Last updated: 5/26/2015

## Math-Algebra 1 Core Map Quarter 2

Linear Functions

Function tables and notation

Domain and Range

Discrete and Contiuous

Linear Function Pattern

Special Functions

Comparing Linear and Nonlinear

Arithmetic Sequences

Solving Inequalities using addition and Subtraction

Solving inequalities using multiplication and division

Solving multi-step inequalities

Graphing linear inequalities with two variable with two variables

Solving Geometric problems using inequalities

Solving system of inequalities

Absolute value inequalities and graphing on the number line

Graphing absolute value functions

Key features

Transformation of graph

Polynomials

Operations with polynomials

Multiplying a monomial by a monomial

Multiplying a polynomial by a monomial

Factoring

Factoring polynomials

Factoring greatest common factor

Factoring the difference of two perfect squares

Factoring trinomials

With lead coefficients other than one

Factoring Special Products

Perfect Square Trinomials

Product of the sum and difference

Factoring Completely

Factoring by grouping

Quarter 2

Linear Functions

Discrete and Continuous Domains

Linear Function Patterns

Special Functions-Piecewise, absolute value and step functions

Function Notation

Comparing Linear and Nonlinear Functions

Arithemetic Sequences

Writing and Graphing Inequalities

Solving Inequalities Using Addition or Subtraction

Solving Inequalities Using Mulitplication and Division

Solving Multi-step Inequalities

Solving Compound Inequalities

Graphing Linear Inequalities in two variables

Solving Systems of Inequalities

Polynomials

Multiplying Polynomials

Special Products of Polynomials

Solving Polynomial Equations in Factored Form

Factoring

Factoring Polynomials using GCF

Factoring trinomials with lead coefficient on 1

Factoring trinomials with lead coefficient other than 1

Factoring special products

Factoring by grouping

Factoring completely

Linear Functions

How can we determine if a relation is a function?

How can you find the domain and range of a function?

How are independent variables and dependent variables different?

Why does the vertical line test help determine if a relation is a function?

How can we determine if a function is discrete or continuous?

How can you use a linear function to describe a linear pattern?

Why is a linear function a graph of a non-linear line?

How can you use function notation to represent a function?

How can you recognize when a pettern in real life is linear or nonlinear?

How do graph a piecewise function?

What real life situations can be modeled by piecewise functions?

How do we graph step functions?

What real life situations can be modeled by step functions?

How do we graph absolute value functions?

What real life situations can be modeled by absolute value functions?

Does a non-linear function have a constant rate of change?

How are arithmetic sequences used to describe a pattern?

How does an inequalitiy statement differ from an equation?

How can we determine the solutions to the inequality?

How can we graph (display) the solutions to an inequaltiy?

What are alternate ways we can describe solution sets?

When do we include the stated value and when do we exclude it?

What are real life situations that can be modeled by inequalities?

What properties hold true when solving inequalities?

Can you explain why those that do not, do not?

Can can you use an inequalitiy to describe the area and perimeter of a composite figure?

What does a compound inequality represent?

How does an absolute value inequality look on a graph?

How can we represent solutions to inequalities with two variables on a coordinate plane?

How can we know exclusivity or inclusivity on the boundry lines?

Polynomials

How can you use algebra tilles to model and classify polynomials?

How can you determine the degree of a polynomial?

How can we find a sum of polynomials?

How can we determine the difference of polynomials?

Can you describe the difference in finding a sum and difference of polynomials?

What methods can be used to find the product of two binomials?

Can you determine the patterns of special products?

How can you solve an equation that is written in factored form?

What is the connection between the roots, solutions and zeros of a polynomial equation?

Factoring

How can we rewrite a polynomial as the product of factors?

What is the only type of binomial that factors into two binnomials? Why?

What do the signs in the binomal factors tell you about the polynomial in standard form?

Can you recgonize and factor special products?

How does using commutative and associative properties help us to factor by grouping?

What do like terms physically look like?

 (1) A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (1) A-APR.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. (1) A-CED.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. (1) A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (1) A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (1) A-REI.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). (1) A-REI.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.★ (1) A-REI.12 Graph the solutions to a linear inequality in two variables as a halfplane (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. (1) A-REI.4 Solve quadratic equations in one variable. (1) A-SSE.1 Interpret expressions that represent a quantity in terms of its context. (1) A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients. (1) A-SSE.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. (1) A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2). (1) A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (1) F-IF.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). (1) F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (1) F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Linear Functions

Use the vertical line test to determine if a given relation is a function

Determine the domain and range of a function

Write the domain and range in multiple forms

Determine restrictions of domain and range

Determine if a domain is discrete or continuous

Write functions and graph functions based on real life situations

Examine patterns in functions

Use patterns to write functions

Determine the common differences in linear functions

Graph and state domain and ranges of piecewise, absolute value and step functions

Examine the translations of the functions

Solve multi-step inequalties in one variable

Graph solutions to inequalities on number line

Solve compound inequalities and graph on the number line

Solve absolute value inequalities and graph on the number line

Solve multi-step absolute value inequalities and graph on the number line

Solving and graphing inequalities with two variables and graph on the coordinate plane

Solve geometric problems with inequalities

Polynomials

Determine if a term is a monomial

Determine the number of terms and degree of a given polynomial

Add, subtract, mulitply and divide polynomials (by monomials only)

Factoring

Factoring polynomials using GCF

Factoring binomials

Factoring trinomials

Factoring completely

Factoring by grouping

Functions

relations

function

function notation

discrete function

continuous function

vertical line test

function notation

intercepts

positive, negative, increasing, decreasing, extrema and end behavior

relative minimum

relative maximum

constant function

constant of variation

dependent variable

dependent axis

direct variation

domain

indentity function

independent axis

independent variable

intercept

linear function

parallel

perpendicular

range

rate of change

compound inequalities

inclusive

exclusive

inverses functions

modeling with linear functions

non-linear functions

absolute value functions

absolute value inequalities

sequence

arithmetic sequene

common difference

Polynomials

term

monomial

polynomial

degree of monomial

degree of polynomial

binomial

trinomial

special products

distribute

double distribute

Factoring

factoring

standard

non-standard form

factored form

zero-property

roots

greatest common factor

differene of two perfect squares

factoring by grouping

prime polynomial

factored completely

Pass the paper

Pair share

Exit Notes

Classroom Assessments

Writing prompt

Dailly spiral review

Weekly spiral review

Benchmarks

Self-Correcting Lab Assessment

Algebra I Core Assessment

STARS Assessment

Algebra 1 - McGraw Hill Education

Algebra 1- Amsco School Publications

Big Ideas Algebra 1- Big Ideas Learning

NYS Modules