Last updated: 5/26/2015

## Math-Algebra 1 Core Map Quarter 1

Algebra I Core

Number Sense and Operations/Solving Equations and Inequalities

Order of Operations

Algebraic Properties

Evaluating Algebraic Expressions and Formulas

Algebraic Operations

Solving Linear Equations

Solving Linear Equations by adding and subtracting

Solving Linear Equations by multiplying and dividing

Solving Multi-step Equations

Solving Equations with Variables on Both Sides

Solving Equations using LCM

Solving Literal Equations

Rewriting Formulas

Solving Proportional Equations

Exponents and Operations with Exponents

Cube and other Roots

Classifying Real Numbers

Scientific Notation

Significant Digits

Units of Measure

Accuracy and Precision

Solving Inequalities

Modeling Equations and Inequalities

Linear Equations/Functions

Graphing Linear Equations

Direct Variation

Slope of a Line from a graph

Slope Formula

Graphing and Writing Linear Equations Using Slope-Intercept Form/Point-slope form and Standard form

Slopes with parallel and perpendicular lines

Functions- determining

Domain and Range

Inverse Functions

Modeling with Functions

Arithmetic Function

Systems of Linear Functions

Solving Systems of Equations by Graphing

Solving Systems of Equations by Substituting

Solving Systems of Equations by Elimination

Solving Systems of Inequalities by graphing

Quarter 1

Number Sense and Operations/Solving Equations and Inequalities

Defining Expressions and Equations

Real number system and subsets of real numbers

Operations with integers and rational numbers

Properties of real numbers:

Commutative, Associative, Distributive, Additive Identity and Inverse,

Multiplicative Identity and Inverse and Closure

Order of Operations with absolute value, powers, fractional groups and mixed numbers

Utilizing the graphing calculator TI-84 plus

Solving two step equations

Solving equations with variables on both sides

Solving equations with multi-steps including distributive property

Solving proportional equations

Solving fractional equations by creating an equivalent equation (mult by LCM)

Literals/Rewriting formulas

Exponents

Laws of Exponents (product, quotient and power to exp)

Zero and negative exponents

Multiplying and dividing monomials

Simplifying expressions with powers

Rewrite expressions with positive exponents

Scientific Notation and Significant Digits

Accuracy and precision

Rational and Irrational numbers (define and classify)

Rationalizing square roots

Writing and translating Algebraic Expressions

Translating and writing formulas

Solving problems

*Word problems-find missing values

*Consecutive integer problems

*Age problems

*Coin problems

*Geometric application

*Work problems

*Motion problems

Ratios, rates and proportions

Solving simple inequalities, examining solution sets

Solving multi-step inequalities

Solving compound inequalities

Solving absolute value equations

Linear Equations/Linear Functions

Graphing lines parallel to an axis

Graphing proportional lines -direct variation

Proportional and non-proportional graphs

Determining the slope of lines

Slopes of parallel and perpendicular lines

Graphing lines using table

Graphing lines from the equations

Finding intercepts on the graph

Finding intercepts algebraically

Graphing from intercepts

Zeros of a graph

Writing equations of lines (slope-intercept, point-slope, standard form)

Arithmetic Sequences as linear functions

Technology involving linear functions

Defining a function

Determining its domain and range

Inverse functions

Systems of Equations

The shared points of equations are solutions to the system of equations

There are three methods to solving systems of equations:graphing, substitution, elimination

There are cases where all points are shared and situations where there are no shared points-no solution

You can determine the cases by examining slopes and intercepts

Systems of Equations

Consistent

dependent

inconsistent

independent

system of equations

intersection

solution

elimination

substitution

Number Sense and Operations/Solving Equations and Inequalities

How do describe a value mathematically?

How do we calculate the value of an expression containing multiple operations?

How do we create one statement of division to represent signed mixed numbers?

How do groups affect our plan for evaluating an expression?

How do expressions and equations differ?

What is equality?

What happens when you multiply, divide, add, and subtract real numbers?

Is it useful to write numbers in different ways?

How can we use exponents to write products?

How do we define a zero exponent?

What does a negative exponent mean?

How do we write numbers in scientific notation?

How can we determine sides of a square when given the area?

Why and when might you need cubed and square roots?

Where are irrational numbers on the number line?

How many numbers lie between two numbers on the number line?

What is equivalence?

How do we determine the values that make two expressions equivalent?

What properties maintain equivalence?

How can you solve a multi-step equation?

How can you be sure your solution is reasonable?

Can we determine the correctness of a solution?

Can we solve equations that have variables on both sides?

Why would we need to rewrite formulas?

What does absolute value tell you?

Why can absolute value not result in negative values?

How can we use equations and inequalities to represent real life situations?

Do all properties hold true when applied to solving inequalities?

How can we determine if roots represent rational or irrational numbers?

Can we add, subtract, multiply and divide square roots?

Why would we not leave an irrational number as the denominator of a fraction?

How can we use inductive reasoning to observe patterns and write rules involving properties of exponents?

How can we determine the accuracy of an value in measurement?

Can we predict future situations using ratios, rates and proportions?

Linear Equations/Functions

How can you recognize a linear equation?

How can slopes be used to describe a line?

How can you describe a line in y = mx + b?

How can you describe the graph of the line of the equation ax+by=c?

How can we determine if points are on a given line?

What information would we need to write the equation of a line?

How many points do we need to define a line?

How can we determine if a set of points lie on the same line?

How can we write equations of lines when given the slope and a point?

Can we use a linear equation to model and solve real-life problems?

How can we describe the behavior of a graphed line?

Systems of Linear Equations

Why are points of intersection considered the solution to systems?

Are there cases where their would be either no-solutions or infinite solutions?

How can we confirm a point is a shared solution to equations?

 (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.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-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. (1) A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (1) 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.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.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (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) F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (1) 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-IF.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. (1) F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ (1) F-IF.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.★ (1) F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (1) F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima. (1) F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (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). (1) N-Q.1 Use units as a way to understand problems and to guide the 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. (1) N-Q.2 Define appropriate quantities for the purpose of descriptive modeling. (1) N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (1) N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. (1) N-RN.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.

Number Sense and Operations/Solving Equations and Inequalities

Evaluate expressions using order of operations

Evaluate expression in graphing calculator

Evaluate algebraic expressions using algebraic properties

Recognize and use algebraic properties

Classify and describe real number sets and subsets

Solve one, two and multi-step equations

Solve equations with distributing and variables on both sides

Solve fractional equations by creating an equivalent equation (mult by LCM)

Solving literals using algebraic properties

Solving proportional equations

Recognizing powers, their bases and exponents

Expand and evaluate powers

Write products as powers

Evaluate/simplify powers using laws of exponents (product, quotient, power to exp)

Demonstrate understanding of zero and negative exponents

Evaluate powers using laws (with negative and zero exponents)

Evaluate expressions with powers

Determine if the root of a number is rational or irrational

Find square and cubed roots of numbers

Simplifying square and cubed roots

Identify the significant digits of given numerical values

Determine the measure of precision and greatest possible error

Translate verbal situation to algebraic expressions and equations

Determine the rate of described situations

Solve problems using rations, rates and proportions

Solve and graph inequalities and their solution sets

Determine if an element in a given set is a solution to a given inequality

Solve and graph compound inequalities

Write the solutions to inequalities in set notation form

Model linear equations and inequalities

Linear Equations/Functions

Recognize the parts of the coordinate plane (axes, quadrants, origin)

Define a linear equation

Graph linear equations (from points, intercepts, slope-intercept form of equation)

Determine if points are on a given line

Determine if three or more points are co-linear

Recognized the different forms of linear equations

Rewrite linear equations in different forms of equations

Determine the zeros of a linear function

Solve linear functions by graphing

Interpret slope and intercept of situations modeled by linear functions

Graph linear functions with graphing calculator-predict coordinates of other points on the line

Determine the slope of a line from a graph, from two points, from the formula

Use the slope to find a missing coordinate of two points

Explain reasoning of slopes of lines parallel to the axes

Recognize equation of direct variation

Graph and recognize proportional graphs

State the constant of proportionality of proportional lines

Use an equation of direct variation to predict values

Recognize an arithmetic sequence, predict future terms of the sequence

Write linear equations representing arithmetic sequences

Writing equations of non-proportional lines from verbal situations

Systems of Equations

Graph systems of equations and determine and check solutions

Solve systems of equations using substitution property and check solutions

Solve systems of equations using elimination and check solutions

Identify by slopes and intercept if there is one distinct solution, infinite or no-solutions

Number Sense and Operations/Solving Equations and Inequalities

absolute value

accuracy

algebraic equation

algebraic expression

associative property

base

closed

coefficient

commutative property

compound inequalities

constant

cross products

cubed root

distributive property

element

evaluate

exponent

factor

formula

greatest possible error

grouping symbols

identity property

index

inequality

integer

interval of measure

irrational number

like terms

literal equations

multiplicative inverse

opposites

order of operations

open sentence

perfect square

proportions

non-perfect square

null/empty set

power

precision

principal square root

product

properties of arithmetic operations

rate

rational number

reciprocal property

replacement set

root

scientific notation

significant digits

simplest form

solution set

square

square root

solution set

term

variable

zero property

Linear Equations/Linear Functions

arithmetic sequence

common difference

constant

constant of variation

direct variation

deductive reasoning

inductive reasoning

linear equation

linear function

rate of change

root

sequence

slope

standard form

terms of a sequence

x-intercept

y-intercept

zero of a function

independent variable

dependent variable

abscissa

ordinate

coordinates

domain

range

parent function

parallel

perpendicular

domain

range

Systems of Equations

consistent

inconsistent

dependent

independent

intersection

substitution

elimination

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