.7 Congruence in Overlapping Triangles 1 G-GPE.1 G10.6 Circles and arcs Students will derive the equation of a circle using Pythagorean Theorem. 1 G-CO.1 G-C.3 G.12.6 Locus: A Set of Points Students will define a circle as a locus of points equidistant from a given point and use the distance formula to prove a figure is a circle. Students will identify and name radii, diameters, angles, arcs, and construct polygons inscribed in circles and circles inscribed in polygons. 1 G-C.5 G.10.7 Areas of Circles and Sectors Students will derive the formula for area of sectors and arc length. 2 Summative assessment

3 Unit 2 - Trigonometry Days CCSS Pearson Alignment Objective 1 G SRT.4 G.7.3 Proving Triangles Similar G.7.5 Proportions in Triangles Students will prove that a line parallel to one side of triangle divides the other two proportionally. Prove that the altitude of a right triangle drawn to the hypotenuse will produce 3 similar right triangles. Use the Pythagorean Theorem to prove 1 G-SRT.2 G-SRT.3 G.8.1 The Pythagorean Theorem and its Converse Students will prove figures are similar by showing their sides have the same ratio (find the scale factor) and corresponding angles are congruent. Include similar solids. Students will use GSP to prove the AA theorem of triangle similarity 2 G-SRT.5 G.8.2 Special Right Triangles G.8.3 Trigonometry 1 F-TF.1 A Angles and the Unit Circle A Radian Measure Students will use similarity of right triangles and trig ratios to find missing sides and angles of right triangles. Students will discover rules of special right triangles Students will develop an understanding of radian measure and how it is related to the intercepted arc created by a central angle. Use the fact that 360 o = 2π. Use special right triangles to fill in a unit circle 3 F-TF.2 T.TF.5 A The Sine Function A The Cosine Function A The Tangent Function A Translating Sine and Cosine Functions Students will use the unit circle to explain the horizontal/vertical distance of a rider on a Ferris wheel and graph the resulting points. Understand the relationship between the points on the unit circle and the graph of sine and cosine 1 T-TF.8 A Trigonometric Identities Students will prove trig identities including sin 2 + cos 2 = 1

4 Unit 3 Key Features of Functions Days CCSS Pearson Alignment Objective 3 A.REI.1 A.CED.4 F.IF.1 F.IF.4 A2.1.4 Solving Equations A2.2.1 Relations and Functions A2.2.3 Linear Functions and Slope- Intercept Form A2.2.5 Using Linear Models Students will solve linear and simple quadratic equations by hand and justify each step using a property from algebra, solve literal equations. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 1 F.BF.3 A2.2.6 Families of functions A2.2.7 Absolute value functions and graphs 2 A.CED.3 A2.2.8 Two-Variable Inequalities A2.3.1 Solving Systems Using Tables and Graphs A2.3.2 Solving Systems Algebraically A2.3.3 Systems of Inequalities A2.3.4 Linear Programming Students will identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Students will use linear programming, restrictions and constraints of inequalities and equations 2 F.BF.1 A2.6.6 Function Operations Students will write a function that describes a relationship

5 F.BF.4a A2.6.7 Inverse Relations and Functions between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x 3 or f(x) = (x+1)/(x 1) for x 1. 3 F.BF.2 A2.9.1 Mathematical patterns A2.9.2 Arithmetic sequences A2.9.3 Geometric sequences Students will write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 2 Summative assessment

6 Unit 4 Quadratics Days CCSS Pearson Alignment Objective 2 F.BF.3 A.CED.1 F.IF.4 F.IF.6 F.IF.8 F.IF.9 A2.4.1 Quadratic Functions and Transformations A2.4.2 Standard Form of a Quadratic Functions Students will identify and graph quadratic functions. Students will graph quadratic functions written in standard form. 1 F.IF.4 F.IF.5 4 A.SSE.2 A.SSE.3 A.CED.1 A.REI.4 A.APR.3 1 N.CN.1 N.CN.2 N.CN.7 N.CN.8 3 A.CED.3 A.REI.7 A.REI.11 G.GPE.1 G.GPE.2 A2.4.3 Modeling with Quadratic Functions A2.4.4 Factoring Quadratic Expressions A2.4.5 Quadratic Equations A2.4.6 Completing the Square A2.4.7 The Quadratic Formula A2.4.8 Complex Numbers A Parabolas A Circles A Translating Conic Sections A2.4.9 (Supplement more non-linear systems) Quadratic Systems Students will model data with quadratic functions Students will solve quadratic functions in a variety of ways including factoring, graphing, completing the square, and using the quadratic formula Students will identify, graph, and perform operations with complex numbers. Find solutions of quadratic equations that involve complex numbers. Students will write and graph the equation of a circle Find the center and radius of a circle and use them to graph the circle Solve and graph non-linear systems of equations Find the focus and directrix of parabolas and write equation of parabola with leading coefficient 1 using focus and directrix

7 It would be ideal to complete Unit 4 before the midterm

8 Unit 5 Polynomial Functions Day CCSS Pearson Alignment Objective 2 A.APR.1 A.APR.4 2 A.APR.3 N.CN.1 N.CN.9 A2.5.1 Polynomial functions A2.5.2 Polynomials, linear factors and zeros A2.5.3 Solving polynomial equations A2.5.4 Dividing polynomials A2.5.5 Theorems about Roots of Polynomial Equations A2.5.6 The Fundamental Theorem of Algebra Students will add, subtract, and multiply polynomials prove polynomial identities Key features of the graphs of polynomial functions identify zeroes and show end behavior Students will solve polynomial function by factoring, use the degree of the polynomial to find number of solutions and determine the number of imaginary solutions from the graph FTA a polynomial with degree n has n roots Solve polynomial functions by graphing synthetic division of polynomials to find zeroes. rewrite rations expressions using long division a q = r/b 1 F.IF.4 F.IF.5 F.IF Polynomial Models in the Real World Students will compare properties of two functions each represented in a different way given a context, write equations in two variables that represent the relationship

9 Unit 6 Rational and Radical Functions Day CCSS Pearson Alignment Objective 3 A.SSE.2 A.REI.1 A.REI.2 A.REI.11 2 F.IF.7 F.BF.1 A.SSE.1 A.SSE.2 2 A.APR.7 N.RN.3 A2.6.1 Roots and Radical Expressions A2.6.2 Multiplying and Dividing Radical Expressions A2.6.5 Solving Square Root and Other Radical Equations A2.8.3 Rational Functions and Their Graphs A Rational Expressions A2.8.5 Adding and Subtracting Rational Expressions A2.8.6 Solving Rational Equations Students will explain each step in solving Solve and find extraneous solutions Explain why the x-coordinate of the points where f(x) intersects g(x) are the solutions Students will identify properties of rational functions and graph Simplify, multiply, and divide rational expressions Students will add, subtract, multiply, and divide rational expressions as well as adding and multiplying rational numbers

10 Unit 7 Exponential and Logarithmic Day CCSS Pearson Alignment Objective 2 A.CED.2 A.SSE.1 F.IF.7 F.IF.8 F.BF.1 F.BF.4 A2.7.1 Exploring Exponential Models A2.7.2 Properties of Exponential Functions A2.7.3 Logarithmic Functions and Inverses Students will interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. 1 F.LE.4 A2.7.4 Properties of Logarithms Students will use properties of logarithms 2 F.LE.3 F.LE.4 A2.7.5 Exponential and logarithmic equations A2.7.6 Natural logarithms Students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically For exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology

11 Unit 8 Statistics Day CCSS Pearson Alignment Objective 1 S.IC.1 S-IC.6 2 S.IC.3 S.IC.4 G13.5 Probability models G.13.6 Conditional Probability Formulas G.13.7 Modeling Randomness A Probability Models A Standard Deviation A Samples and Surveys Students will understand statistics as a process for making inferences about population parameters based on a random sample from that population Students will recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling 1 S-ID.4 A Normal Distributions Students will use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal cure Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant