jamesburg public schools

Jamesburg Public Schools Algebra Curriculum Map

JAMESBURG PUBLIC SCHOOLS

ALGEBRA CURRICULUM FRAMEWORK

ALGEBRA


Pacing September October November December January February March April May June

Topics and Chapter Titles

Topic 1: Solving Equations and Inequalities

Topic 2: Linear Equations Topic 3: Linear Functions

Topic 4: Systems of Linear Equations and Inequalities

Topic 4: Systems of Linear Equations and Inequalities Topic 5: Piecewise Functions

Topic 6: Exponents and Exponential Functions

Topic 7: Polynomials and Factoring

Topic 8: Quadratic Functions

Topic 9: Solving Quadratic Equations

Topic 10: Working with Functions

Topic 11: Statistics

September October November December January February March April May June

NJSLS

Domain

HSN.RN The Real Number System HSN.Q.A Quantities HSA.CED Creating Equations HSA.REI Reasoning with Equations and Inequalities

HSA.CED Creating Equations HSS.ID Interpreting Categorical and Quantitative Data HSF.LE Linear and Exponential Models HSF.IF InterpretingFunctions HSF.LE Linear and

HSA.REI Reasoning with Equations and Inequalities HSA.CED Creating Equations

HSA.REI Reasoning with Equations and Inequalities HSA.CED Creating Equations HSF.IF Interpreting Functions

HSN.RN Number and Quantity HSF.IF Interpreting Functions HSF.LE Linear and EXponential Models HSA.CED Creating Equations HSA.SSE See Structure in Expressions

HSA.APR Arithmetic with Polynomials and Rational Expressions HSA.SSE Seeing Structure in Expressions

HSA.CED HSF.IF Interpreting Functions HSF.BF Building Functions HSS.ID Interpreting Categorical and Quantitative Data HSA.REI Reasoning with Equations and

HSA.CED Creating Equations that describe numbers or relationships HSA.REI Reasoning with Equations and Inequalities HSA.SSE Seeing Structure in Expressions HSA.APR

HSF.IF InterpretingFunctions HSF.BF Building Functions

HSS.ID Interpreting Categorical and Quantitative Data


Exponential Models HSF.BF Building Functions HSS.ID Interpreting Categorical and Quantitative Data

HSF.BF Building Functions

Inequalities HSF.F.IF Interpreting Functions HSF.LE Linear and Exponential Models

Arithmetic with Polynomials and Rational Expressions HSF.IF InterpretingFunctions HSN.RN The Real Number System

District Assessments

-Fluency Assessment -Standard Based LinkIt

-Formative and Summative EnVision Assessments

-Formative and Summative EnVision Assessments enVision Cumulative Benchmarks Assessment Topics 1-2


-Formative and Summative Assessment -Standard Based LinkIt enVision Cumulative Benchmarks Assessment Topics 1-4



-Formative and Summative EnVision Assessments enVision Cumulative Benchmarks Assessment Topics 1-6

-Formative and Summative EnVision Assessments -NJSLA -Fluency Assessment

-Formative and Summative enVision Cumulative Benchmarks Assessment Topics 1-8 - Standard Based LinkIt



Mathematic Practices

MP.1 Make Sense of Problems and Persevere in Solving Them MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.5 Use Appropriate Tools Strategically MP.6 Attend to Precision

MP.1 Make Sense of Problems and Persevere in Solving Them MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.6 Attend to Precision MP.7 Look for and Make Use of Structure



MP.1 Make Sense of Problems and Persevere in Solving Them MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.5 Use Appropriate Tools Strategically MP.7 Look for and Make Use of

MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.6 Attend to Precision MP.7 Look for and Make Use of Structure MP.8 Look for and Express Regularly in Repeated Reasoning


MP.1 Make Sense of Problems and Persevere in Solving Them MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.5 Use Appropriate Tools Strategically MP.6 Attend to

MP.1 Make Sense of Problems and Persevere in Solving Them MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.6 Attend to Precision MP.7 Look for and Make Use of Structure

MP.2 Reason Abstractly and Quantitatively MP.3 Construct Viable Arguments & Critique the Reasoning of others MP.4 Model with Mathematics MP.5 Use Appropriate Tools Strategically MP.7 Look for and Make Use of Structure MP.8 Look for and Express Regularly in Repeated Reasoning


MP.7 Look for and Make Use of Structure MP.8 Look for and Express Regularly in Repeated Reasoning

MP.8 Look for and Express Regularly in Repeated Reasoning



Structure


Precision MP.7 Look for and Make Use of Structure MP.8 Look for and Express Regularly in Repeated Reasoning

MP.8 Look for and Express Regularly in Repeated Reasoning


NJSLS

Technology

NJSLS – Career Ready Practices

CRP2 CRP4 CRP6 CRP8 CRP11 CRP12










NJSLS- Interdisciplinary Connections

HS-ETS1-1 HS-ETS1-3

HS-ETS1-3 HS-ESS2-5 HS-ETS1-4

HS-ESS3-3 HS-ESS3-3 HS-ESS3-6 HS-LS2-1 HS-LS2-2

HS-ETS1-4 HS-ETS1-2 HS-ETS1-3

HS-ETS1-2 HS-ETS1-3

HS-PS3-3 HS-ETS1-2 HS-ESS3-2


Unit 1

Solving Equations and Inequalities

Unit Summary NJSLS Standards Essential Questions

Unit (Topic) 1: Focuses on extending students’ understanding of writing and solving equations and inequalities to include equations and inequalities that require multiple steps to solve, as well as those that have variables on both sides of the equation or inequality

HSN.RN.B.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.

HSA.CED.A.3

Represent constraints by equations or inequalities, and by

systems of equations and/or inequalities, and interpret

solutions as viable or nonviable options in a modeling

context. For example, represent inequalities describing

nutritional and cost constraints on combinations of different

foods.

HSA.CED.A.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. R

HSA.REI.A.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.

HSA.REI.B.3

Solve linear equations and inequalities in one variable,

including equations with coefficients represented by letters.

HSN.Q.A.1

Use units as a way to understand problems and to guide the

What general strategies can you use to solve simple equations and inequalities?


solution of multi-step problems; choose and interpret units

consistently in formulas; choose and interpret the scale and

the origin in graphs and data displays.

HSN.Q.A.2

Define appropriate quantities for the purpose of descriptive

modeling

Learning Goals:

● Find the sum or product of two rational numbers and explain why the sum or product is rational.

● Find the sum or product of a rational and irrational number and explain when the sum or product is irrational.

● Explain that each step in solving a linear equation follows from the equality in the previous step.

● Create and solve linear equations with one variable using the properties of equality.

● Use the properties of equality to solve linear equations with variables on both sides.

● Identify whether linear equations have one, infinitely many, or no solution.

● Rearrange formulas and equations to highlight a quantity of interest by isolating the variable using the same reasoning used to solve equations.

● Use formulas and equations to solve problems.

● Create and solve inequalities in one variable.

● Interpret solutions to inequalities within the context.

● Identify inequalities as true or false based on the number of solutions.

● Use mathematical modeling to represent a problem situation and to propose a solution.

● Interpret the solution to a compound inequality within a modeling context.

● Solve absolute value equations and inequalities.

● Use absolute value equations and inequalities to solve problems.

Vocabulary: element of a set, set, subset, identity, formula, literal equation, compound inequality

Modifications for Special Ed, ELL, Gifted Students, Students At-Risk of School Failure, Students with 504 Plans:

Re-teach/Intervention and Enrichment Activities (i.e. Diagnostic and Intervention System Lessons, ELL Toolkit resources, Project Based Learning

Math and Science STEM projects, Online tools and Practice Buddy, Vocabulary Cards)

Core Instructional Materials: Envision Algebra I series materials, Holt Algebra

Unit 1 Student Goals: End of topic assessments mastery, based on teacher expectations and student growth goals.


Unit 2

Linear Equations


Unit (Topic) 2: Focuses on extending students’ understanding of linear equations. Students analyze descriptions of lines and write their equation in different forms

HSA.CED.A.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 and

exponential functions.

HSA.CED.A.2

Create equations in two or more variables to represent

relationships between quantities; graph equations on

coordinate axes with labels and scales.

HSA.CED.A.3






foods.

HSA.CED.A.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.

HSS.ID.C.7

Interpret the slope (rate of change) and the intercept

(constant term) of a linear model in the context of the data.

HSF.LE.A.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).

Why is it useful to have different forms on linear equations?

Learning Goals:


● Write linear equations in two variables using slope-intercept form to represent the relationship between two quantities.

● Interpret the slope and the intercept of a linear model.

● Write and graph linear equations in point- slope form.

● Analyze different forms of a line to interpret the slope and y-intercept of a linear model in the context of data.

● Write and graph linear equations in standard form.

● Use linear equations in standard form to interpret both the x- and y-intercepts in the context of given data.

● Create equations to represent lines that are parallel or perpendicular to a given line.

● Graph lines to show an understanding of the relationship between the slopes of parallel and perpendicular lines.

● Solve real world problems with parallel or perpendicular lines.

Vocabulary:slope-intercept form, y-intercept, point-slope form, standard form of a linear equation, parallel lines, perpendicular lines, reciprocal




Core Instructional Materials: Envision Algebra I Series Materials, Holt Algebra


Unit 3

Linear Functions


Unit (Topic)3: Focuses on extending students’ understanding of linear equations to linear functions. Students learn methods to write, graph, and transform linear functions. They also apply analytic methods to tabular and graphic data sets that have linear relationships

HSF.IF.A.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).

HSF.IF.A.2

How can linear functions be used to model situations and solve problems?


Use function notation, evaluate functions for inputs in their

domains, and interpret statements that use function

notation in terms of a context.

HSF.IF.A.3

Recognize that sequences are functions, sometimes defined

recursively, whose domain is a subset of the integers. For

example, the Fibonacci sequence is defined recursively by

f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1

HSF.IF.B.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 n engines in a factory,

then the positive integers would be an appropriate domain

for the function.

HSF.IF.C.7

Graph functions expressed symbolically and show key

features of the graph, by hand in simple cases and using

technology for more complicated cases.

HSF.LE.A.2




(include reading these from a table).

HSF.BF.A.1

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. For

example, build a function that models the temperature of a

cooling body by adding a constant function to a decaying


exponential, and relate these functions to the model.

HSF.BF.A.2

Write arithmetic and geometric sequences both recursively

and with an explicit formula, use them to model situations,

and translate between the two forms.

HSF.BF.B.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

HSS.ID.B.6

Represent data on two quantitative variables on a scatter

plot, and describe how the variables are related.

a. Fit a function to the data (including with the use of

technology); 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, including with the use of technology.

C. Fit a linear function for a scatter plot that suggests a

linear association.

HSS.LD

Interpret linear models

C.7

Interpret the slope (rate of change) and the intercept

(constant term) of a linear model in the context of the data.

C.8

Compute (using technology) and interpret the correlation

coefficient of a linear fit.


C.9 Distinguish between correlation and causation.

Learning Goals:

● Understand that a relation is a function if each element of the domain is assigned to exactly one element in the range.

● Determine a reasonable domain and identify constraints on the domain and based on the context of real-world problem.

● Write and evaluate linear functions using function notation.

● Graph a linear function and relate the domain of a function to its graph.

● Interpret functions represented by graphs, tables, verbal descriptions, and function notation in context.

● Graph transformations of linear functions by identifying the effect of multiplying or adding specific values of k to the input or output of a function.

● Interpret the key features of the graph a linear function and use them to write the function that the graph represents.

● Write arithmetic and geometric sequences both recursive and with an explicit formula.

● Use explicit formulas and recursive formulas to model real-world situations.

● Fit a function to linear data shown in a scatter plot and use fitted functions to solve problems in the context of data.

● Interpret the slope of a trend line within the context of data.

● Compute and interpret the correlation coefficient for linear data.

● Plot and analyze residuals to assess the fit of a function.

● Distinguish between correlation and causation.

Vocabulary: continuous, discrete, domain, function, range, relation, function notation, linear function, transformation, translations, arithmetic sequence,

common difference, explicit formula, recursive formula, sequence, term of a sequence, negative association, negative correlation, no association, positive

association, trend line, causation, correlation, coefficient, extrapolation, interpolation, line of best fit, linear regression, residual






Unit 4

Systems of Linear Equations and Inequalities



Unit (topic) 4: Focuses on students extending their understanding of linear equations and inequalities to systems of linear equations and inequalities. Students learn methods to solve systems of linear equations and inequalities. Students identify when each solution method is most useful.

HSA.CED.A.2




HSA.CED.A.3






foods.

HSA.REI.C.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. New Jersey Student Learning Standards

for Mathematics 12

HSA.REI.C.6

Solve systems of linear equations exactly and approximately

(e.g., with graphs), focusing on pairs of linear equations in

two variables.

HSA.REI.D.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.

How do you use systems of equations and inequalities to model situations and solve problems?

Learning Goals:

● Graph systems of linear equations in two variables to find an appropriate solution. ● Write a system of linear equations in two variables to represent real-world problems. ● Use the substitution method to solve systems of equations. ● Represent situations as a system of equations and interpret solutions as viable/nonviable options for the situation. ● Solve systems of linear equations and prove that the sum of one equation and a multiple of the other produces a system with the same solutions as the


original system. ● Represent constraints with a system of equations in a modeling context. ● Graph solutions to linear inequalities in two variables ● Represent constraints with inequalities and interpret solutions as viable or nonviable options in a modeling context. ● Graph the solution set of a system of linear inequalities in two variables. ● Interpret solutions of linear inequalities in a modeling context.

Vocabulary: Linear inequality in two variables, solution of an inequality in two variables, solution of a system of linear inequalities






Unit 5

Piecewise Functions


Unit (Topic) 5: Focuses on extending the concept of functions to include absolute value functions and other piecewise-defined functions. Students identify the characteristics of each of these types of functions and understand that transformations can be applied to these functions.

HSF.IF.B.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.

HSF.IF.B.6

Calculate and interpret the average rate of change of a

How do you use piecewise-defined functions to model situations and solve problems?


function (presented symbolically or as a table) over a

specified interval. Estimate the rate of change from a graph.

HSF.IF.C.7.B

Graph square root, cube root, and piecewise-defined

functions, including step functions and absolute value

functions.

HSF.IF.C.9

Compare properties of two functions each represented in a

different way (algebraically, graphically, numerically in

tables, or by verbal descriptions). For example, given a

graph of one quadratic function and an algebraic expression

for another, say which has the larger maximum.

HSF.BF.B.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





expressions for them.

Learning Goals:

● Graph an absolute value function and identify the key features of the graph.

● Calculate and interpret the rate of change an absolute value function over a specified interval.

● Understand and graph piecewise-defined functions.

● Analyze the key features of the graph of a piecewise-defined function.

● Write and interpret a piecewise-defined function to solve application problems.

● Graph step functions including ceiling functions and floor functions.

● Calculate and interpret the average rate of change of step functions.

● Graph transformations of piecewise-defined functions.

● Identify the effect of changing constants and coefficients of absolute value functions on their graphs.

Vocabulary: absolute value function, piecewise-defined function, ceiling function, floor function, step function,







Unit 6

Exponents and Exponential Functions


Unit (Topic) 6: Focuses on extending knowledge of functions to include the exponential function. Students learn to identify, write, graph, and transform exponential functions. Students use exponential functions to model real-world situations and make predictions

HSN.RN.A.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 51/3 to be the cube root of 5 because we want (51/3)

3 = 5(1/3) 3 to hold, so (51/3) 3 must equal 5.

HSN.RN.A.2

Rewrite expressions involving radicals and rational

exponents using the properties of exponents.

HSN.Q.A.3

Choose a level of accuracy appropriate to limitations on

measurement when reporting quantities.

HSF.IF.A.3

Recognize that sequences are functions, sometimes defined

recursively, whose domain is a subset of the integers. For

example, the Fibonacci sequence is defined recursively by

How do you use exponential functions to model situations and solve problems?


f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

HSF.IF.B.4








periodicity

HSF.IF.B.5




person-hours it takes to assemble n engines in a factory, then

the positive integers would be an appropriate domain for the

function

HSF.IF.C.9


different way (algebraically, graphically, numerically in tables,

or by verbal descriptions). For example, given a graph of one

quadratic function and an algebraic expression for another,

say which has the larger maximum.

HSF.BF.A.1


quantities.

HSF.BF.A.2

Write arithmetic and geometric sequences both recursively

and with an explicit formula, use them to model situations,

and translate between the two forms.

HSF.BF.B.3









HSF.LE.A.1

Distinguish between situations that can be modeled with

linear functions and with exponential functions.

HSF.LE.A1.A

Prove that linear functions grow by equal differences over

equal intervals, and that exponential functions grow by equal

factors over equal intervals

HSF.LE.A




(include reading these from a table)

HSF.LE.B.5

Interpret the parameters in a linear or exponential function

in terms of a context.

HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of

their parts as a single entity. For example, interpret P(1+r) n

as the product of P and a factor not depending on P

HSA.SSE.B.3.C

Use the properties of exponents to transform expressions for

exponential functions. For example the expression 1.15t can

be rewritten as (1.151/12) 12t ≈1.01212t to reveal the

approximate equivalent monthly interest rate if the annual

rate is 15%

Learning Goals:

● Extend the properties of integer exponents to rational exponents to rewrite radical expressions using rational exponents.

● Solve equations with rational exponents using the properties of exponents


● Sketch graphs showing key features of exponential functions

● Write exponential functions using tables and graphs.

● Compare linear and exponential functions.

● Construct exponential growth and decay functions given a description of a relationship.

● Recognize if a situation can be modeled with exponential growth or exponential decay, and interpret the parameters of the model in context.

● Find explicit and recursive formulas for geometric sequences.

● Translate between recursive and explicit formulas for geometric sequences.

● Construct exponential functions to represent geometric sequences.

● Translate the graph of an exponential function vertically and horizontally, identifying the effect different values of h and k have on the graph of the

function.

● Compare characteristics of two exponential functions represented in different ways, such as tables and graphs.

Vocabulary: rational exponent, asymptote, constant ratio, exponential function, compound interest, decay factor, exponential decay, exponential growth,

growth factor, geometric sequence






Unit 7

Polynomials and Factoring


Unit (Topic) 7: Focuses on extending polynomials. Students identify the parts and factors of polynomials. Students understand how to factor trinomials using the

HSA.APR.A.1

HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of

How do you work with polynomials to rewrite expressions and solve problems?


greatest common factor, binomial factors, and special patterns. Students learn methods to add, subtract, and multiply polynomials.

its context.

1.A

Interpret parts of an expression, such as terms, factors, and

coefficients. b. Interpret complicated expressions by viewing

one or more of their parts as a single entity. For example,

interpret P(1+r) n as the product of P and a factor not

depending on P

HSA.SSE.A.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 ).

HSA.APR.A.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.

Learning Goals:

● Identify the parts of a polynomial ● Classify polynomials by number of terms and by degree ● Write a polynomial in standard form ● Add or subtract two polynomials ● Use the Distributive Property with polynomials, recognizing that polynomials are closed under multiplication ● Multiply polynomials using a table and an area model ● Determine the square of a binomial ● Find the product of a sum and difference of two squares ● Solve real-world problems involving the square of a binomial ● Find the greatest common factor of the terms of a polynomial ● Use the structure of a polynomial to rewrite it in factored form ● Factor polynomials that represent real-world problems ● Factor a trinomial in the form x^2+bx+c by finding two binomial factors whose product is equal to the trinomial ● Identify and use patterns in the signs of the coefficients of the terms of a trinomial expression ● Identify the common factor of the coefficients in the terms of a trinomial expression when a is not equal to 1 ● Write a quadratic trinomial as a product of two binomial factors ● Identify and factor a trinomial that is a perfect square or a binomial that is a difference of two squares


● Factor special cases of polynomials within the context of real-world Vocabulary: Closure property, degree of a monomial, degree of a polynomial, monomial, polynomial, standard form of polynomial, differences of two squares,

perfect square trinomial






Unit 8

Quadratic Functions


Unit (Topic) 8: Focuses on extending students’ previous understanding of functions to include quadratic functions: graphing them, using them to model real-world situations, and comparing them to linear and exponential functions

HSA.CED.A.2




HSF.IF.A.2

Use function notation, evaluate functions for inputs in their

domains, and interpret statements that use function

notation in terms of a context. 3. Recognize that sequences

are functions, sometimes defined recursively, whose

domain is a subset of the integers. For example, the

Fibonacci sequence is defined recursively by f(0) = f(1) = 1,

f(n+1) = f(n) + f(n-1) for n ≥ 1.

HSF.IF.B

How can you use sketches and equations of quadratic functions to model situations and make predictions?


Interpret functions that arise in applications in terms of the

context

B.4








periodicity.

B.6



specified interval. Estimate the rate of change from a graph

C. 7

Graph functions expressed symbolically and show key

features of the graph, by hand in simple cases and using

technology for more complicated cases.

C.7.A

Graph linear and quadratic functions and show intercepts,

maxima, and minima.

C.8

Write a function defined by an expression in different but

equivalent forms to reveal and explain different properties of

the function.

C.9


different way (algebraically, graphically, numerically in tables,

or by verbal descriptions). For example, given a graph of one

quadratic function and an algebraic expression for another,

say which has the larger maximum.

HSF.BF.A.1



quantities

HSF.BF.B.3








HSS.ID.B.6.A

Fit a function to the data (including with the use of

technology); 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.

HSS.ID.B.6.B

Informally assess the fit of a function by plotting and

analyzing residuals, including with the use of technology.

HSA.REI.D.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)

Learning Goals:

● Identify key features of the graph of a quadratic function using graphs, tables, and equations

● Explain the effect of the value of a on the quadratic parent function

● Identify key features of the graph of quadratic functions written in vertex form

● Graph quadratic functions in vertex form

● Graph quadratic functions in standard form and show intercepts, maxima, and minima

● Determine how the values of a,b,and c affect the graph of f(x)=ax^2+bx+c

● Identify key features of parabolas

● Compare properties of quadratic functions presented in different forms (algebraically, in a table, graphically)

● Use quadratic functions fitted to data to model real-world situations

● Use the vertical motion model to write an equation


● Compare a model to a data set by analyzing and evaluating residuals

● Determine which model-linear, exponential, or quadratic - best fits a set of data

● Use fitted functions to solve problems in the context of data

Vocabulary: parabola, quadratic parent function, vertex form of a quadratic function, vertical motion regression,






Unit 9


Unit (Topic) 9: Focuses on extending knowledge of quadratic functions. Students learn to solve quadratic equations using tables, graphs and factoring. Students also solve quadratic equations using square roots, completing the square, and the quadratic formula. Students learn different methods, such as graphing, elimination, and substitution, for solving linear-quadratic systems

HSA.CED.A

A.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 and exponential

functions.

A.2




A.3




How do you use quadratic equations to model situations and solve problems?




foods

HSA.SSE.A.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 ).

HSA.SSE.B.3

Choose and produce an equivalent form of an expression to

reveal and explain properties of the quantity represented by

the expression.

B.3.A

Factor a quadratic expression to reveal the zeros of the

function it defines.

B.3.B

Complete the square in a quadratic expression to reveal the

maximum or minimum value of the function it defines.

HSF.IF.C.8.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.

HSA.REI.B.4.A and B

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.

HSA.REI.D.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.

HSA.REI.C.7

Solve a simple system consisting of a linear equation and a

quadratic equation in two variables algebraically and

graphically. For example, find the points of intersection

between the line y = –3x and the circle x2 + y2 = 3.

HSA.APR.B.3

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

HSN.RN.A.2

Rewrite expressions involving radicals and rational

exponents using the properties of exponents.

Learning Goals

● Use a graph to identify the x-intercepts as solutions of a quadratic equation

● Use a graphing calculator to make a table of values to approximate or solve a quadratic equation

● Use the Zero-Product Property and factoring to find the solutions of a quadratic equation

● Apply factoring to solve real-world problems

● Use the zeros of a quadratic equation to sketch a graph


● Write the factored form of a quadratic function from a graph

● Use properties of exponents to rewrite radical expressions

● Multiply radical expressions

● Write a radical expression to model or represent a real-world problem

● Solve quadratic equations by finding square roots

● Determine reasonable solutions for real-world problems

● Solve a quadratic trinomial by completing the square to transform a quadratic equation into a perfect square trinomial

● Use completing the square to write a quadratic equation i n vertex form

● Derive the quadratic formula by completing the square

● Solve quadratic equations in one variable by using the quadratic formula

● Use the discriminant to determine the number and type of solutions to a quadratic equation

● Describe a linear-quadratic system of equations

● Solve a linear-quadratic system of equations by graphing, elimination, or substitution

Vocabulary: quadratic equation, zeros of a function, standard form of a quadratic function, Zero-Product Property, Product Property of Square Roots, completing

the square, discriminant, quadratic formula, root, linear-quadratic system






Unit 10

Working with Functions


Unit (Topic) 10: Extends students’ knowledge of functions to include radical functions. Students identify the key features

HSF.IF.B.4


What are some operations on functions that you can use to create models and solve problems?


of the graphs of radical functions. They also learn to transform functions, combine functions, and find inverse functions.







periodicity.

HSF.IF.B.5




person-hours it takes to assemble n engines in a factory,

then the positive integers would be an appropriate domain

for the function.

HSF.IF.B.6



specified interval. Estimate the rate of change from a graph.

HSF.IF.C.7.B

Graph square root, cube root, and piecewise-defined

functions, including step functions and absolute value

functions.

HSF.BF.A.1.B

Combine standard function types using arithmetic

operations. For example, build a function that models the

temperature of a cooling body by adding a constant

function to a decaying exponential, and relate these

functions to the model.

HSF.BF.B.3









HSF.BF.B.4

Find inverse functions.

HSF.BF.B.4.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.

Learning Goals:

● Graph translations of the square root function ● Calculate and interpret the average rate of change for a square root function over a specified interval ● Identify key features of the graph of cube root functions and graph translations of them ● Model real-world situations using the cube root function ● Calculate and interpret The average rate of change of a cube root function over a specific interval ● Relate the domain and range of a function to its graph ● Analyze the key features of the graph of a function to identify the type of function it represents ● Graph translations of absolute value, exponential, quadratic, and radical functions ● Determine how combining translations affects the key features of the graph of a function ● Identify the effect on the graph of a function of multiplying the output by -1 ● Identify the effect on the graph of a function of replacing f(x) by kf(x) or F(kx) for specific values of k ● Combine functions using arithmetic operations, including addition, subtraction, and multiplication ● Combine functions to solve real world problems ● Write an equation for the inverse of a linear function ● Write the inverse of a quadratic function after restricting the domain so the original function is one-to-one

Vocabulary: square root function, cube root function, inverse of a function







Unit 11

Statistics


Unit (Topic) 11: Focuses on extending students’ knowledge of dot plots, box plots, and histograms. Students identify that standard deviation is used to compare a specific value to other values. Students understand how to find joint, marginal, and relative frequencies. Students learn methods to interpret data displays and create inferences based on the data

HSS.ID.A

A.1

Represent data with plots on the real number line (dot

plots, histograms, and box plots).

A.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.

A.3

Interpret differences in shape, center, and spread in the

context of the data sets, accounting for possible effects of

extreme data points (outliers).

HSS.ID.B.5

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

How do use statistics to model situations and solve problems?

Learning Goals:

● Represent data using dot plots, box plots, and histograms ● Interpret the data displayed in dot plots, box plots, and histograms within the context of the data that it represents ● Use measures of center to interpret and compare data sets displayed in dot plots, box plots, and histograms ● Explain and account for the effect of outliers on measures of center and variability ● Use measures of variability, such as the MAD and IQR, to interpret the compare the data sets ● Interpret and compare differences in the shape, center, and spread of data of different data sets


● Determine the relationship between the mean and median of a data set when the shape of the data is evenly spread, skewed right, or skewed left ● Interpret differences in the variability of spread in the context of a data set ● Calculate the standard deviation of a data set and use it to compare and interpret data sets ● Organize and summarize categorical data by creating two-way frequency tables ● Calculate and interpret joint and marginal frequencies, joint and marginal relative frequencies, and conditional relative frequencies, and use them to make

inferences about a population Vocabulary: normal distribution, standard deviation, variance, conditional relative frequency, joint frequency, joint relative frequency, marginal frequency,

marginal relative frequency,






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