Algebra 1 Duxbury Middle School > > Grade 8 > Mathematics > Algebra 1 > Iacadoro, Stephanie Tuesday, February 28, 2017, 11:58AM

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1 Algebra 1 Duxbury Middle School > > Grade 8 > Mathematics > Algebra 1 > Iacadoro, Stephanie Tuesday, February 28, 2017, 11:58AM Unit Unit 0: Preparing for Algebra * for 282 only (Week 1, 9 Skills needed to prepare for Algebra Why is it helpful to write numbers and data in different ways? Demonstrate mastery of pre-algebra, basic geometry and basic statistics skills plan for problem solving classify and use real numbers operations with integers compare and order rational number multi-digit operations with rational numbers using the percent proport find simple probabilities find the perimeter of 2-deminssional figures find the area of 2- deminssional figures calculate volume and surface area of prisms and cylinders finding simple probability and odds Representing data with graphs and measures of central tendency Prerequisites: whole number operations fraction operations Topic List: plan for problem solving real numbers operations with integers adding and subtracting rational numbers multiplying and dividing rational numbers the percent proportion perimeter area volume surface area simple probability and odds measures of center, variation and position representing data Vocabulary: positive number, negative number, natural numbers, whole number, integer, rational number, square root, perfect square root, irrational number, graph coordinate, absolute value, opposites, additive inverse, multiplicative inverse, reciprocal, percent proportion, area, volume, surface area, probability, sample space equally likely, complements, tree diagram, odds, variable, dat, measurement or qualitative data, univariate data, measures of center or central tendency,mean, median, mode, range, quartile, measures of position, lower quartile, upper quartile, inter-quartile range, outliers, frequency table, bar graph, cumulative frequency, histogram, line graph, box-and-whisker plot

2 Unit 1: Relations Between Quantities *All courses (Week 1, 6 Relationships between quantities. What is equivalence? How can you communicate mathematical ideas effectively? How do we determine the value of an unknown quantity? Write algebraic expressions Use the Order of Operations Solve equations Use Properties of Addition and Multiplication Represent and interpret relations Use function notation Interpret the graphs of functions Create equations that describe relationships Solve linear equations in one variable Solve proportions Find Percent of Change Use formulas to solve real-world problems Prerequisites Operations on whole numbers Evaluate and Simplify algebraic expressions Topic List Variables and Expressions Order of Operations Properties of Numbers The Distributive Property Equations Relations Functions Interpreting Graphs of Functions Writing Equations Solving One-Step and Multi-Step Equations Solving Equations with the Variable on Each Side Solving Equations Involving Absolute Value, Ratios and Proportions Percent of Change Find percentile for a given set of data Literal Equations and Dimensional Analysis Weighted Averages Vocabulary algebraic expression, variable, term, factor, product, power, exponent, base, evaluate, order of operations,equivalent expressions, additive identity, multiplicative identity, multiplicative inverse, reciprocal, like terms, simplest form, coefficient,open sentence, equation, solving, solution, replacement set, set, element, solution set, identity,coordinate system, coordinate plane, x- and y- axes, origin, ordered pair, x- and y- coordinates, relation, mapping, domain, range, independent variable, dependent variable, function, discrete function, continuous function, vertical line test, function notation, nonlinear function, intercept, x-intercept, y-intercept line symmetry, positive, negative, increasing, decreasing, extrema, relative maximum, relative minimum, end behavior, formula, solve an equation, equivalent equations, multi-step equation, identity, ratio, proportion, rate, unit rate, scale model, percent of change, percentile, literal equation, dimensional analysis, weighted average

3 Unit 2: Linear Relations *All courses (Week 7, 13 Linear Relationships What is equivalence? How can you communicate mathematical ideas effectively? How do we determine the value of an unknown quantity? How can we model relationships between quantities? How do tables and graphs represent relations? How does the domain affect the range in a function? How can functions be used to solve real-world situations? identify linear equations, intercepts and zeros graph and write linear equations use rate of change to solve problems write and graph linear equations in various forms Use scatter plots and lines of fit, and write equations for best-fit lines using linear regression find inverse linear functions Prerequisites: solving linear equations algebraically graphing linear functions Topic List: graphing linear equations solving linear equations by graphing rate of change and slope direct variation arithmetic sequences and linear functions proportional and non-proportional relationships graphing equations in slope-intercept form writing equations in slope-intercept form writing equations in point-slope form parallel and perpendicular lines scatter plots and lines of fit correlation and causation regression and median fit lines inverse linear functions Vocabulary: linear equation, standard form, constant, x-intercept, y- intercept, linear function, parent function, family of graphs, root, rate of change, slope, direct variation, constant of variation, arithmetic sequence, inductive reasoning, deductive reasoning, slope-intercept form, linear extrapolation, point-slope form, parallel lines, perpendicular lines, scatter plot, line of fit, linear interpolation, best-fit line, linear regression, correlation coefficient, median-fit line, inverse relation, inverse function Unit 3: Inequalities and Solve linear inequalities, and systems of What is equivalence? Solve one-step and multi-step inequalities;; Solve compound inequalities and Prerequisites Solve linear equations in one variable Graph linear equations

4 Systems *All courses (Week 20, 4 equations and inequalities How can you communicate mathematical ideas effectively? How do we determine the value of an unknown quantity? inequalities involving absolute value;; Graph inequalities in two variables;; Solve systems of linear equations by graphing, substitution, and elimination;; Solve systems of linear inequalities by graphing Topic List Solving Inequalities by Addition and Subtraction Solving Inequalities by Multiplication and Division Solving Multi-Step Inequalities Solving Compound Inequalities Inequalities Involving Absolute Value Graphing Inequalities in Two Variables Graphing Systems of Equations Substitution Method Elimination Using Addition and Subtraction Elimination Using Multiplication Applying Systems of Linear Equations Use Matrices to Solve Systems of Euqations Systems of Inequalities Vocabulary Inequality, set-builder notation, compound inequality, intersection, union, boundary, half-plane, closed halfplane, open half-plane, matrix, elements, dimensions, augmented matrix Unit 4: Exponential Functions & Relations *280/281 (Week 24, 6 Exponential Functions and Relations Why is it helpful to write numbers in different ways? Why is it important to understand and use scientific notation? How can we represent non-linear functions? How do geometric concepts relate to real world situations? simplify and preform operations on expressions involving exponents extend the properties of integer exponents to rational exponents using scientific notation graph and use exponential functions simplify, add, subtract and multiply radical expressions graph and transform radical functions solve radical equations Prerequisites: evaluate expressions involving exponents Topic List: multiplication properties of exponents division properties of exponents rational exponents scientific notation exponential functions solving exponential functions and inequalities growth and decay geometric sequences as exponential functions average rate of change of exponential functions recursive formulas square root functions simplifying radical expressions operations with radical expressions radical equations

5 use the Pythagorean Theorem the Pythagorean Theorem Vocabulary: monomial, constant, zero exponent, negative exponent, order of magnitude, rational exponent, cube root, nth root, exponential equation, scientific notation, exponential function, exponential growth, exponential decay, compound interest, geometric sequence, common ratio, recursive formula, radicand, radical function, conjugate, radical equation, hypotenuse, legs, converse, midpoint Unit 5: Quadratic Relationships *280/281 only (Week 30, 8 Understand Quadratic Expressions, Equations, and Functions How do quadratic expressions and equations model real world situations? Why is it important to learn about nonlinear functions? Add, subtract, and multiply polynomials Factor trinomials Factor differences of squares Graph quadratic functions Solve quadratic equations Solve quadratic equations by graphing, completing the square, and using the Quadratic Formula Analyze functions with successive differences and ratios Identify and graph special functions Prerequisites * Apply laws of exponents * Understand exponential functions Solve quadratic equations by factoring and using the Square Root Property Topic List Adding and subtracting polynomials Multiplying a polynomial by a monomial Multiplying polynomials Special Products Using the Distributive Property Factoring and solving a trinomial with no leading coefficient Factoring and solving a trinomial with a leading coefficient Differences of Squares Perfect Squares Graphing quadratic functions Solving quadratic equations by graphing Transformations of quadratic functions * Exploring quadratic inequalities, families of quadratic functions, systems of quadratic equations Solving quadratic equations by completing the square Solving quadratic equations by using The Quadratic Formula Analyzing functions with successive differences Special Functions: Piecewise-Linear Functions

6 Vocabulary polynomial, binomial, trinomial, degree of a monomial, degree of a polynomial standard form of a polynomial, leading coefficient, FOIL method, quadratic expression, factoring, factoring by grouping, Zero Product Property, quadratic equation, prime polynomial, difference of two squares, perfect square trinomial, Square Root Property Atlas Version 8.2 Rubicon International All rights reserved