Θ Δ Π Σ SECONDARY MATHEMATICS CURRICULUM ... Arts Mathematics 1 2015 – 2016...

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SECONDARY MATHEMATICS CURRICULUM GUIDE

LIBERAL ARTS MATHEMATICS 1 Course 1207300

HILLSBOROUGH COUNTY SCHOOL DISTRICT 2015 – 2016

Updated Summer 2015

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Liberal Arts Mathematics 1 2015 – 2016

Last Updated Summer 2015

1

QUARTER 1 Section 1: Working With Expressions

Algebra Nation Section/ Video

Topic MAFS Benchmark Days Allotted

Remarks/ Possible Activities/

Additional Resources: Section 1 Video 1 Understanding Expressions MAFS.912.A-SSE.1.1 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.

1

Section 1 Video 2 Section 1 Video 3

Algebraic Expressions Using the Distributive Property Algebraic Expressions Using the Commutative and Associative Properties

*MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4- y4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

1 *Standard MAFS.912.A-SSE.1.2 is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra 1 FSA.


Understanding Polynomials Adding and Subtracting Polynomials

MAFS.912.A-APR.1.1 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.

1

Section 1 Video 6 Multiplying Polynomials

MAFS.912.A-APR.1.1 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.

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2

Section 2: Solving Equations and Inequalities with One Variable




Additional Resources: Section 2 Video 1 Equations: True or False? MAFS.912.A-CED.1.1 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 Additional resource – “One Step Equations WS”


Solving Equations Part 1 Solving Equations Part 2

MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3 Additional resource – “Solve 2-Step Equations”

Creating and Solving Equations Real-World Examples

MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

1 AN book page 22 “Beat The Test” Additional resource –“Word Problems for Linear Equations” (addresses creating equations, real-world problem solving)

Section 2 Video 4 Solving Inequalities MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

2 Additional resource – “solving inequalities”

Section 2 Video 5 Compound Inequalities MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

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3

Continued Section 2: Solving Equations and Inequalities with One Variable




Additional Resources: Section 2 Video 6 Solving Absolute Value

Equations and Inequalities MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MAFS.912.A-CED.1.3 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)

Section 2 Video 7 Solving Equations Using the Zero Product Property

MAFS.912.A-REI.1.1 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.

1

Section 2 Video 8 Equations with Variables in the Denominator

MAFS.912.A-CED.1.3 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.

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4

Continued Section 2: Solving Equations and Inequalities with One Variable




Additional Resources: Section 2 Video 9 Solving Equations in Real-Life

Situations MAFS.912.A-CED.1.1 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 Additional Resource – “More Word Problems Linear”

Section 2 Video 10 Rearranging Formulas MAFS.912.A-CED.1.4 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.

1 Additional Resource – “Literal Equations” (addresses geometry examples)



5

Section 3: Solving Equations and Inequalities with Two Variables




Additional Resources: Section 3 Video 2 Section 3 Video 3

Discovering Slope Discovering Slope and Y-Intercept

MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *MAFS.912.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.912.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

2 *Standards MAFS.912.F-IF.2.4 and MAFS.912.S-ID.3.7 are not explicitly stated in Algebra 1 curriculum, but are necessary prerequisites for review.



6

Continued Section 3: Solving Equations and Inequalities with Two Variables Algebra Nation Section/ Video




Solution Sets to Equations with Two Variables Solution Sets to Inequalities with Two Variables

MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MAFS.912.A-CED.1.3 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.912.A-REI.4.10 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.912.A-REI.4.12 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.

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7

Continued Section 3: Solving Equations and Inequalities with Two Variables Algebra Nation Section/ Video




Finding Solution Sets to Systems of Equations Using Substitution and Graphing Finding Solution Sets to System of Equations Using Elimination

MAFS.912.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.912.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. MAFS.912.A-REI.4.11 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.

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.912.A-REI.4.12 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



8

QUARTER 2 Section 4: Introduction to Functions




Additional Resources: Section 4 Video 2 Input and Output Values MAFS.912.F-IF.1.1 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). MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

1 Review function notation to fully cover standard MAFS.912.F-IF.1.2 Additional Resource – “Function Notation review”

Section 4 Video 3 Representing, Naming, and Solving Functions

MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

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9

Continued Section 4: Introduction to Functions Algebra Nation Section/ Video




Graphs of Functions part 1 Graphs of Functions part 2

MAFS.912.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.912.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.

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Continued Section 4: Introduction to Functions Algebra Nation Section/ Video



Additional Resources: Section 4 Video 6 Transformations of Linear

Functions *MAFS.912.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.

1 *Standard MAFS.912.F-BF.2.3 is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra 1 FSA.



11

Section 5: Piecewise-Defined Functions




Additional Resources: Section 5 Video 4 Graphing Absolute Value

Functions *MAFS.912.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.

*MAFS.912.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.

1 *\*Standards MAFS.912.F-BF.2.3 and MAFS.912.F-IF.3.7b are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra 1 FSA.



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Continued Section 5: Piecewise-Defined Functions Algebra Nation Section/ Video



Additional Resources: Section 5 Video 5 Transformations with Absolute

Value Functions *MAFS.912.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.

*MAFS.912.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.


1 *Standards MAFS.912.F-BF.2.3 and MAFS.912.F-IF.3.7b are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra 1 FSA.



13

Continued Section 5: Piecewise-Defined Functions Algebra Nation Section/ Video



Additional Resources: Section 5 Video 1 Section 5 Video 2 Section 5 Video 3

Understanding Piecewise-Defined Functions Graphing Piecewise-Defined Functions Writing Piecewise-Defined Functions

MAFS.912.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.


1 *Piecewise functions not explicitly stated in Algebra 1 or Liberal Arts standards, but could be introduced for enrichment.



14

Section 6: Radicals and Rational Exponents Algebra Nation Section/ Video




Graphing Square Root Functions Transformations of Square Roots Functions

MAFS.912.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.


1 *Square Root functions not explicitly stated in Algebra 1 or Liberal Arts standards, but could be introduced for enrichment.

Section 6 Video 1 Rewriting Radical Expressions with Rational Exponents

*MAFS.912.N-RN.1.1 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 5!! to be the cube root of 5 because

we want (5!!)! = 5

!! ! to hold, so

(5!! )! must equal 5.

1 *Standard MAFS.912.N-RN.1.1 is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra 1 FSA.



15

Continued Section 6: Radicals and Rational Exponents Algebra Nation Section/ Video



Additional Resources: Section 6 Video 2 Operations with Expressions

with Rational Exponents *MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. *MAFS.912.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.

2 *Standards MAFS.912.N-RN.1.2 and MAFS.912.N-RN.2.3 are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra 1 FSA.

Section 6 Video 3 Solving Radical Functions with Rational Exponents

MAFS.912.A-CED.1.1 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



16

Continued Section 6: Radicals and Rational Exponents Algebra Nation Section/ Video



Additional Resources: Section 6 Video 4 Operations with Rational and

Irrational Numbers *MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. *MAFS.912.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.

1 *Standards MAFS.912.N-RN.1.2 and MAFS.912.N-RN.2.3 are not explicitly stated in Liberal Arts curriculum, but necessary skills for Algebra 1 FSA.



17

Section 7: Quadratics (Part 1) Section 8: Quadratics (Part 2)




Additional Resources: Section 7 Video 1 Real-World Examples of

Quadratic Functions *MAFS.912.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.912.A-SSE.2.3a is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra 1 FSA.

Section 8 Video 1 Observations from a Graph of a Quadratic Function

MAFS.912.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.

1 Additional resource – “Quadratic Graphs”



18

Continued Section 7: Quadratics (Part 1) Continued Section 8: Quadratics (Part 2)




Additional Resources: Section 8 Video 5

Deriving the Quadratic Formula Solving Quadratics Using the Quadratic Formula

*MAFS.912.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.

1 *Standard MAFS.912.A-REI.2.4a is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra 1 FSA.

Section 7 Video 2 Solving Quadratics Using the Quadratic Formula

*MAFS.912.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.

2 *Standard MAFS.912.A-REI.2.4a is not explicitly stated in Liberal Arts curriculum, but a necessary skill for Algebra 1 FSA.



19





Additional Resources: Section 7 Video 3 Section 7 Video 4 Section 7 Video 5

Solving Quadratics by Factoring part 1 Solving Quadratics by Factoring part 2 Solving Quadratics by Factoring Special Cases

MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4- y4as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²). MAFS.912.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.912.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.

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20





Additional Resources: Section 7 Video 7 Solving Quadratics by

Completing the Square MAFS.912.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.921.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

1



21





Additional Resources: Section 8 Video 2 Graphing Quadratics –

Finding the Vertex, Using Intercepts, and Using a Table

MAFS.912.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. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

2

Section 8 Video 3 Graphing Quadratics – Vertex Form

MAFS.912.A-REI.2.4a Solve quadratic equations in one variable. c. Use the method of completing the square


1

Section 8 Video 4 Transformations of Quadratic Functions

MAFS.912.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.

1 Also covers operations with functions.



22





Additional Resources: Section 7 Video 8 Quadratics in Action MAFS.912.A-REI.2.4 Solve quadratic

equations in one variable. d. Use the method of completing the square


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.

1 Use as a review of quadratics in preparation for Semester 1 Exam.

Section 8 Video 6 Graphing Polynomial Functions

MAFS.912.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.

1 Also reviews Algebra Nation Section 1 Video 4 – Understanding Polynomials Additional Resource – “Classifying and Simplifying Polynomials”

END OF SEMESTER 1



23

QUARTER 3 Section 9: Exponential Functions





Arithmetic Sequences Geometric Sequences

MAFS.912.F-LE.1.2 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).

1

Section 9 Video 2 Real-World Examples of Arithmetic and Geometric Sequences


2 Additional resource – “Geometric Sequences Power Point” (addresses geometric examples of sequences)



24

Continued Section 9: Exponential Functions




Additional Resources: Section 9 Video 3 Exponential Functions MAFS.912.A-CED.1.1 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.912.F-LE.1.1 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.


2 Additional resource – “Exponential Growth and Decay” (website link)



25





Additional Resources: Section 9 Video 5 Transformations of

Exponential Functions MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal




MAFS.912.F-LE.1.2 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.912.F-LE.1.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

2

Section 9 Video 4 Real-World Examples of Exponential Functions

MAFS.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context.

1



26





Additional Resources: Section 10 Video 5 Modeling Exponential

Functions MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal





1



27

Section 10: Elements of Modeling




Additional Resources: Section 10 Video 1 Identifying Key Features of

Parent Function Graphs MAFS.912.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.

1



28

Continued Section 10: Elements of Modeling




Additional Resources: Section 10 Video 2 Comparing the Rate of

Change for Linear, Quadratic, and Exponential Functions

MAFS.912.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.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal




1 Additional Resource – “Linear Quadratic Exponential Tables”



29

Continued Section 10: Elements of Modeling




Additional Resources: Review of Linear

Functions Utilize formative A and semester 1 exam data to determine specific topics for FSA review.

4 Additional Resource - “Modeling With Linear Functions” Algebra Nation Section 10 Video 3

Review of Quadratic Functions

Utilize formative A and semester 1 exam data to determine specific topics for FSA review.

5 Additional Resource - “Modeling With Quadratics” Algebra Nation Section 10 Video 4



30

Section 11: Quantitative Data in One Variable




Additional Resources: Section 11 Video 1 Dot Plots and Histograms MAFS.912.S-ID.1.1 Represent data

with plots on the real number line (dot plots, histograms, and box plots).

1

Section 11 Video 3 Measures of Center and Shapes of Distributions

MAFS.912.S-ID.1.2 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.

1


Box Plots Measuring Spread

MAFS.912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). MAFS.912.S-ID.1.2 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.912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

3



31

Continued Section 11: Quantitative Data in One Variable




Additional Resources: Section 11 Video 5 Outliers in Data Sets MAFS.912.S-ID.1.3 Interpret

differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

1

Section 11 Video 6 Comparing Distributions MAFS.912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

1

Descriptive Statistics Review of measures of central tendency, measures of variation, and measures of spread

MAFS.912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). MAFS.912.S-ID.1.2 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.912.S-ID.1.3 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”



32

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

Topic Student Objectives Days Allotted


Additional Resources: Unit 1 Section 1-1

Applying Postulates and Undefined Terms

• Students can identify the three undefined terms of geometry.

• Students can identify four non-coplanar points given a 3-dimensional figure.

• Students can give real-world examples for the three undefined terms in geometry.

1

Unit 1 Section 1-2

Measuring, Drawing, and Naming Rays and Angles

• 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.

1



33

HMH Digital

Geometry text Section




Applying Properties of Complementary and Supplementary Angles

• 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.

1

Unit 2 Section 1-4

Angle Pairs Using the Angle Addition Postulate Using Properties of Angle Bisectors

• 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.

1

Unit 2 Section 1-2 Section 1-3

Constructions using Compass and Protractor

• 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.)

1

Unit 2 Section 1-4

Investigating Vertical Angles and Linear Pairs

• 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



34

QUARTER 4

HMH Digital Geometry text

Section




Finding the Midpoint of a Segment

• 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.

1

Unit 2 Section 1-6

Finding the Distance Between Two Points - Distance Formula

• Students can apply the distance formula, given the coordinates of two points, and express the answer to the nearest tenth.

1



35

HMH Digital




Additional Resources: Unit 3 Section 3-1 Section 3-2 Section 3-3

Determining the Measure of Angles Made by Parallel Lines and a Transversal Angle Pair Relationships Proving Lines Parallel

• 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.

3 Additional Resources – “Parallel Lines Worksheet” “Parallel Lines – Transversals”


Classifying Triangles and Applying Angle Relationships

• 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.

1 By sides, angles, and on the coordinate plane.



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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.

1

Unit 4 Section 4-3

Applying the Triangle Sum Theorem Applying the Exterior Angle Theorem

• 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.

3 Additional Resource – “Angle Relationships in Triangles” (exterior angle activity)

Unit 4 Section 6-1 Section 6-2 Section 6-3

Properties of Quadrilaterals Classifying Quadrilaterals

• 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 – “Quad Flow Chart”

Unit 4 Section 1-7

Transformations of Quadrilaterals

Focus on Reflections and Rotations



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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.

2 Identifying side lengths Finding the hypotenuse Finding leg measures

Unit 6 Section 5-7

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.

1 Real-world examples On a coordinate plane, using distance formula



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Additional Resources: Unit 5 Section 4-1 Section 7-2

Comparing Congruent and Similar Figures

• Students will define differences between congruent and similar figures.

1 Additional Resource – “Triangle Congruence”

Unit 5 Section 7-1

Determining Parts of Similar Figures Similarity Statements

• Students can determine corresponding parts of similar triangles given a similarity statement and diagram.

2 Corresponding parts Missing measurements


Similar Figures using Proportions

• 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.

1 Additional Resource – “Determining Similarity of Triangles”

Unit 5 Section 7-5

Perimeter and Area of Similar Figures

• 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.

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Additional Resources: Unit 7 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.)

2 Additional Resource – “Volume and Surface Area” (website link) Limited formulas provided on reference sheet

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).

2

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.)

2

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.)

2

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)

2

END OF SEMESTER 2

Θ Δ Π Σ SECONDARY MATHEMATICS CURRICULUM ... Arts Mathematics 1 2015 – 2016...

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