Math-Algebra 1 Core Map Quarter 1
| Subject/Grade Level/Unit Title | Timeframe/Grading Period | Big Idea/Themes/Understandings | Essential Questions | Standards | Essential Skills | Vocabulary | Assessment Tasks | Resources | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
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 Roots and Radicals Cube and other Roots Simplifying Square Root Radical Classifying Real Numbers Operations with Radicals 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 Roots and Radicals Rational and Irrational numbers (define and classify) Simplifying square root radicals Rationalizing square roots Simplifying radicals Operations with radicals 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?
|
|
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 Perform operations (add, subtract, multiply and divide) with radicals 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 additive identity additive inverse 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 radical radicand 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
|
