The School District of Palm Beach County ALGEBRA … Usingand ... Interpret parts of an expression,...

Topic & SuggestedPacing

Student Target Core

Students will…MAFS.912.A‐APR.1.1

Calculator: NoUnderstand 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.

MAFS.912.A‐SSE.1.1Calculator: Neutral

Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients.b. Interpret complicated expressions by viewing one or more of their parts as a single entity.


Use the structure of an expression to identify ways to rewrite it.

MAFS.912.N‐RN.1.1Calculator: No

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.


Rewrite expressions involving radicals and rational exponents using the properties of exponents.


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.

LAFS.910.SL.1.1

Initiate and participate effectively in a range of collaborative discussions (one‐on‐one, in groups, and teacher‐led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well‐reasoned exchange of ideas.b. Work with peers to set rules for collegial discussions and decision‐making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

LAFS.910.SL.1.2Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source.

LAFS.910.SL.1.3Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence.

LAFS.910.SL.2.4Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task.

LAFS.910.RST.1.3Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

LAFS.910.RST.2.4Determine the meaning of symbols, key terms, and other domain‐specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.

LAFS.910.RST.3.7Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.

The School District of Palm Beach CountyALGEBRA 1 REGULAR / HONORS (REVISED 9-18-17)

Section 1: Expressions2017 - 2018

Standards

Mathematics Florida Standards August 15 ‐ August 30

Using Expressions to Represent Real World Situations

Understanding Polynomial Expressions

Algebraic Expressions Using the Distributive Property

Algebraic Expressions Using the Commutative and Associative

Properties

Properties of Exponents

Radical Expressions and Expressions with Rational

Exponents

Adding Expressions with Radicals and Rational

Exponents

More Operations with Radicals and Rational Exponents

Operations with Rational and Irrational Numbers

Math Nation1.11.21.31.41.51.61.71.81.9

• relate the addition, subtraction, and multiplication of integers to the addition, subtraction, and multiplication of polynomials with integral coefficients through application of the distributive property. • apply their understanding of closure to adding, subtracting, and multiplying polynomials with integral coefficients. • add, subtract, and multiply polynomials with integral coefficients.• interpret parts of an expression, such as ters, factors and coefficients.• rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure.• rewrite algebraic expressions in different equivalent forms by simplifying expressions (e.g., combining like terms, using the distributive property, and other operations with polynomials).• use the properties of exponents to rewrite a radical expression as an expression with a rational exponent.• use the properties of exponents to rewrite an expression with a rational exponent as a radical expression.• apply the properties of operations of integer exponents to expressions with rational exponents.• apply the properties of operations of integer exponents to radical expressions.• write algebraic proofs that show that a 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 of 21 School District of Palm Beach County September 2017

LAFS.910.WHST.1.1

Write arguments focused on discipline‐specific content. a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. b. Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline‐appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented.

LAFS.910.WHST.2.4Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

LAFS.910.WHST.3.9 Draw evidence from informational texts to support analysis, reflection, and research.

ELD.K12.ELL.MA.1English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

ELD.K12.ELL.SI.1 English language learners communicate for social and instructional purposes within the school setting.FSQ Section 1



Student Target Core

Students will…MAFS.912.A‐CED.1.1Calculator: Neutral

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.A‐CED.1.2Calculator: Neutral

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.


Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

MAFS.912.A‐REI.1.1Calculator: No

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.912.A‐REI.2.3Calculator: Neutral

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.


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).



LAFS.910.SL.1.1








• write an equation in one variable that represents a real‐world context.• write an inequality in one variable that represents a real‐world context.• identify the quantities in a real world situation that should be represented by distinct variables..• solve multi‐variable formulas or literal equations for a specific variable.• solve formulas and equations with coefficients represented by letters.• complete an algebraic proof of solving a linear equation.• construct a viable argument to justify a solution method.• solve a linear equation.• solve a linear inequality.• verify if a set of ordered pairs is a solution of a function.• rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure.• rewrite algebraic expressions in different equivalent forms by simplifying expressions (e.g., combining like terms, using the distributive property, and other operations with polynomials).

Math Nation2.12.22.32.42.52.62.72.82.9

August 31 ‐ October 2

Equations: True or False?

Identifying Properties When Solving Equations

Solving Equations

Solving Equations Using the Zero Product Property

Solving Inequalities

Solving Compound Inequalities

Rearranging Formulas

Solution Sets to Equations with Two Variables


Section 2: Equations and Inequalities 2017 - 2018

Standards

Mathematics Florida Standards


LAFS.910.WHST.1.1








Student Target Core

Studens will… MAFS.912.A‐APR.1.1

Calculator: NoUnderstand 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.





MAFS.912.F‐BF.1.1Calculator: Neutral

Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context.b. Combine standard function types using arithmetic operations. c. Compose functions.


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.1.1Calculator: Neutral

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).


Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

MAFS.912.F‐IF.2.4Calculator: No

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.


Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.


Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

LAFS.910.SL.1.1





• relate the addition, subtraction, and multiplication of integers to the addition, subtraction, and multiplication of polynomials with integral coefficients through application of the distributive property. • apply their understanding of closure to adding, subtracting, and multiplying polynomials with integral coefficients. • add, subtract, and multiply polynomials with integral coefficients.• rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure.• rewrite algebraic expressions in different equivalent forms by simplifying expressions (e.g., combining like terms, using the distributive property, and other operations with polynomials).• write a function that combines functions using arithmetic operations and relate the result to the context of the problem.• write a function to model a real‐world context by composing functions and the information within the context.• determine the value of k when given a graph of the function and its transformation.• identify differences and similarities between a function and its transformation.• identify a graph of a function given a graph or a table of a transformation and the type of transformation that is represented.• graph by applying a given transformation to a function.• identify ordered pairs of a transformed graph.• complete a table for a transformed function.• use the definition of a function to determine if a relationship is a function, given tables, graphs, mapping diagrams, or sets of ordered pairs.• determine the feasible domain of a function that models a real‐world context.• evaluate functions that model a real‐world context for inputs in the domain.• interpret the domain of a function within the real‐world context given. • interpret statements that use function notation within the real‐world context given.• determine and relate the key features of a function within a real‐world context by examining the function’s table.• determine and relate the key features of a function within a real‐world context by examining the function’s graph.• use a given verbal description of the relationship between two quantities to label key features of a graph of a function that model the relationship.• calculate the average rate of change of a continuous function that is represented algebraically, in a table of values, on a graph, or as a set of data.• interpret the average rate of change of a continuous function that is represented algebraicailly, in a table of values, on a

h f d i h l ld

Standards


Section 3: Introduction to Functions2017 - 2018

October 3 ‐ October 20

Input and Output Values

Representing, Naming, and Evaluating Functions

Adding and Subtracting Functions

Multiplying Functions

Closure Property

Real World Combinations and Compositions of Functions

Key Features of Graphs of Functions

Average Rate of Change Over an Interval

Transformations of Functions

Math Nation3.13.23.33.43.53.63.73.83.93.10






LAFS.910.WHST.1.1





ELD.K12.ELL.SI.1 English language learners communicate for social and instructional purposes within the school setting.

graph, or as a set of data with a real‐world context.

USA Sections 1‐3



Student Target Core

Students WillMAFS.912.A‐CED.1.2Calculator: Neutral



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.


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.


Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.


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).


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.


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.




Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

MAFS.912.F‐LE.1.2Calculator: Neutral

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.2.5Calculator: No

Interpret the parameters in a linear or exponential function in terms of a context.

MAFS.912.S‐ID.3.7Calculator: Neutral

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

LAFS.910.SL.1.1




Standards

Math Nation4.14.24.34.44.54.64.74.84.94.10

• identify the quantities in a real‐world situation that should be represented by distinct variables. • write a system of equations given a real‐world situation. • graph a system of equations that represents a real‐world context using appropriate axis labels and scale. • write constraints for a real‐world context using equations, inequalities, a system of equations, or a system of inequalities. • interpret the solution of a real‐world context as viable or not viable. • provide steps in an algebraic proof that shows one equation being replaced with another to find a solution for a system of equations. • solve systems of linear equations.• identify systems whose solutions would be the same through examination of the coefficients.• graph a system of equations that represents a real‐world context using appropriate axis labels and scale.• verify if a set of ordered pairs is a solution of a function.• find a solution or an approximate solution for f(x) = g(x) using a graph, table of values, or successive approximations that give the solution to a given place value.• justify why the intersection of two functions is a solution to f(x) = g(x).• identify the graph that represents a linear inequality. • graph a linear inequality. • identify the solution set to a system of inequalities. • identify ordered pairs that are in the solution set of a system of inequalities. • graph the solution set to a system of inequalities. • write an explicit function, define a recursive process, or complete a table of calculations that can be used to mathematically define a real‐world context. • write a function that combines functions using arithmetic operations and relate the result to the context of the problem. • write a function to model a real‐world context by composing functions and the information within the context. • write a recursive definition for a sequence that is presented as a sequence, graph, or table.• write a linear function, an arithmetic sequence, an exponential function, or a geometric sequence when given a graph, a verbal description, a table of values or a set of ordered pairs that models a real world context.• interpret the y‐intercept of a linear model that represents a set of data with a real‐world context.• interpret the rate of change and intercepts of a linear function when given an equation that models a real‐world context.

Mathematics Florida Standards October 26 ‐ November 14

Arithmetic Sequences

Rate of Change of Linear Functions

Interpreting Rate of Change and y‐Intercept in a Real‐World

Context

Introduction to Systems of Equations

Finding Solution Sets to Systems of Equations Using Substitution and Graphing

Using Equivalent Systems of Equations

Finding Solution Sets to Systems of Equations Using

Elimination

Solution Sets to Inequalities with Two Variables

Finding Solution Sets to Systems of Linear Inequalities


Section 4: Linear Functions and Inequalities2017 - 2018






LAFS.910.WHST.1.1








Student Target Core

Students will …


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.




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.b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.c. Use the properties of exponents to transform expressions for exponential functions.




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.b. Use the properties of exponents to interpret expressions for exponential functions.

LAFS.910.SL.1.1









Standards

The School District of Palm Beach CountyALGEBRA 1 REGULAR / HONORS (REVISED 9-18-17)Section 5: Quadratic Equations and Functions Part 1

2017 - 2018

Math Nation5.15.25.35.45.55.65.75.85.95.10

• rewrite a quadratic equation in vertex form by completing the square.• use the vertex form of a quadratic equation to complete steps in the derivation of the quadratic formula.• solve a simple quadratic equation by inspection or by taking square roots.• solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring).• validate why taking the square root of both sides when solving a quadratic equation wil yield two solutions.• recognize that the quadratic formula can be used to find complex solutions.• rewrite algebraic expressions in different equivalent forms by recognizing the expression's structure.• use equivalent forms of a quadratic expression to interpret the expression’s terms, factors, zeros, maximum, minimum, coefficients, or parts in terms of the real‐world situation the expression represents.• rewrite algebraic expressions in different equivalent forms using factoring techniques (e.g., common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely) or simplifying expressions (e.g., combining like terms, using the distributive property, and other operations with polynomials).• determine and relate the key features of a function within a real‐world context by examining the function’s table.• determine and relate the key features of a function within a real‐world context by examining the function’s graph.• use a given verbal description of the relationship between two quantities to label key features of a graph of a function that models the relationship.• identify zeros, extreme values, and symmetry of a quadratic function written symbolically.

November 15 – January 12

Real‐World Examples of Quadratic Functions

Factoring Quadratic Expressions

Solving Quadratic Equations by Factoring

Solving Other Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring ‐ Special Cases

Solving Quadratic Equations by Taking Square Roots

Solving Quadratic Equations by Completing the Square

Deriving the Quadratic Formula

Solving Quadratic Equations Using the Quadratic Formula

Quadratics in Action


LAFS.910.WHST.1.1








Student Target Core

Students will…MAFS.912.A‐CED.1.2Calculator: Neutral













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. b. Graph square root, cube root, and piecewise‐defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.




Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

January 16 – January 29

Observations from a Graph of a Quadratic Function

Nature of the Solutions of Quadratic Equations and

Functions

Graphing Quadratic Functions Using a Table

Graphing Quadratic Functions Using the Vertex and Intercepts

Graphing Quadratic Functions Using Vertex Form

Transformations of the Dependent Variable of Quadratic Functions

Transformations of the Independent Variable of Quadratic Functions

Finding Solution Sets to Systems of Equations Using

Tables of Values and Successive Approximations


The School District of Palm Beach CountyALGEBRA 1 REGULAR / HONORS (REVISED 9-18-17)Section 6: Quadratic Equations and Functions Part 2

2017 - 2018Standards

• identify the quantities in a real‐world situation that should be represented by distinct variables. • write a system of equations given a real‐world situation. • graph a system of equations that represents a real‐world context using appropriate axis labels and scale.• rewrite a quadratic equation in vertex form by completing the square.• use the vertex form of a quadratic equation to complete steps in the derivation of the quadratic formula.• solve a simple quadratic equation by inspection or by taking square roots.• solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring).• validate why taking the square root of both sides when solving a quadratic equation wil yield two solutions.• recognize that the quadratic formula can be used to find complex solutions.• find a solution or an approximate solution for f(x) = g(x) using a graph, table of values, or successive approximations that give the solution to a given place value.• justify why the intersection of two functions is a solution to f(x) = g(x).• use equivalent forms of a quadratic expression to interpret the expression’s terms, factors, zeros, maximum, minimum, coefficients, or parts in terms of the real‐world situation the expression represents.• determine the value of k when given a graph of the function and its transformation. • identify differences and similarities between a function and its transformation. • identify a graph of a function given a graph or a table of a transformation and the type of transformation that is represented. • graph by applying a given transformation to a function. • identify ordered pairs of a transformed graph. • complete a table for a transformed function.• determine and relate the key features of a function within a real‐world context by examining the function’s table or graph. • use a given verbal description of the relationship between two quantities to label key features of a graph of a function that

Larson Math Nation6.16.26.36.46.56.66.76.86.9


LAFS.910.SL.1.1








LAFS.910.WHST.1.1





ELD.K12.ELL.SI.1 English language learners communicate for social and instructional purposes within the school setting.USA Sections 4‐6

q y g pmodel the relationship. • use the x‐intercepts of a polynomial function and end behavior to graph the function.• identify the x‐ and y‐intercepts and the slope of the graph of a linear function. • identify zeros, extreme values, and symmetry of the graph of a quadratic function.• graph a linear function using key features. • graph a quadratic function using key features.• identify and interpret key features of a graph within the real world context that the function represents.• 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.• differentiate between different types of functions using a variety of descriptors (e.g., graphically, verbally, numerically, and algebraically).• compare and contrast properties of two functions using a variety of function representations (e.g., algebraic, graphic, numeric in tables, or verbal descriptions).



Student Target Core

Students will …


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.b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.c. Use the properties of exponents to transform expressions for exponential functions.








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. b. Graph square root, cube root, and piecewise‐defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift.



MAFS.912.F‐LE.1.2Calculator: Neutral

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input‐output pairs (including reading these from a table).


Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.


Interpret the parameters in a linear or exponential function in terms of a context.

Standards

• use equivalent forms of an exponential expression to interpret the expression's terms, factors, zeros, maximum, minimum, coefficients, or parts in terms of the real‐world situation the expression represents.• determine the value of k when given a graph of the function and its transformation. • identify differences and similarities between a function and its transformation. • identify a graph of a function given a graph or a table of a transformation and the type of transformation that is represented. • graph by applying a given transformation to a function. • identify ordered pairs of a transformed graph. • complete a table for a transformed function.• write a recursive definition for a sequence that is presented as a sequence, a graph, or a table.• determine and relate the key features of a function within a real‐world context by examining the function’s table. • determine and relate the key features of a function within a real‐world context by examining the function’s graph. • use a given verbal description of the relationship between two quantities to label key features of a graph of a function that model the relationship.• identify and interpret key features of a graph within the real world context that the function represents.• graph an exponential function using key features.• classify the exponential function as exponential growth or decay by examining the base, and give the rate of growth or decay. • use the properties of exponents to interpret exponential expressions in a real‐world context. • write an exponential function defined by an expression in different but equivalent forms to reveal and explain different properties of the function, and determine which form of the function is the most appropriate for interpretation for a real‐world context.• compare a linear function and an exponential function given in real‐world context by interpreting the functions’ graphs.• compare a linear function and an exponential function given in a real‐world context through tables.


Section 7: Exponential Functions2017 - 2018

Mathematics Florida Standards Math Nation7.17.27.37.47.57.6

February 2 – February 14

Geometric Sequences

Comparing Arithmetic and Geometric Sequences

Exponential Functions

Graphs of Exponential Functions

Growth and Decay Rates of Exponential Functions

Transformations of Exponential Functions


LAFS.910.SL.1.1








LAFS.910.WHST.1.1






g• compare a quadratic function and an exponential function given in real‐world context by interpreting the functions’ graphs.• compare a quadratic function and an exponential function given in a real‐world context through tables.• write a linear function, an arithmetic sequence, an exponential function, or a geometric sequence when given a graph that models a real world context. • write a linear function, an arithmetic sequence, an exponential function, or a geometric sequence when given a verbal description of a real world context. • write a linear function, an arithmetic sequence, an exponential function, or a geometric sequence when given a table of values or a set of ordered pairs that model a real‐world context.• interpret the x‐intercept, y‐intercept, and/or rate of growth or decay of an exponential function given in a real‐world context.

FSQ Section 7



Student Target Core

Students will …MAFS.912.A‐APR.2.3Calculator: Neutral

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.


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.




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.










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).


Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.






Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.


Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.


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. b. Graph square root, cube root, and piecewise‐defined functions, including step functions and absolute value functions. c. Graph polynomials, identifying zeros when suitable factorizations are available, & showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift.

February 15 – March 7

Comparing Linear, Quadratic, and Exponential Functions

Comparing Arithmetic and Geometric Sequences

Exploring non‐Arithmetic, non‐Geometric Sequences

Modeling with Functions

Understanding Piecewise‐Defined Functions

Absolute Value Functions

Graphing Power Functions

Finding Zeros of Polynomial Funtions of Higher Degrees

End Behavior of Graphs of Polynomials

Graphing Polynomial Functions of Higher Degrees

Recognizing Even and Odd Functions

Solutions to Systems of Functions

Math Nation8.18.28.38.48.58.68.78.88.98.108.118.128.138.14

• identify zeros, extreme values, and symmetry of a quadratic function written symbolically.• find the zeros of a polynomial function when the polynomial is in factored form. • write an equation in one variable that represents a real‐world context.• identify the quantities in a real‐world situation that should be represented by distinct variables.• write a system of equations given a real‐world situation.• graph a system of equations representing a real‐world context using appropriate axis labels and scale.• write constraints for a real‐world context using equations, inequalities, a system of equations, or a system of inequalities. • interpret the solution of a real‐world context as viable or not viable.• solve a simple quadratic equation by inspection or by taking square roots.• solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring).• validate why taking the square root of both sides when solving a quadratic equation wil yield two solutions.• recognize that the quadratic formula can be used to find complex solutions.• create a rough graph of a polynomial function in factored form by examining the zeros of the function. • find a solution or an approximate solution for f(x) = g(x) using a graph. • find a solution or an approximate solution for f(x) = g(x) using a table of values.• find a solution or an approximate solution for f(x) = g(x) using successive approximations that give the solution to a given place value.• justify why the intersection of two functions is a solution to f(x) = g(x).• write an explicit function, define a recursive process, or complete a table of calculations that can be used to mathematically define a real‐world context.• write a function that combines functions using arithmetic operations and relate the result to the context of the problem. • write a function to model a real‐world context by composing functions. • determine the value of k when given a graph of the function and its transformation. • identify differences and similarities between a function and its transformation. • identify a graph of a function given a graph or a table of a transformation and the type of transformation that is represented. • graph by applying a given transformation to a function. • identify ordered pairs of a transformed graph. • complete a table for a transformed function.• use the definition of a function to determine if a relationship


Section 8: Summary of Functions2017 - 2018

Standards




Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).


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.


Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

LAFS.910.SL.1.1

Initiate and participate effectively in a range of collaborative discussions (one‐on‐one, in groups, and teacher‐led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well‐reasoned exchange of ideas.b. Work with peers to set rules for collegial discussions and decision‐making (e.g., informal consensus, votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.c. Propel conversations by posing/responding to questions that relate current discussion to broader themes or larger ideas; actively incorporate others into the discussion; clarify, verify, or challenge ideas and conclusions.d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.







LAFS.910.WHST.1.1

Write arguments focused on discipline‐specific content. a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. b. Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline‐appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. c. Use words, phrases, clauses to link major sections of text, create cohesion, & clarify the relationships between claim(s) & reasons, between reasons & evidence, and between claim(s) & counterclaims. d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented.





• use the definition of a function to determine if a relationship is a function, given tables, graphs, mapping diagrams, or sets of ordered pairs.• evaluate functions that model a real‐world context for inputs in the domain.• interpret statements that use function notation within the real‐world context given.write a recursive definition for a sequence that is presented as a sequence, a graph, or a table.• determine and relate the key features of a function within a real‐world context by examining the function’s table. • determine and relate the key features of a function within a real‐world context by examining the function’s graph. • use a given verbal description of the relationship between two quantities to label key features of a graph of a function that model the relationship.• interpret the domain of a function within the real‐world context given.• determine the feasible domain of a function that models a real‐world context.• calculate the average rate of change of a continuous function that is represented algebraically, in a table of values, on a graph, or as a set of data. • interpret the average rate of change of a continuous function that is represented algebraically, in a table of values, on a graph, or as a set of data with a real‐world context. • use the x‐intercepts of a polynomial function and end behavior to graph the function.• use the x‐intercepts of a polynomial function and end behavior to graph the function.• identify and interpret key features of a graph within the real world context that the function represents.• differentiate between different types of functions using a variety of descriptors (e.g., graphically, verbally, numerically, and algebraically).• compare and contrast properties of two functions using a variety of function representations (e.g., algebraic, graphic, numeric in tables, or verbal descriptions).• determine whether the real‐world context may be represented by a linear function or an exponential function and give the constant rate or the rate of growth or decay. • choose an explanation as to why a context may be modeled by a linear function or an exponential function. • compare a linear function and an exponential function given in real‐world context by interpreting the functions’ graphs.• compare a linear function and an exponential function given in a real‐world context through tables.• compare a quadratic function and an exponential function given in real‐world context by interpreting the functions’ graphs.• compare a quadratic function and an exponential function given in a real‐world context through tables.

FSQ Section 8



Student Target Core

Students will …MAFS.912.S‐ID.1.1Calculator: Neutral

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


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.


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

LAFS.910.SL.1.1

Initiate and participate effectively in a range of collaborative discussions (one‐on‐one, in groups, and teacher‐led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. Come to discussions prepared, having read, researched material under study; explicitly draw on that preparation by referring to evidence from texts & research on the topic or issue to stimulate a thoughtful, well‐reasoned exchange of ideas.b. Work with peers to set rules for collegial discussions and decision‐making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.d. Respond thoughtfully to diverse perspectives, summarize points of agreement & disagreement, and, when warranted, qualify/justify their own views & understanding & make new connections in light of the evidence & reasoning presented.







LAFS.910.WHST.1.1

Write arguments focused on discipline‐specific content. a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. b. Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline‐appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. c. Use words, phrases, & clauses to link the major sections of the text, create cohesion, & clarify the relationships between claim(s) & reasons, between reasons & evidence, & between claim(s) & counterclaims. d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented.

LAFS.910.WHST.2.4 Produce clear, coherent writing in which the development, organization, style are appropriate to task, purpose, & audience.





Section 9: One Variable Statistics2017 - 2018

• represent data using a dot plot, a histogram, or a box plot.• identify similarities and differences in shape, center, and spread when given two or more data sets.• use their understanding of normal distribution and the empirical rule to answer questions about data sets.• interpret similarities and differences in shape, center, and spread when given two or more data sets within the real‐world context given.• predict the effect that an outlier will have on the shape, center, and spread of a data set.

Math Nation9.19.29.3 9.49.59.69.79.89.9

March 8 – April 3

Dot Plots

Histograms

Box Plots

Measures of Center and Shapes of Distributions

Measures of Spread

The Empirical Rule

Outliers in Data Sets

FSQ Section 9


Standards



Student Target Core

Students will…

MAFS.912.S‐ID.2.5Calculator: Yes

Summarize categorical data for two categories in two‐way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.


Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association.


Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.


Compute (using technology) and interpret the correlation coefficient of a linear fit.


Distinguish between correlation and causation.

LAFS.910.SL.1.1









Standards

Math Nation10.110.210.310.410.510.610.7

April 4 – April 11

Relationship between Two Categorical Variables ‐ Marginal

and Joint Probabilities

Relationship between Two Categorical Variables

Conditional Relative Frequency

Scatter Plots and Function Models

Residuals and Residual Plots

Examining Correlation

• create or complete a two‐way frequency table to summarize categorical data.• determine if associations/trends are appropriate for the data.• interpret data displayed in a two‐way frequency table.• calculate joint, marginal, and conditional relative frequencies.• represent data on a scatter plot.• identify a linear function, a quadratic function, or an exponential function that was found using regression.• use a regression equation to solve problems in the context of the data.• calculate residuals.• create a residual plot and determine whether a function is an appropriate fit for the data.• interpret the slope and y‐intercept of a linear model that represents a set of data with a real‐world context.• determine the fit of a function by analyzing the correlation coefficient.• distinguish between situations where correlation does not imply causation.• distinguish variables that are correlated because one is the cause of another.


Section 10: Two Variable Statistics2017 - 2018


LAFS.910.WHST.1.1





ELD.K12.ELL.SI.1 English language learners communicate for social and instructional purposes within the school setting.USA Sections 7‐10



Student Target Core

Students will… MAFS.912.A‐APR.2.2Calculator: Neutral

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

MAFS.912.A‐APR.4.6Calculator: Neutral

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + 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), using inspection, long division, or, for the more complicated examples, a computer algebra system.


Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.


Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.


Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1.b. Verify by composition that one function is the inverse of another.c. Read values of an inverse function from a graph or a table, given that the function has an inverse.


Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

LAFS.910.SL.1.1








The School District of Palm Beach CountyALGEBRA 1 HONORS ONLY

Required Algebra 1 Honors Content2017 - 2018

Standards

Mathematics Florida Standards May 14 – May 25

Use Inverse Functions

Apply the Remainder & Factor Theorem

Find Rational Zero

Solve Radical Equations

Rewrite Rational Expressions

Solve Rational Equations

Analyze Geometric Sequences & Series

Find Sums of Infinite Geometric Series.

Use Normal Distributions

Math Nation

(Algebra 2)Various Topics

Larson Algebra 18.2 pt. 4

Larson Algebra 2

2.52.63.65.25.66.37.37.4

• Find and apply inverse functions. • Use theorems to factor polynomials.• Find all real zeros of polynomial functions.• Solve radical equations.• Graph rational functions.• Solve rational equations.• Study geometric sequences and series.• Find the sums of infinite geometric series.• Study normal distributions.


LAFS.910.WHST.1.1







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