# % <! $ ± Θ Δ Π Σ SECONDARY MATHEMATICS CURRICULUM GUIDE LIBERAL ARTS MATHEMATICS Course 207300 HILLSBOROUGH COUNTY SCHOOL DISTRICT Updated Summer 205 # % <! $ ± Θ Δ Π Σ
QUARTER Section : Working With Expressions Section Video Understanding Expressions MAFS.92.A-SSE.. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of P and a factor not depending on P. Section Video 2 Section Video 3 Section Video 4 Section Video 5 Algebraic Expressions Using the Distributive Property Algebraic Expressions Using the Commutative and Associative Properties Understanding Polynomials Adding and Subtracting Polynomials *MAFS.92.A-SSE..2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 - y 4 as (x²)² (y²)², thus recognizing it as a difference of squares that can be factored as (x² y²)(x² + y²). MAFS.92.A-APR.. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Section Video 6 Multiplying Polynomials MAFS.92.A-APR.. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. *Standard MAFS.92.A-SSE..2 is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra FSA.
Section 2: Solving Equations and Inequalities with One Variable Section 2 Video Equations: True or False? MAFS.92.A-CED.. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions Section 2 Video 2 Solving Equations Part MAFS.92.A-REI.2.3 Solve linear equations and inequalities in one variable, including Section 2 Video 3 Solving Equations Part 2 equations with coefficients represented by letters. Creating and Solving Equations Real-World Examples MAFS.92.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Section 2 Video 4 Solving Inequalities MAFS.92.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Section 2 Video 5 Compound Inequalities MAFS.92.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 2 Additional resource One Step Equations WS 3 Additional resource Solve 2-Step Equations AN book page 22 Beat The Test Additional resource Word Problems for Linear Equations (addresses creating equations, real-world problem solving) 2 Additional resource solving inequalities 2
Continued Section 2: Solving Equations and Inequalities with One Variable Section 2 Video 6 Section 2 Video 7 Section 2 Video 8 Solving Absolute Value Equations and Inequalities Solving Equations Using the Zero Product Property Equations with Variables in the Denominator MAFS.92.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MAFS.92.A-CED..3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. MAFS.92.A-REI.. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. MAFS.92.A-CED..3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 3 Additional resource Absolute Value Inequalities (addresses absolute value equation and inequality practice) 3
Section 2 Video 9 Continued Section 2: Solving Equations and Inequalities with One Variable Solving Equations in Real-Life Situations MAFS.92.A-CED.. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions Section 2 Video 0 Rearranging Formulas MAFS.92.A-CED..4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R. 2 Additional Resource More Word Problems Linear Additional Resource Literal Equations (addresses geometry examples) 4
Section 3: Solving Equations and Inequalities with Two Variables Section 3 Video 2 Section 3 Video 3 Discovering Slope Discovering Slope and Y- Intercept MAFS.92.A-CED..2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *MAFS.92.F-IF.2.4 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 2 *Standards MAFS.92.F-IF.2.4 and MAFS.92.S-ID.3.7 are not explicitly stated in Algebra curriculum, but are necessary prerequisites for review. *MAFS.92.S-ID.3.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data 5
Continued Section 3: Solving Equations and Inequalities with Two Variables Section 3 Video Section 3 Video 4 Solution Sets to Equations with Two Variables Solution Sets to Inequalities with Two Variables MAFS.92.A-CED..2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MAFS.92.A-CED..3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. MAFS.92.A-REI.4.0 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). MAFS.92.A-REI.4.2 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 5 6
Continued Section 3: Solving Equations and Inequalities with Two Variables Section 3 Video 5 Section 3 Video 6 Finding Solution Sets to Systems of Equations Using Substitution and Graphing Finding Solution Sets to System of Equations Using Elimination MAFS.92.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. MAFS.92.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 2 Additional resource Solving Systems of Equations (3 Different Methods) (addresses practice for 3 solution methods) Section 3 Video 7 Finding Solution Sets to Systems of Linear Inequalities MAFS.92.A-REI.4. Explain why the x- coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. MAFS.92.A-REI.4.2 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 2 Additional resource Systems of Inequalities (useful for homework/practice) FORMATIVE ASSESSMENT WEEK 7
QUARTER 2 Section 4: Introduction to Functions Section 4 Video 2 Input and Output Values MAFS.92.F-IF.. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Review function notation to fully cover standard MAFS.92.F-IF..2 Additional Resource Function Notation review Section 4 Video 3 Representing, Naming, and Solving Functions MAFS.92.F-IF..2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. MAFS.92.F-IF..2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 8
Continued Section 4: Introduction to Functions Section 4 Video 4 Section 4 Video 5 Graphs of Functions part Graphs of Functions part 2 MAFS.92.F-IF.2.4 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. MAFS.92.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function. 2 9
Continued Section 4: Introduction to Functions Section 4 Video 6 Transformations of Linear Functions *MAFS.92.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. *Standard MAFS.92.F-BF.2.3 is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra FSA. 0
Section 5: Piecewise-Defined Functions Section 5 Video 4 Graphing Absolute Value Functions *MAFS.92.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. *\*Standards MAFS.92.F-BF.2.3 and MAFS.92.F-IF.3.7b are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra FSA. *MAFS.92.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Continued Section 5: Piecewise-Defined Functions Section 5 Video 5 Transformations with Absolute Value Functions *MAFS.92.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. *Standards MAFS.92.F-BF.2.3 and MAFS.92.F-IF.3.7b are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra FSA. *MAFS.92.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 2
Continued Section 5: Piecewise-Defined Functions Section 5 Video Section 5 Video 2 Section 5 Video 3 Understanding Piecewise- Defined Functions Graphing Piecewise-Defined Functions Writing Piecewise-Defined Functions MAFS.92.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. *Piecewise functions not explicitly stated in Algebra or Liberal Arts standards, but could be introduced for enrichment. 3
Section 6: Radicals and Rational Exponents Section 6 Video 5 Section 6 Video 6 Graphing Square Root Functions Transformations of Square Roots Functions MAFS.92.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. *Square Root functions not explicitly stated in Algebra or Liberal Arts standards, but could be introduced for enrichment. Section 6 Video Rewriting Radical Expressions with Rational Exponents b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. *MAFS.92.N-RN.. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define *Standard MAFS.92.N-RN.. is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra FSA. 5!! to be the cube root of 5 because we want (5!! )! = 5!!! to hold, so (5!! )! must equal 5. 4
Continued Section 6: Radicals and Rational Exponents Section 6 Video 2 Section 6 Video 3 Operations with Expressions with Rational Exponents Solving Radical Functions with Rational Exponents *MAFS.92.N-RN..2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. *MAFS.92.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. MAFS.92.A-CED.. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. 2 *Standards MAFS.92.N-RN..2 and MAFS.92.N-RN.2.3 are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra FSA. 2 5
Continued Section 6: Radicals and Rational Exponents Section 6 Video 4 Operations with Rational and Irrational Numbers *MAFS.92.N-RN..2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. *MAFS.92.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. *Standards MAFS.92.N-RN..2 and MAFS.92.N-RN.2.3 are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra FSA. 6
Section 7: Quadratics (Part ) Section 8: Quadratics (Part 2) Section 7 Video Real-World Examples of Quadratic Functions *MAFS.92.A-SSE.2.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. 2 *Standard MAFS.92.A-SSE.2.3a is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra FSA. Section 8 Video Observations from a Graph of a Quadratic Function MAFS.92.F-IF.2.4 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. Additional resource Quadratic Graphs 7
Continued Section 7: Quadratics (Part ) Continued Section 8: Quadratics (Part 2) Section 8 Video 5 Section 7 Video 2 Deriving the Quadratic Formula Solving Quadratics Using the Quadratic Formula Solving Quadratics Using the Quadratic Formula *MAFS.92.A-REI.2.4a Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)² = q that has the same solutions. Derive the quadratic formula from this form. *MAFS.92.A-REI.2.4a Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)² = q that has the same solutions. Derive the quadratic formula from this form. *Standard MAFS.92.A-REI.2.4a is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra FSA. 2 *Standard MAFS.92.A-REI.2.4a is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra FSA. 8
Continued Section 7: Quadratics (Part ) Continued Section 8: Quadratics (Part 2) Section 7 Video 3 Section 7 Video 4 Section 7 Video 5 Solving Quadratics by Factoring part Solving Quadratics by Factoring part 2 Solving Quadratics by Factoring Special Cases MAFS.92.A-SSE..2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 - y 4 as (x²)² (y²)², thus recognizing it as a difference of squares that can be factored as (x² y²)(x² + y²). MAFS.92.A-SSE.2.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. MAFS.92.F-IF.3.8a Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 3 9
Continued Section 7: Quadratics (Part ) Continued Section 8: Quadratics (Part 2) Section 7 Video 7 Solving Quadratics by Completing the Square MAFS.92.A-REI.2.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)² = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. MAFS.92.F-IF.3.8a Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context 20
Continued Section 7: Quadratics (Part ) Continued Section 8: Quadratics (Part 2) Section 8 Video 2 Graphing Quadratics Finding the Vertex, Using Intercepts, and Using a Table MAFS.92.F-IF.3.7a Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 2 Section 8 Video 3 Graphing Quadratics Vertex Form Section 8 Video 4 Transformations of Quadratic Functions a. Graph linear and quadratic functions and show intercepts, maxima, and minima. MAFS.92.A-REI.2.4a Solve quadratic equations in one variable. c. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)² = q that has the same solutions. Derive the quadratic formula from this form. MAFS.92.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. Also covers operations with functions. 2
Continued Section 7: Quadratics (Part ) Continued Section 8: Quadratics (Part 2) Section 7 Video 8 Quadratics in Action MAFS.92.A-REI.2.4 Solve quadratic equations in one variable. d. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)² = q that has the same solutions. Derive the quadratic formula from this form. e. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Section 8 Video 6 Graphing Polynomial Functions MAFS.92.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. END OF SEMESTER Use as a review of quadratics in preparation for Semester Exam. Also reviews Algebra Nation Section Video 4 Understanding Polynomials Additional Resource Classifying and Simplifying Polynomials 22
QUARTER 3 Section 9: Exponential Functions Section 4 Video Section 9 Video Section 9 Video 2 Arithmetic Sequences Geometric Sequences Real-World Examples of Arithmetic and Geometric Sequences MAFS.92.F-LE..2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). MAFS.92.F-LE..2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 2 Additional resource Geometric Sequences Power Point (addresses geometric examples of sequences) 23
Continued Section 9: Exponential Functions Section 9 Video 3 Exponential Functions MAFS.92.A-CED.. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. MAFS.92.F-LE.. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. MAFS.92.F-LE..2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 2 Additional resource Exponential Growth and Decay (website link) 24
Continued Section 9: Exponential Functions Section 9 Video 5 Transformations of Exponential Functions MAFS.92.F-LE.. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. MAFS.92.F-LE..2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 2 Section 9 Video 4 Real-World Examples of Exponential Functions MAFS.92.F-LE..3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. MAFS.92.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context. 25
Continued Section 9: Exponential Functions Section 0 Video 5 Modeling Exponential Functions MAFS.92.F-LE.. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. MAFS.92.F-LE..2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 26
Section 0: Elements of Modeling Section 0 Video Identifying Key Features of Parent Function Graphs MAFS.92.F-IF.2.4 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. 27
Continued Section 0: Elements of Modeling Section 0 Video 2 Comparing the Rate of Change for Linear, Quadratic, and Exponential Functions MAFS.92.F-IF.2.4 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. MAFS.92.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MAFS.92.F-LE.. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Additional Resource Linear Quadratic Exponential Tables 28
Continued Section 0: Elements of Modeling Review of Linear Functions Utilize formative A and semester exam data to determine specific topics for FSA review. 4 Additional Resource - Modeling With Linear Functions Review of Quadratic Functions Utilize formative A and semester exam data to determine specific topics for FSA review. Section 0 Video 3 5 Additional Resource - Modeling With Quadratics Section 0 Video 4 29
Section : Quantitative Data in One Variable Section Video Dot Plots and Histograms MAFS.92.S-ID.. Represent data with plots on the real number line (dot plots, histograms, and box plots). Section Video 3 Section Video 2 Section Video 4 Measures of Center and Shapes of Distributions Box Plots Measuring Spread MAFS.92.S-ID..2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. MAFS.92.S-ID.. Represent data with plots on the real number line (dot plots, histograms, and box plots). 3 MAFS.92.S-ID..2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. MAFS.92.S-ID..3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 30
Continued Section : Quantitative Data in One Variable Section Video 5 Outliers in Data Sets MAFS.92.S-ID..3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Section Video 6 Comparing Distributions MAFS.92.S-ID..3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of Descriptive Statistics Review of measures of central tendency, measures of variation, and measures of spread extreme data points (outliers). MAFS.92.S-ID.. Represent data with plots on the real number line (dot plots, histograms, and box plots). MAFS.92.S-ID..2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. MAFS.92.S-ID..3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 3 Additional Resources Descriptive Statistics Review Power Point Descriptive Statistics Activity 3
Geometry Unit Geometry lessons from HMH Digital Geometry text found at www.my.hrw.com Daily instruction should include a Geometry topic as well as correlated Algebra skill for review. Algebra skills are not explicitly tested on the Semester 2 Exam, but should be used for remediation purposes and FSA preparation. HMH Digital Geometry text Section Unit Section - Unit Section -2 Applying Postulates and Undefined Terms Topic Student Objectives Days Measuring, Drawing, and Naming Rays and Angles Students can identify the three undefined terms of geometry. Students can identify four noncoplanar points given a 3- dimensional figure. Students can give real-world examples for the three undefined terms in geometry. Students can identify a ray given a picture. Students can differentiate between the symbols for line, ray and segment. Students can identify the appropriate picture of an angle given the classification name. Students can identify the correct classification name of an angle, given a figure. Students can classify an angle given an angle measurement. 32
HMH Digital Geometry text Section Unit 2 Section -4 Unit 2 Section -4 Unit 2 Section -2 Section -3 Unit 2 Section -4 Applying Properties of Complementary and Supplementary Angles Angle Pairs Using the Angle Addition Postulate Topic Student Objectives Days Using Properties of Angle Bisectors Constructions using Compass and Protractor Investigating Vertical Angles and Linear Pairs Students can determine the measurements of a complement and supplement to a given angle. Students can identify the pair of angle measurements that are supplementary. Students can apply Angle Addition Postulate and definition of complementary angles to set up an equation to solve for the value of x and find the measurement of each complementary angle. Students will make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.) Students can apply the definition of vertical angles to set up an equation to solve for the value of x and find the measurement of the vertical angles. Students can apply the definition of linear pairs to determine the measurement of a missing angle. 2 Review angle relationships 33
QUARTER 4 HMH Digital Geometry text Section Unit 2 Section -6 Unit 2 Section -6 Finding the Midpoint of a Segment Topic Student Objectives Days Finding the Distance Between Two Points - Distance Formula Students can apply the midpoint formula to determine the coordinates of the midpoint of a segment given the coordinates of the two endpoints of the segment. Students can apply the distance formula, given the coordinates of two points, and express the answer to the nearest tenth. 34
HMH Digital Geometry text Section Unit 3 Section 3- Section 3-2 Section 3-3 Unit 3 Section 3-2 Section 4-2 Topic Student Objectives Days Determining the Measure of Angles Made by Parallel Lines and a Transversal Angle Pair Relationships Proving Lines Parallel Classifying Triangles and Applying Angle Relationships Students can apply angle pair relationships to find the measurement of a marked angle, given a diagram of 2 parallel lines cut by a transversal. Students can identify the type of angle pair relationship marked, given a diagram of 2 parallel lines cut by a transversal. Students can identify the angle pair relationship that will guarantee two givens lines are parallel. Students can classify triangles by side, given the measurements of the sides. Students can classify triangles by angle, given triangle diagrams with angle markings. Students can identify a set of three side measurements that determine a right triangle. Students can classify a triangle by side, graphed on a coordinate plane. 3 Additional Resources Parallel Lines Worksheet Parallel Lines Transversals By sides, angles, and on the coordinate plane. 35
HMH Digital Geometry text Section Unit 4 Section 4-3 Unit 4 Section 4-3 Unit 4 Section 6- Section 6-2 Section 6-3 Unit 4 Section -7 Topic Student Objectives Days Properties of Triangles Students can apply the Triangle Sum Theorem to solve for the measurement of the third angle of a triangle, given the measurements of the other two angles. Applying the Triangle Sum Theorem Applying the Exterior Angle Theorem Properties of Quadrilaterals Classifying Quadrilaterals Transformations of Quadrilaterals Students can apply the Triangle Sum Theorem to set up an equation with variable expressions and solve for x, given a diagram of a triangle. Students can apply the Triangle Exterior Angle Theorem to solve for a missing remote interior angle. Students can find the measurement of the fourth angle of quadrilateral given the measurements of the other three. Students can identify the quadrilateral given specific properties of sides and angles (not diagonals). 3 Additional Resource Angle Relationships in Triangles (exterior angle activity) 3 Additional Resource Quad Flow Chart Focus on Reflections and Rotations 36
HMH Digital Geometry text Section Unit 6 Section 5-7 Unit 6 Section 5-7 Topic Student Objectives Days Using the Pythagorean Theorem Students will be able to apply Pythagorean Theorem to solve for the length of the hypotenuse, given a labeled diagram. Students will be able to apply the Pythagorean Theorem to find the missing leg measurement, given a diagram labeled with one leg and the hypotenuse. Applying the Pythagorean Theorem Students will be able to sketch a representation of a real-world situation, and solve for the missing side using Pythagorean Theorem. 2 Identifying side lengths Finding the hypotenuse Finding leg measures Real-world examples On a coordinate plane, using distance formula 37
HMH Digital Geometry text Section Unit 5 Section 4- Section 7-2 Unit 5 Section 7- Unit 5 Section 7- Section 7-5 Unit 5 Section 7-5 Comparing Congruent and Similar Figures Topic Student Objectives Days Determining Parts of Similar Figures Similarity Statements Similar Figures using Proportions Perimeter and Area of Similar Figures Students will define differences between congruent and similar figures. Students can determine corresponding parts of similar triangles given a similarity statement and diagram. Students can express a ratio (x out of y) in simplest form using the form x:y. Students can set up a proportion to solve for a missing side length of a triangle given a similarity statement and diagram of similar triangles. Students can set up a proportion to solve for the missing side of similar right triangles, given a diagram representing a real-world situation. Students can express the perimeter of a figure in simplified form given a diagram labeled with side lengths in 3 different variables. Students can express the ratio of areas of two similar triangles given the ratio of the corresponding side lengths of the triangles. Additional Resource Triangle Congruence 2 Corresponding parts Missing measurements Additional Resource Determining Similarity of Triangles 38
HMH Digital Geometry text Section Unit 7 Topic Student Objectives Days Finding Volume of Prisms Finding Volume of Right Triangular Prisms Students can solve for the exact volume of a prism given the side lengths and/or the area of the base. Students can solve for the volume of a right triangular prism given the height of the triangular base, the side length of the triangular base and the distance between the bases. (Diagram may be oriented on side.) Unit 7 Finding Volume of a Cylinder Students can solve for the exact volume of a cylinder given the radius and the height (leaving answer in terms of π). Unit 7 Finding Volume of a Pyramid Students can solve for the volume of a pyramid given side lengths and/or area of the base, and the height. (Diagram may be oriented on side.) Unit 7 Finding Volume of a Cone Students can solve for the volume of a right cone given the radius of the base and the height of the cone. (Diagram may be oriented on side.) Unit 7 Finding Surface Area of a Cube and Cylinder Students can solve for the surface area of a cube given the side length. Students can solve for the surface area of a cylinder given the radius and the height (leaving the answer in terms of π) END OF SEMESTER 2 2 Additional Resource Volume and Surface Area (website link) 2 2 2 2 Limited formulas provided on reference sheet 39