SCOPE & SEQUENCE Algebra I Standard Course Arranged by Unit

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1 TEXTBOOK - AI.N.1 Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of n th roots of positive real numbers for any positive integer n; the inverse relationship between taking the n th root of and the n th power of a positive real number; and the density of the set of rational numbers in the set of real numbers. (10.N.1) AI.N.2 Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(2 4 1) = 45, = 14; apply such simplifications in the solution of problems. (10.N.2) How to represent numbers How to represent number operations How to use grouping symbols How exponents are used to indicate repeated multiplication How to use standard order of operations to solve algebraic expressions Identify real and irrational numbers Solve several examples using multiplication, division, subtraction, and addition. Use an exponent to represent repeated multiplication Use parenthesis to re-write expressions. Prioritize the operation according to P.E.M.D.A.S. How to use exponents and how to evaluate exponent expressions including everyday applications How to use standard order of operations to simplify algebraic expressions How to evaluate variable expressions How to use exponents and how to evaluate exponent expressions How to check possible solutions to equations UNIT I - Connections to Algebra Introduce order of operations with an acronym Walk through several number operational examples following order of operations Demonstrate through example how repeated multiplication can be shown with exponents Give mini-lecture on variable, expression, and exponent definitions Walk though several examples involving variable expressions both with and without exponents Demonstration on use of a calculator to check solutions Small game to reinforce order of operations, variable expressions, and using exponents. Student can correctly evaluate number expressions using multiplication, division, subtraction, and addition Order of operations memorized Student can apply order of operations to evaluate expressions correctly Student can correctly transfer repeated multiplication to an exponent Students can correctly apply order of operations to simplify expressions Understands definition and use of a variable Student can use calculator to check solutions Students can check solutions by plugging in correctly Students can correctly evaluate exponent expressions Sept Students will DO: Apply grouping to exponents 1

2 AI.P.2 Use properties of the real number system to judge the validity of equations and, to prove or disprove statements, and to justify every step in a sequential argument. Use everyday formulas involving exponents Evaluate expressions using P.E.M.D.A.S. both with and without a calculator. Evaluate algebraic equations for their given value to check solution How to translate verbal phrases into expressions and verbal sentences into equations and Steps of the problem solving plan How to use algebra to solve simple everyday problems Phrases to expressions mini-lecture Problem Solving Plan Powerpoint List and define several words indicating operation converting phrases to expressions using the problem-solving plan. Student can correctly transfer verbal phrases into mathematical expressions Student can correctly solve word problems using the steps of the problem solving plan Student can apply algebra appropriately to solve everyday problems Al.D.1 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-andleaf plots, circle graph, line graph and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. AI.N.1 Identify and use the properties of operations on Recognize significant words that indicate specific operations Translate sentences into equations or Use the problem solving plan to solve simple everyday problems How to use tables to organize data How to use graphs to model data visually Answer questions based on a table of values Construct and interpret frequency distribution, line plot, and bar graph How to add real numbers Tabulating and Graphing data Project Show several examples of the different types of visual representation of data and answer corresponding questions regarding the data. UNIT II - UNIT II: Rules of Algebra involving addition, subtraction, Students can correctly tabulate data Use the appropriate graph for the data given Student can correctly interpret graphs and answer questions regarding it. Students can correctly add, subtract, multiply, and divide real numbers Oct- Nov 2

3 real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of n th roots of positive real numbers for any positive integer n; the inverse relationship between taking the n th root of and the n th power of a positive real number; and the density of the set of rational numbers in the set of real numbers. (10.N.1) AI.N.2 Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(2 4 1) = 45, = 14; apply such simplifications in the solution of problems. (10.N.2) How to subtract real numbers How to add and subtract two matrices How to multiply real numbers How to use the distributive property Divide real numbers Use number line, additions rules, and a calculator to add real numbers Use number line, subtraction rules, and a calculator to subtract real numbers Organize data into a matrix Add or subtract matrices using rules for real numbers Investigate multiplication patterns to identify the rules for multiplication of real numbers Practice finding products both with and without a calculator Multiply an expression by a number or variable by applying the distributive property Express division as multiplication Use the division rules or a calculator to find the quotient Evaluate expressions involving division of real numbers. How to find the opposite and the absolute value of a real number How to simplify the difference of two algebraic expressions Use the number line and properties of opposites Simplify algebraic expression using the properties of subtraction multiplication, and division Present the distributive property in a generalized way Matrix use mini-lecture using distributive property Review definition of opposite and absolute value or a real number Walk through examples of absolute value and opposite number problems finding the difference between two algebraic expressions Students can use matrices correctly to organize numbers Students can correctly add two matrices Students memorize distributive property and correctly use it to solve problems Students understand meaning of absolute value Students can correctly find the absolute value and opposite of a number Students can correctly find the difference between two algebraic expressions 3

4 AI.P.2 Use properties of the real number system to judge the validity of equations and, to prove or disprove statements, and to justify every step in a sequential argument. 8.N.3 Use ratios and proportions in the solutions of problems, in particular, problems involving unit rates, scale factors, and rate of change. AI.P.10 Solve equations and including those involving absolute value of linear expressions (e.g., x - 2 > 5) and apply to the solution of problems. (10.P.6) How to graph and compare real numbers using the real number line How to simplify expressions by combining like terms Use the number line and definition of absolute value Construct their own number line Graph numbers and order numbers on a number line Recognize like terms Combine like terms by adding or subtracting the coefficients Students will Know: How to use rates and ratios to compare quantities Students will be able to Do: Understand the definitions of rates and ratios Apply the definitions to evaluate quantities involving both rates and ratios Demonstrate where real numbers are found with the visual aid of a number line Introduce meaning of coefficient Introduce combining like terms with an analogy Present simply way to combine like terms combining like terms Rates and Ratios powerpoint Give several real-life examples of where rates and ratios are used everyday Walk through several rates and ratios examples UNIT III - Solving Linear Equations How to solve equations systematically using addition, subtraction, and division How to use reciprocals to solve equations. How to use two or more transformations to an equation How to collect variables on one side of an equation by transposing How to find exact and approximate solutions of equations containing decimals The socks and shoes method Solving equations mini-lecture Present the method of transforming and reciprocals to solve equations solving equations using transformations and reciprocals Demonstrate how to collect variables on one side collecting variables on one side Demonstrate the socks and shoes Students can use a number line to aid in understanding real numbers Students know what a coefficient is Students can correctly combine like terms Students can correctly distinguish between a rate and a ratio Students can correctly set up a rate or ratio to compare quantities Students can correctly solve and equation using the four number operations Students can demonstrate the socks and shoes method to solving equations Students can correctly use transformations to solve equations Students can correctly solve equations using reciprocals Students can correctly collect variables on one side Nov-Dec 4

5 AI.P.11 Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (10.P.7) AI.D.1 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-andleaf plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these Problems involving the undo and balance method Exercises involving fractional coefficient Use the socks and shoes method in problems involving two + transformations Apply collecting like terms to solve more advanced equations Solve equations involving decimals both manually and with technology. How to use algebraic models to answer questions about real-life situations How to solve problems that use decimal measurements How to solve literal equations, especially formulas, for a specified variable Able to read and interpret a situation and apply the algebraic model to it. Apply the rules of decimal to real-life algebraic situations Apply equation solving rules across disciplines. How to use a coordinate plane to match points with ordered pairs of numbers How to use a scatter plot Graph coordinates on a Cartesian plane. Construct scatter plots. method of solving equations Present the proper algebraic model method Review of decimal operation decimal operation Literal Equation mini-lecture Walk through many literal equations Coordinate Plane powerpoint Coordinate Plane demonstration with board grid using a scatter plot plotting points Students can rearrange literal equations for one variable Students can correctly add, subtract, multiply, and divide decimals Students understand and can use algebraic model to answer real-life problems Students understand orientation of coordinate plane Students can correctly label parts of coordinate plane Students can correctly plot ordered pairs 5

6 notions to compare different sets of data. (10.D.1) AI.P.5 Demonstrate an understanding of the relationship between various representations of a line. Determine a line s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the point-slope or slope y- intercept formulas. Explain the significance of a positive, negative, zero, or undefined slope. (10.P.2) UNIT IV - Writing and Graphing Linear Equations How to graph horizontal and vertical lines in a coordinate plane. How to interpret graphs of linear equations How to find the intercepts of the graph of a linear equation How to use intercepts to sketch a quick graph of a line How to find the slope of a line using two of its points How to interpret slope as a constant rate of change or an average rate of change How to find the slope and y-intercept from an equation How to use slope-intercept from to sketch a line and solve real-life problems How to use the slop-intercept form to write an equation of a line How to use slope and any point on a line to write an equation of the line How to write an equation of a line given two points on the line How to use the point-slope form to write an equation of a line Review definition of horizontal and vertical Present general equations for vertical and horizontal lines graphing horizontal and vertical lines Introduce finding intercepts using intercepts to graph a line Introduce slope and its various definitions Present slope-intercept, standard, and point-slope form using slope-intercept, standard, and point-slope form Demonstrate how to find and equation of a line given two points finding an equation given two points Demonstrate how point-slope form can be used to find a linear model Students can identify a horizontal and vertical line given the equation and vise versa Students can correctly identify intercepts Students have memorized slope definition and equation Students can correctly graph lines given an equation in slope-intercept, standard, and point-slope form Student can correctly transform between different equation forms Students can correctly find equation in any form based on given graph Students can correctly apply the concept of slope to real world problems involving rate of change Students can correctly graph equations of lines given a variation of things (slope and a point, two points, intercepts, etc.) Students can correctly make a linear model from point-slope form Graph horizontal and vertical lines From a graph be able to match it to an equation Quickly sketch the graph of a linear equation by plotting its intercepts See relationships between the variables Use slope to represent the rate of change of 6

7 AI.P.10 Solve equations and including those involving absolute value of linear expressions (e.g., x - 2 > 5) and apply to the solution of problems. (10.P.6) AI.P.4 Translate between different representations of functions and relations: graphs, equations, point sets, and tabular. one quantity with respect to another Apply the concept of slope to problems involving distanced traveled compared to time Write an equation of a line in slopeintercept so that it is easier to understand a line Take the slope and the y-intercept and create the slope intercept form Given the slope and a point and write the equation of the line in slope-intercept form Given two points on a line, find the equation of the line in slope-intercept form. Use the point-slope form as the most efficient way to find a linear model How to graph an absolute value equation How to solve and check absolute value equations using algebra How to use a graph to check solutions of absolute value equations Students will DO: Model some real-life situations with absolute value equations such as billiard balls Use absolute value equations to model many real-life situations, such as representing minimum and maximum amounts Students will know: How to graph a linear equation from a table of values How to use a graph as a quick check of a solution found algebraically How to transform a linear equation into standard form Review definition of absolute value absolute value Explain how to graph an absolute value equation graphing absolute value equation Demonstrate absolute value equation usage in the real world by example Demonstrate how to graph a linear equation from a table of values graphing a linear equation from table Transforming a linear equation into standard form mini-lecture Students can correctly graph absolute value equations Students can correctly apply concept of absolute value equations to real-life models AI.P.4 Translate between different representations of functions and relations: graphs, equations, point sets, and tabular. Student can correctly take a table of values and graph them, creating a line Student can correctly transform a table of values to a line Jan 7

8 AI.D.2 Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate. (10.D.2) From a table of values (t-table) be able to plot the points and connect them to create a line Use a graph to approximate the related values by estimating coordinates of points on the graph Convert an equation into standard form How to find a linear equation that approximates a set of data points How to use scatter plots to determine positive correlation, negative correlation, or no correlation Plot a set of data points, find the line of best fit, choose two points on the line, and find the equation of that line Distinguish between positive, negative, and no correlation given a graph of data points. Use technology to plot a set of data point and find the equation of the line. Line of Best fit powerpoint Spaghetti Project Correlation mini-lecture finding line of best fit Demonstrate how to use calculator to find line of best fit. Student can find a line of best fit both manually and with a calculator AI.P.6 Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the pointslope form of the equation. (10.G.8) AI.D.3 Describe and explain how the relative sizes of a sample and the population How to use points slope to find linear equations of perpendicular and parallel lines Student will be able to DO: From the line of a parallel line, be able to find the equation of another line parallel to that line From the slope of a line, be able to find the equation of another line perpendicular to the line How the size of a sample will affect the accuracy of predictions based on the best-fit Review of definition of perpendicular and parallel Review of point slope form finding linear equations of perpendicular and parallel lines Using several sets of varying amounts of data, graph it and demonstrate how more is better Student can identify a perpendicular and parallel line Student can correctly find the equation of a perpendicular and parallel line using point-slope form Student understands the amount of data needed to make a prediction accurate 8

9 affect the validity of predictions from a set of data. (10.D.3) AI.P.11 Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (10.P.7) AI.P.5 Demonstrate an understanding of the relationship between various representations of a line. Determine a line s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the point-slope or slope y- intercept formulas. Explain the significance of a positive, negative, zero, or undefined equation from a set of data in a scatter plot Predict how accurate a prediction is after taking into account the size of the data set that they use to create a scatter plot and line of best fit. How to create and use linear models to solve problems How to make linear models that are accurate but simple to use Make simple and accurate linear models Use linear models efficiently with good results Linear Model Powerpoint real life problems using the linear model UNIT V - Solving and Graphing Linear Inequalities How to graph linear in one variable How to solve and graph compound How to graph a linear inequality in two variables Students will DO: Graph linear in one variable Graph numerous examples of compound Exercises in checking solutions of linear Exercises in sketching the graph of a linear inequality Linear inequality mini-lecture Introduce simple and compound Demonstrate graphing linear with two variables graphing simple and compound Understand and accurately use the linear model to solve real life problems Student can correctly graph linear in one and two variables Student can correctly graph simple and compound Feb 9

10 slope. (10.P.2) AI.P.10 Solve equations and including those involving absolute value of linear expressions (e.g., x - 2 > 5) and apply to the solution of problems. (10.P.6) Use slope-intercept form to graph a linear inequality. How to solve linear in one variable How to solve and graph compound How to solve absolute value How to write and use a linear inequality as a model for a real-life situation How to model a real-life situation with an absolute value inequality How to model a real-life situation using a linear inequality in two variables Solving linear minilecture Review of solving linear equations Show how to apply equation solving techniques to solving linear solving linear using linear in real world examples Students can model real-life situations using linear Students can correctly solve linear in both one and two variables Students can correctly solve real-life problems involving linear AI.D.1 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-andleaf plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, Solve linear inequality problems in which the students will have to use one transformation Solve linear inequality problems in which reversing of an inequality is necessary Solve linear inequality problems with on both sides. Solve compound that model real life examples. Solve problems involving absolute value Write an absolute value inequality Check solutions of linear How to draw and interpret visual models, such as time lines, picture graphs, and circle graphs Examine a variety of examples of real-life problems and answer questions based on the Time line, Picture graph, and Circle graph mini-lecture Demonstrate how to make these graphs Graph Project Student can properly construct a time line, picture graph, and circle graph Student can interpret these graphs and answer questions based on them 10

11 range, and mode) to communicate information about the data. Use these notions to compare different sets of data. (10.D.1) AI.P.12 Solve everyday problems that can be modeled using systems of linear equations or. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. (10.P.8) corresponding graphs UNIT VI - Systems of Linear Equations How to solve a system of linear equations by graphing How to model a real-life situation using a system of linear equations. How to use substitution to solve a linear system How to use linear combinations to solve a linear system How to visualize the solution possibilities for linear systems How to identify a linear system as having many solutions. How to solve a system of linear by graphing How to solve a linear programming problem How to model a real-life situation using linear programming Graph a system of linear equations Given a problem, be able to translate into a model of systems of equations. Solve several examples of linear equations using the method of substitution Solve several examples of linear equations using the method of linear combinations Look at a system of equations and be able to identify the solution by visualizing the graph Solve several examples of linear equations Review what a linear equation means Introduce solving a system using substitution solving a system using substitution Introduce solving a system using graphing solving a system using graphing Introduce solving a system using linear combination solving a system using linear combination Review what linear inequality means Introduce solving a linear inequality using graphing solving a linear inequality using graphing Student understands definition of a system Student can solve a system of equations using substitution, graphing, and linear combination Student can solve a system of linear using graphing Students can apply the three methods to real-world examples March 11

12 AI.N.1 Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of n th roots of positive real numbers for any positive integer n; the inverse relationship between taking the n th root of and the n th power of a positive real number; and the density of the set of rational numbers in the set of real numbers. (10.N.1) AI.N.2 Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(2 4 1) = 45, = 14; apply such simplifications in the solution of problems. (10.N.2) using the method of graphing Solve several examples of linear equations using linear programming Solve real-life examples using one of the following: substitution, linear programming, graphing, and linear combination. How to use scientific notation to express large and small numbers. How to perform operations with numbers in scientific notation, with and without a calculator How to use scientific notation to solve reallife problems requiring very large or very small numbers. Perform calculations using scientific notations with a calculator Perform calculations using scientific notation without a calculator Solve real-life problems that involve scientific numbers especially those involving the sciences. How to use the multiplication properties of exponents to evaluate powers and simplify expressions How to use powers and the exponential change equation as models in real-life settings How to use negative and zero exponents in algebraic expressions Using powers as models in real-life settings How to use the division properties of UNIT VII - Powers and Exponents Demonstrate the importance of scientific notation Rules of scientific notation minilecture using scientific notation Show how important scientific notation is to science by working through several scientific problems Rules of Exponents mini-lecture Work through several examples using rules of exponents Demonstrate how the rules of exponents can be helpful in real-life examples Compound Interest powerpoint Work through several examples involving compound interest Explain the properties of exponential decay and growth Students can correctly convert large numbers into scientific notation Students can correctly convert scientific notation into decimal from Students can correctly apply rules of scientific notation to science real world problems Students memorized rules of exponents Students can correctly use the rules of exponents to solve problems Students can correctly apply the rules of exponents to real-life problems Students can correctly use exponents in problems of exponential decay and growth April 12

13 exponents to evaluate powers and simplify expressions How to use powers as models in real-life settings. How to use the compound interest formula How to use models for exponential growth to solve real-life problems How to use models for exponential growth and decay to solve real-life problems exponential decay and growth Apply rules of exponents to various problems involving powers Solve a variety of applied problems of powers Solve problems in which the student will need to simplify the expression using laws of exponents Solve problems involving compound interest Solve problems involving exponential decay and growth. AI.P.9 Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods. (10.P.5) How to evaluate and approximate square roots How to use the Pythagorean theorem How to use quadratic models in real-life settings How to use the quadratic formula to solve a quadratic equation. How to find the number of solutions of a quadratic equation by using the discriminant UNIT VIII: Quadratic Equations Review square roots Pythagorean theorem derivation and powerpoint Introduce quadratic models Introduce quadratic formula using quadratic equation Student has memorized quadratic equation Student understands and can correctly use the Pythagorean theorem Student can use the quadratic equation to solve quadratics Student can approximate square roots using the properties of square roots Student can solve real-life examples using Pythagorean theorem May 13

14 AI.P.4 Translate between different representations of functions and relations: graphs, equations, point sets, and tabular. AI.P.7 Add, subtract, and multiply polynomials. Divide polynomials by monomials. (10.P.3) Approximate square roots with and without a calculator Find missing sides of right triangles using the Pythagorean theorem Use the Pythagorean theorem to find lengths of shadows, heights of trees, and in other problem context. Use quadratic formula to solve quadratic equations Use the methods of the discriminant to find the number of solutions of a quadratic equation. How to sketch the graph of a quadric inequality How to sketch the graph of a quadratic equation Sketch a graph of a quadric inequality both with and without a calculator Sketch a graph of a quadric equation both with and without a calculator Review meaning of inequality Introduce quadratic graphing quadratic Demonstrate how to sketch the graph of a quadratic equation sketching quadratic equations Demonstrate using a calculator to graph quadric equations UNIT IX: Polynomials and Factoring How to add and subtract polynomials How to multiply two polynomials using the distributive properties and the FOIL method Solve various polynomial problems using addition, subtraction, and the FIOL method FOIL powerpoint Explain FOIL acronym Demonstrate how to add and subtract polynomials by example Review the distributive property Reinforce meaning of polynomial Work through several examples of multiplying two polynomials using the distributive property Student can correctly graph quadric equations both with and without a calculator Student can correctly graph quadratic Student can recognize polynomial Student can correctly multiply polynomials using the foil method and distributive property Student can correctly add and subtract polynomials June 14

15 AI.P.8 Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms, factoring (e.g., a 2 b 2 = (a + b)(a - b), x x + 21 = (x + 3)(x + 7), 5x x 3 5x 2 = 5x 2 (x 2 + 2x 1)), identifying and canceling common factors in rational expressions, and applying the properties of positive integer exponents. (10.P.4) AI.P.9 Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods. (10.P.5) How to use polynomials as models in reallife settings How to use special-product patterns for the product of a sum and difference and for the square of a binomial How to factor polynomials that have a monomial factor, that are the difference of two squares, and that are perfect-square trinomials Solve real-life problems that involving polynomials Multiply polynomials that are special squares like (a+b) 2, (a-b) 2 Factor polynomials that involve special squares like the ones above. How to factor a quadratic trinomial or recognize that it cannot be factored How to use factoring to solve a quadratic equation. How to solve quadratic equations by completing the square Recognize that quadratic trinomials sometimes may not be able to be factored Factor quadratic trinomials that can be factored. Complete the square. Demonstrate how polynomials can be applied to real-life settings Introduce special product patters using the special product pattern Introduce the difference of two squares and the perfect-square trinomials involving product of two squares and perfect-square trinomials Demonstrate how to factor polynomials that are special squares factoring these special products Demonstrate how to factor quadratic trinomial Review quadratic formula and equation Introduce method of completing the square completing the square Student can correctly use polynomials as models in real-life settings Student can correctly factor polynomials that involve special squares. Student can correctly find the difference of two squares. Student can properly complete the square Student can correctly factor quadratic trinomials Student can correctly use factoring to solve a quadratic equation 15