Math 3 SSE. SSE.b SSE.2 REI. F-IF.4 F-BF. Overarching Standards for Math 3 Interpret expressions that represent a quantity in terms of its context. Interpret expressions composed of multiple parts by viewing one or more of their parts as a single entity to give meaning in terms of a context. Use the structure of an expression to identify ways to write equivalent expressions. Justify a solution method for equations and explain each step of the solving process using mathematical reasoning. Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities to include periodicity and discontinuities. Write a function that describes a relationship between two quantities. Course Description Multiple strategies, including variations on common procedures and procedures using different representations, are needed to solve problems within mathematics and within other contexts. At all levels, students generalize, model, and analyze situations that are purely mathematical or ones that arise in real-world phenomena. (NCTM 204) High school students extend their ability to use and see structure in symbolic expressions as they create and reason with equations, inequalities, and systems (cf. Kieran 2007c). In Math 3, students extend their study of algebra and functions to new families of functions including logarithmic, polynomial, rational, and trigonometric functions. Math 3 also includes a geometric emphasis on circles and their properties. Probability rules learned in previous courses are extended to the statistics of making inferences and justifying conclusions. Each topic within the algebra and functions strands should be experienced as an integration of concepts, procedures, and applications. Concepts such as variable and equivalence and procedures such as solving equations and inequalities are equally important. The following list should be considered overarching standards, continually developed each unit. Unit 0 Setting Up Classroom Culture Week of Inspirational Math Activities Materials & YouCubed Website (You will need to create a free account.) Grouping & Cooperative & Discourse & Growth Mindset Materials 206-207 Math 3
Quarter ctions and their Develop and extend the concept of inverse functions using tables, graphs, equations, and written descriptions of functions. Verifying that two functions are inverses. 2 Logarithmic ctions Evaluate and compare logarithmic expressions. Graph logarithmic functions with transformations. Develop understanding of log properties using transformations. Use log properties to evaluate expressions. with exponential and logarithmic functions and equations. Quarter 2 3 Polynomial ctions 4 Rational Expressions and ctions 5 metric Figures Compare graphs, growth rates, and end behavior of polynomial functions and expressions. Use graphical representations of arithmetic operations on polynomial functions to build other polynomial functions. Apply the damental Theorem of Algebra and Remainder Theorem to factor and solve polynomial functions and equations. Explore rational expressions and functions through connections to rational numbers and improper fractions. with rational functions and equations. Analyze characteristics of various families of functions to identify characteristics of rational functions. Identify the end behavior of rational functions. Graph rational functions using their features. Solve rational equations. Learn the structures and reasoning of formal proofs through theorems about triangle angle sum, lines and angles, triangles and parallelograms. Prove properties of triangles and parallelograms. Examine parallelism from a transformational perspective. Quarter 3 6 : A metric Perspective 7 ing with metry 8 onometric ctions Develop and justify formulas for perimeter, area, circumference. Use proportional reasoning to calculate arc length and area of sectors and other circular relationships. Develop concept of radian as ratio of arc length to radius. Solve problems using geometric modeling. Visualize two dimensional cross sections of three -dimensional objects and solids of revolution. Approximate volumes of solids of revolution. Understanding circular trigonometry by using angles of rotation, reference angles, right angle trigonometry, unit circle and the proportionality and symmetry of a circle to extend to radian measure, arc length and trigonometric functions. Graph trigonometric functions, identify horizontal transformations and other graphical characteristics, use them to model periodic behavior Quarter 4 9 ing with ctions Examine transformations of familiar functions defined by tables graphs, or equations by arithmetic combinations. 0 Statistics Compare and contrast methods of sampling, surveys, observational studies, and experiments. Use data from a survey to estimate population mean or proportion. Use simulations to develop a margin of error and decide if differences between parameters are significant. Use data from randomized experiment to compare treatments. Use probabilities to make fair decisions. Analyze decisions and strategies using probability concepts. 206-207 Math 3 2
N-CN.9 SSE.a SSE.3c APR.2 APR.3 APR.6 APR.7 CED. Number and Quantity Use the damental Theorem of Algebra to determine the number and potential types of solutions for polynomial functions. Logs Algebra Identify and interpret parts of a piecewise, absolute value, polynomial, exponential and rational expressions including terms, factors, coefficients, and exponents. Logs Write an equivalent form of an exponential expression by using the property of exponents to transform expressions to reveal rates based on different intervals of the domain. Understand and apply the Remainder Theorem. Understand the relationship among factors of a polynomial expression, the solutions of a polynomial equation and the zeros of a polynomial function. Logs Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q (x) Units 2 3 4 5 6 7 8 9 0 + r(x) b(x), where a(x), b(x), q(x) and r(x) are polynomials with the degree of r(x) less than the degree of b(x). Polys Rational Figures Polys Rational Figures Logs Polys Rational Figures Logs Logs Polys Understand the similarities between arithmetic with rational expressions and arithmetic with rational numbers. a. Add and subtract two rational expressions, a (x) and b (x), where the denominators of both a (x) and b (x) are linear expressions. b. Multiply and divide two rational expressions. Logs Polys Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically. Logs Polys Polys Rational Figures Polys Rational Figures Rational Figures Rational Figures Rational Figures CED.2 CED.3 REI.2 REI. Create and graph equations in two variables to represent absolute value, polynomial, exponential, and rational relationships between quantities Create systems of equations and/or inequalities to model situations in context. Solve and interpret one variable rational equations arising from a context, and explain how extraneous solutions may be produced. Extend an understanding that the x-coordinates of the points where the graphs of two equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using a graphing technology or successive approximations with a table of values. ctions Logs Polys Rational Figures Logs Polys Rational Figures Logs Polys Rational Figures Logs Polys Rational Figures 206-207 Math 3 3
F-IF. F-IF.2 F-IF.7 F-IF.9 F-BF.a F-BF.b F-BF.3 F-BF.4 F-BF.4ab F-BF.5 F-LE.3 F-LE.4 F-TF. Extend the concept of a function by recognizing that trigonometric ratios are functions of angle measure. Logs Polys Rational Figures Use function notation to evaluate piecewise defined functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table). Build a new function, in terms of a context, by combining standard function types using arithmetic operations. Extend an understanding of the effects on the graphical and tabular representations of a function when replacing f(x) with kf(x), f(x) + k, f(x + k) to include f(kx) for specific values of (both positive and negative). Build an inverse function to: A. Determine if an inverse function exists by analyzing tables, graphs, and equations. B. Solve an equation of the form for a linear, quadratic, and exponential function that has an inverse and write an expression for the inverse. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving exponential equations. Compare the end behavior of functions using their rates of change over intervals of the same length to show that a quantity increasing exponentially eventually exceeds a quantity Logs Polys Rational Figures Logs Logs Logs Polys Polys Rational Figures Rational Figures Polys Rational Figures Logs Polys Rational Figures Logs Polys Rational Figures Logs Polys Rational Figures Logs Polys Rational Figures Polys Rational Figures increasing as a polynomial function. Logs Use logarithms to express the solution to ab ct =d where a, c, and d are numbers and evaluate the logarithm using technology. Understand radian measure of an angle as: The ratio of the length of an arc on a circle subtended by the angle to its radius. A dimensionless measure of length defined by the quotient of arc length and radius that is a real number. The domain for trigonometric functions. Logs Polys Rational Figures Logs Polys Rational Figures 206-207 Math 3 4
F-TF.2 F-TF.5 G-CO.0 G-CO. G-CO.4 G-C.2 G-C.5 G-GPE. G-GMD.3 G-GMD.4 G-MG. Build an understanding of trigonometric functions by using tables, graphs and technology to represent the cosine and sine functions. Interpret the sine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its y coordinate. Interpret the cosine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its x coordinate. Logs Polys Rational Figures Use technology to investigate the parameters, a, b, and h of a sine function, f(x) = asin(bx) + h to represent periodic phenomena and interpret key features in terms of a context. Logs Polys Rational Figures metry Verify experimentally properties of the centers of triangles (centroid, incenter, and circumcenter). Logs Polys Rational Prove theorems about parallelograms. Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Logs Polys Rational Apply properties, definitions, and theorems of two- dimensional figures to prove geometric theorems and solve problems. Logs Polys Rational Understand and apply theorems about circles. Understand and apply theorems about relationships with angles and circles, including central, inscribed and circumscribed angles. Understand and apply theorems about relationships with line segments and circles including, radii, diameter, secants, tangents and chords. Logs Polys Rational Figures Using similarity, demonstrate that the length of an arc, s, for a given central angle is proportional to the radius, r, of the circle. Define radian measure of the central angle as the ratio of the length of the arc to the radius of the circle, s/r. Find arc lengths and areas of sectors of circles. Logs Polys Rational Figures Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve Logs Polys Rational problems. Logs Polys Rational Figures Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects Figures Figures Figures Figures Logs Polys Rational Figures Apply geometric concepts in modeling situations Use geometric and algebraic concepts to solve problems in modeling situations: Use geometric shapes, their measures, and their properties, to model real-life objects. Use geometric formulas and algebraic functions to model relationships. Apply concepts of density based on area and volume to solve design and optimization problems. Logs Polys Rational Figures 206-207 Math 3 5
S-IC. S-IC.3 S-IC.4 S-IC.5 S-IC.6 Statistics Understand the process of making inferences about a population based on a random sample from that population. Logs Polys Rational Figures Recognize the purposes of and differences between sample surveys, experiments, and observational studies and understand how randomization should be used in each. Logs Polys Rational Figures Use simulation to understand how samples can be used to estimate a population mean or proportion and how to determine a margin of error for the estimate. Logs Polys Rational Figures Use simulation to determine whether observed differences between samples from two distinct populations indicate that the two populations are actually different in terms of a parameter of interest. Logs Polys Rational Figures Evaluate articles and websites that report data by identifying the source of the data, the design of the study, and the way the data are graphically displayed. Logs Polys Rational Figures 206-207 Math 3 6
Unit : Inverse ctions ~2 Total Days Suggested Resource Task Name Days F-IF.9 F-BF.4a F-BF.4b D MVP M2 4.5 What s Your Pace S MVP M2 4.6 Bernie s Bikes D MVP M3. Brutus Bites Back 2 S MVP M3.2 Flipping Ferraris 2 S MVP M3.3 Tracking the Tortoise 2 3 S MVP M3.4 Pulling a Rabbit Out of a Hat P MVP M3.5 Inverse Universe Task adjusted to fully address properties of invertible functions. F-IF.9 F-BF.4 F-BF.4a F-BF.4b Unit Standards ctions Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). Build an inverse function to: Determine if an inverse function exists by analyzing tables, graphs, and equations. Solve an equation of the form for a linear, quadratic, and exponential function that has an inverse and write an expression for the inverse. 206-207 Math 3 7
Unit 2: Logarithmic ctions ~6 Total Days 2 3 Suggested F- F- F- F- F- F- Resource Task Name Days CED. CED.2 SSE.a SSE.3c BF.3 IF.7 IF.9 BF.a BF.5 LE.4 D MVP M3 2. Log Logic S MVP M3 2.2 Falling Off A Log 2 S MVP M3 2.3 Chopping Logs 2 P MVP M3 2.4 Log Arithmetic P MVP M3 2.5 Powerful Tens D MVP M3 2.6 Compounding the Problem Can Two Transformations be S CPM 3..3 Equivalent? S MVP M3 2.7 Logs Go Viral 2 S MVP M3 2.8 Choose This, Not That P MVP M3 2.9 Don t Forget Your Login added to hit F.BF.3 Unit Standards Algebra CED. Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically. CED.2 Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities. SSE.a Identify and interpret parts of a piecewise, absolute value, polynomial, exponential and rational expressions including terms, factors, coefficients, and exponents. SSE.3c Write an equivalent form of an exponential expression by using the property of exponents to transform expressions to reveal rates based on different intervals of the domain. ctions F-BF.3 Extend an understanding of the effects on the graphical and tabular representations of a function when replacing f(x) with k f(x), f(x) + k, f(x + k ) to include f (kx) for specific values of (both positive and negative). F-IF.7 Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. F-IF.9 Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). F-BF.a Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table). F-BF.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving exponential equations. F-LE.4 Use logarithms to express the solution to ab ct = d where a, c, and d are numbers and evaluate the logarithm using technology. 206-207 Math 3 8
Unit 3: Polynomial ctions ~6 Total Days Resource D MVP M3 3. Task Name N- CN.9 Suggested Days SSE.a APR.2 APR.3 CED. CED.2 Scott s Macho March Madness 2 S MVP M3 3.2 Which is Greater P MVP M3 3.3 All About Behavior S MVP M3 3.4 Polynomial Connections 2 2 D MVP M3 3.5 The Expansion 2.5 S MVP M3 3.6 Seeing Structure.5 2 S MVP M3 3.7 Graphing All Poly s 3 2 P MVP M3 3.8 I Know, What do you Know? 2 Additional contextual problem included to address A.CED. and A.CED.2 2 Reduction of the number of graphs to cover F.BF.a more explicitly and add multiple representations 3 Last question reworded to more explicitly address N-CN.9, APR.2 F- IF.7 F- IF.9 F- BF.a F- LE.3 N-CN.9 SSE.a APR.2 APR.3 CED. CED.2 F-IF.7 F-IF.9 F-BF.a NC.M2.F-LE.3 Unit Standards Number and Quantity Use the damental Theorem of Algebra to determine the number and potential types of solutions for polynomial functions. Algebra Identify and interpret parts of a piecewise, absolute value, polynomial, exponential and rational expressions including terms, factors, coefficients, and exponents. Understand and apply the Remainder Theorem. Understand the relationship among factors of a polynomial expression, the solutions of a polynomial equation and the zeros of a polynomial function. Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically. Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities. ctions Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table). Compare the end behavior of functions using their rates of change over intervals of the same length to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a polynomial function. 206-207 Math 3 9
Unit 4: Rational ctions ~0 Total Days 2 Resource Task Name Suggested Days SSE.a APR.6 APR.7 CED. CED.2 D MVP M3 4. The Gift S MVP M3 4.2 All in the Family What Does it Mean to be D MVP M3 4.3 2 Rational? Rewriting Rational S MVP M3 4.4 2 Expressions CORE+ Cannery Designs & Concert P C 3 U 5 L 3 Venues REI.2 F- IF.7 F- IF.9 Rational ctions Unit Standards Algebra SSE.a Identify and interpret parts of a piecewise, absolute value, polynomial, exponential and rational expressions including terms, factors, coefficients, and exponents. APR.6 a(x) Rewrite simple rational expressions in different forms; write in the form q (x) r(x), where a (x), b (x), q (x), and r (x) are polynomials with the degree of r (x) less than the degree of b (x). b(x) + b(x) APR.7 CED. CED.2 REI.2 F-IF.7 F-IF.9 Understand the similarities between arithmetic with rational expressions and arithmetic with rational numbers. a. Add and subtract two rational expressions, a (x) and b (x), where the denominators of both a (x) and b (x) are linear expressions. b. Multiply and divide two rational expressions. Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically. Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities. Solve and interpret one variable rational equations arising from a context, and explain how extraneous solutions may be produced. ctions Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). 206-207 Math 3 0
Unit 5: metric Figures ~2 Total Days 2 Resource Task Name Suggested Days G-GPE. G-CO.0 G-CO. G-CO.4 D MVP M2 5.6 Parallelogram Conjectures and Proof 2 S MVP M2 5.7 Guess My Parallelogram P MVP M2 5.8 Centers of a Triangle 2 D MVP M2 8. Circling Triangles S MVP M2 8.2 Getting Centered 2 P MVP M2 8.3 Circle Challenges G-GPE. G-CO.0 G-CO. G-CO.4 Unit Standards metry Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Verify experimentally properties of the centers of triangles (centroid, incenter, and circumcenter). Prove theorems about parallelograms. Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Apply properties, definitions, and theorems of two- dimensional figures to prove geometric theorems and solve problems. 206-207 Math 3
Unit 6: - A metric Perspective ~6 Total Days 2 Suggested G.MG. Resource Task Name F-TF. G-C.2 G-C.5 G-GMD.3 Days G-CO.4 CORE+ C3 U6 I Tangents to a Circle 2 CORE+ C3 U6 I2 Chords, s, and Central Angles 2 CORE+ C3 U6 I3 Angles Inscribed in a Circle 2 D MVP M2 7.7 Pied 2 P MVP M2 7.8 Madison s Round Garden 2 S MVP M2 7.9 Rays and Radians P MVP M2 7.0 Sand Castles 2 F-TF. G-C.2 G-C.5 G-GMD.3 G-MG. G-CO.4 Unit Standards ctions Understand radian measure of an angle as: The ratio of the length of an arc on a circle subtended by the angle to its radius. A dimensionless measure of length defined by the quotient of arc length and radius that is a real number. The domain for trigonometric functions. metry Understand and apply theorems about circles. Understand and apply theorems about relationships with angles and circles, including central, inscribed and circumscribed angles. Understand and apply theorems about relationships with line segments and circles including, radii, diameter, secants, tangents and chords. Using similarity, demonstrate that the length of an arc, s, for a given central angle is proportional to the radius, r, of the circle. Define radian measure of the central angle as the ratio of the length of the arc to the radius of the circle, s/r. Find arc lengths and areas of sectors of circles. Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems. Apply geometric concepts in modeling situations Use geometric and algebraic concepts to solve problems in modeling situations: Use geometric shapes, their measures, and their properties, to model real-life objects. Use geometric formulas and algebraic functions to model relationships. Apply concepts of density based on area and volume to solve design and optimization problems. Apply properties, definitions, and theorems of two- dimensional figures to prove geometric theorems and solve problems. 206-207 Math 3 2
Unit 7: ing with metry ~0 Total Days 2 Resource Task Name Suggested Days G-GMD.4 G-MG. G-CO.4 D MVP M3 5. Any Way You Slice It D MVP M3 5.2 Any Way You Spin It S MVP M3 5.3 Take Another Spin 2 D MVP M3 5.4 Hard as Nails! 2 P MVP M3 5.5 Special Rights 2 G-GMD.4 G-MG. G-CO.4 Unit Standards metry Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects Apply geometric concepts in modeling situations Use geometric and algebraic concepts to solve problems in modeling situations: Use geometric shapes, their measures, and their properties, to model real-life objects. Use geometric formulas and algebraic functions to model relationships. Apply concepts of density based on area and volume to solve design and optimization problems. Apply properties, definitions, and theorems of two- dimensional figures to prove geometric theorems and solve problems. 206-207 Math 3 3
Unit 8: onometric ctions ~9 Total Days 2 Suggested F-IF. F-IF.7 F-IF.9 F-BF.3 F-TF. F-TF.2 F-TF.5 Resource Task Name Days D MVP M3 6. rge W. Ferris Day Off S MVP M3 6.2 Sine Language 2 S MVP M3 6.3 More Sine Language 2 S MVP M3 6.4 More Ferris Wheels 2 P MVP M3 6.5 Moving Shadows D MVP M3 6.6 Diggin It 2 S MVP M3 6.7 Staking It S MVP M3 6.8 Sine ing and Cosine ing It P MVP M3 6.9 Water Wheels 2 onometric ctions Unit Standards ctions F-IF. Extend the concept of a function by recognizing that trigonometric ratios are functions of angle measure. F-IF.7 Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. F-IF.9 Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). F-BF.3 Extend an understanding of the effects on the graphical and tabular representations of a function when replacing f(x) with k f(x), f(x) + k, f(x + k ) to include f (kx) for specific values of (both positive and negative). F-TF. F-TF.2 Understand radian measure of an angle as: The ratio of the length of an arc on a circle subtended by the angle to its radius. A dimensionless measure of length defined by the quotient of arc length and radius that is a real number. The domain for trigonometric functions. Build an understanding of trigonometric functions by using tables, graphs and technology to represent the cosine and sine functions. Interpret the sine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its y coordinate. Interpret the cosine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its x coordinate. 206-207 Math 3 4
F-TF.5 Use technology to investigate the parameters, a, b, and h of a sine function, f (x) = a sin (b x) + h to represent periodic phenomena and interpret key features in terms of a context. Unit 9: ing with ctions ~5 Total Days Suggested F- F- F- F- F- Resource Task Name Days CED. CED.2 CED.3 REI. IF.2 IF.7 IF.9 BF.b BF.3 D MVP M3 7. ction Family Reunion 3 S MVP M3 7.2 Imagineering 2 P MVP M3 7.3 The Bungee Jump Simulator P CHCCS ction Scrapbook and 8 Imagineering Project ing with ctions Unit Standards Algebra CED. Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically. CED.2 Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities. CED.3 Create systems of equations and/or inequalities to model situations in context. REI. Extend an understanding that the x-coordinates of the points where the graphs of two equations y = f (x) and y = g (x) intersect are the solutions of the equation f (x) = g (x) and approximate solutions using a graphing technology or successive approximations with a table of values. F-IF.2 F-IF.7 F-IF.9 F-BF.b ctions Use function notation to evaluate piecewise defined functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). Build a new function, in terms of a context, by combining standard function types using arithmetic operations. 206-207 Math 3 5
F-BF.3 Extend an understanding of the effects on the graphical and tabular representations of a function when replacing f(x) with k f(x), f(x) + k, f(x + k ) to include f (kx) for specific values of (both positive and negative). Unit 0: Statistics ~8 Total Days 2 3 Suggested S-IC. S-IC.3 S-IC.4 S-IC.5 S-IC.6 Resource Task Name Days D MVP M3 8.5 Would You Like to Try a Sample? 2 S MVP M3 8.6 Let s Investigate P IM Types of Statistical Studies D IM Sarah, The Chimpanzee S IM The Marble Jar S IM Scratch and Win Blues S IM Fred s Flare Formula P/D IM Margin of Error P MVP M3 8.7 Slacker s Simulation D HCPSS 2 Literary Digest ½ S MARS 3 Muddying the Waters 2 ½ P NCTM 4 Soft Drinks and Heart Disease Illustrative Mathematics 2 Howard County Public Schools 3 Mathematics Assessment Resource Service 4 National Council of Teachers of Mathematics S-IC. S-IC.3 S-IC.4 S-IC.5 S-IC.6 Unit Standards Statistics Understand the process of making inferences about a population based on a random sample from that population. Recognize the purposes of and differences between sample surveys, experiments, and observational studies and understand how randomization should be used in each. Use simulation to understand how samples can be used to estimate a population mean or proportion and how to determine a margin of error for the estimate. Use simulation to determine whether observed differences between samples from two distinct populations indicate that the two populations are actually different in terms of a parameter of interest. Evaluate articles and websites that report data by identifying the source of the data, the design of the study, and the way the data are graphically displayed. 206-207 Math 3 6
206-207 Math 3 7