CHAMBERSBURG AREA SCHOOL DISTRICT COURSE OF PLANNED INSTRUCTION


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1 CHAMBERSBURG AREA SCHOOL DISTRICT COURSE OF PLANNED INSTRUCTION SCHOOL CASHS DEPARTMENT MATH DATE 7/12/05 COURSE TITLE ALGEBRA I GRADE 812 COURSE LENGTH 1 YR. LESSON FREQUENCY (PER WEEK) 5 TIME 43 MIN. COURSE REVISED 2005 COURSE CREDIT 1 COURSE REQUIRED ELECTED I. MAJOR COURSE OJBECTIVES AND STUDENT PERFORMANCE INDICATORS All Students Will: A. Make connections to algebra 1. Evaluate a variable expression, and write a variable expression that models a reallive situation. 2. Evaluate expressions containing exponents and use exponents in reallife Anchor: M11.A Use the order of operations to evaluate algebraic expressions and use a calculator to evaluate expressions simulating reallife situations. Anchor: M11.A Check solutions and solve equations using mental math and check solutions of inequalities in a reallife problem. 5. Translate verbal phrases into algebraic expressions and write algebraic equations/inequalities to solve reallife 6. Use tables of organized data and graphs to organize reallife data. Standard: A Anchor: M11.E Identify a function and create an input/output table to represent it. Write equations to represent reallife functions. B. Properties of real numbers. Graph and compare real numbers using a number line and find the opposite and the absolute value 1. of a number in reallife applications. 2. Add real numbers using a numbers line or addition rules and use addition of real numbers to solve reallife 3. Subtract real numbers using the subtraction rule and use subtraction of real numbers to solve real life
2 4. Organize data in a matrix and add and subtract two matrices. Standard: I 5. Multiply real numbers using properties of multiplication and multiply numbers to solve reallife 6. Use the distributive property and simplify expressions by combining like terms. 7. Divide real numbers and use division to simply algebraic expressions. 8. Find the probability of an event and the odds of an event. Standard: A, E Anchor: M11.E.3.1 C. Solving linear equations. 1. Solve linear equations using addition and subtraction and use linear equations to solve reallife 2. Solve linear equations using addition and subtraction and use multiplication and division of equations to solve reallife and geometric 3. Use two or more transformations to solve an equation and use multistep equations to solve reallife 4. Collect variables on one side of an equation and use equations to solve reallife 5. Draw a diagram to help understand reallife problems and use tables and graphs to check answers. 6. Find exact and approximate solutions of equations that contain decimals and solve reallife problems using decimals., E 7. Solve a formula or a literal equation for one of its variables and rewrite an equation in function form. 8. Use rates and ratios to solve reallife problems and use percents to model and solve reallife D. Graphing linear equations and functions. 1. Plot points on the coordinate plane. Draw a scatter plot and make predictions about reallife situations. Standard: D Anchor: M11.E Graph a linear equation using a table or a list of values and graph horizontal and vertical lines. 3. Find the intercepts of the graph of a linear equation and use intercepts to make a quick graph of an equation.
3 4. Find the slope of a line using two points and interpret slope as a rate of change in reallife situations. 5. Write linear equations that represent direct variation and use a ratio to write an equation for direct variation. 6. Graph a linear equation in slope intercept form. Graph and interpret equations in slope intercept form that model reallife situations. 7. Solve a linear equation graphically and use graphs to solve reallife 8. Identify when a relation is a function and use function notation to represent reallife situations. Standard: A, Q Anchor: M11.D.1.1 E. Writing linear equations. 1. Use the slope intercept form to write and equation of a line and model a reallife situation with a linear function. 2. Use slope and any point on a line to write the equation of the line. Use the linear model to make predictions about a reallife situation. 3. Write an equation of a line given two points on the line and use a linear equation to model a reallife problem. 4. Find a linear equation that approximates a set of data points. Determine whether there is a positive or negative correlation in a set of reallife data. 5. Use the pointslope form to write an equation of a line and use the pointslope form to model a reallife situation. 6. Write a linear equation in standard form and use the standard form to model reallife situations. 7. Determine whether a linear model is appropriate and use a linear model to make a reallife prediction. F. Solving and graphing linear inequalities. 1. Graph linear inequalities in one variable and solve onestep linear inequalities. 2. Solve multistep linear inequalities and use linear inequalities to model and solve reallife 3. Write, solve, and graph compound inequalities and model reallife situations with compound inequalities.
4 4. Solve absolute value equations and inequalities. 5. Graph a linear inequality in two variables and model a reallife situation using a linear inequality in two variables. Standard: A, H, J, N 6. Make and use a stemandleaf plot to put data in order and find the mean, median, and mode of a set of data. Standard: A Anchor: M11.E.1.1, M11.E Draw a boxandwhisker plot to organize reallife data and read/interpret boxandwhisker plots. Standard: D Anchor: M11.E.4.1 G. Systems of linear equations and inequalities. 1. Solve a system of linear equations by graphing and model a reallife problem using a linear system., G 2. Use substitution to solve a linear system and model a reallife situation using a linear system., G 3. Use linear combinations to solve a system of linear equations and model a reallife problem using a system of linear equations., G 4. Choose the best method to solve a system of linear equations and use a system to model reallife, G 5. Identify linear systems as having one, two or infinitely many solutions. Model a reallife problem using a linear system., F 6. Solve a system of linear inequalities by graphing and use a system of linear inequalities to model a reallife situations., G H. Exponents and exponential functions. 1. Use properties of exponents to multiply exponential expressions and use powers to model reallife 2. Evaluate expressions that have negative or 0 exponents and graph exponential functions. 3. Use the division properties of exponents to evaluate powers and simplify expressions. Use the division properties of exponents to find a probability. 4. Use scientific notation to represent numbers and perform operations with them. Use scientific notation to describe a reallife situation. 5. Write and use models for exponential growth and graph these models., C
5 6. Write and use models foe exponential decay and graph these models., C I. Quadratic equations and functions. 1. Evaluate and approximate square roots and solve a quadratic equation by finding square roots. 2. Use properties of radicals to simplify radicals and use quadratic equations to model reallife 3. Sketch the graph of a quadratic function and use quadratic models in reallife settings. 4. Solve a quadratic equation graphically and use quadratic models in reallife settings. 5. Use the quadratic formula to solve a quadratic equation and use quadratic models in reallife settings. 6. Use the discriminant to find the number of solutions to a quadratic equation and use the discriminat to solve reallife 7. Sketch the graph of a quadratic inequality and use quadratic inequalities as reallife models. 8. Choose a model that best fits a collection of data and use models in reallife settings. J. Polynomials and Factoring 1. Add and subtract polynomials and use polynomials to model reallife situations. 2. Multiply two polynomials and use polynomial multiplication in reallife situations. 3. Use special product patterns for the product of a sum and a difference and for the square of a binomial. Use special product as reallife models. 4. Solve a polynomial equation in factored form and relate factors and xintercepts. 5. Factor a quadratic expression in the form X 2 + bx + c and solve quadratic equations by factoring. 6. Factor a quadratic expression in the form ax 2 + bx + c and solve quadratic equations by factoring. 7. Use special product patterns to factor quadratic polynomials and solve quadratic equations by factoring. 8. Use the distributive property to factor a polynomial and solve polynomial equations by factoring.
6 K. Rational equations and functions. 1. Solve proportions and use proportions to solve reallife Standard: A, P Anchor: M11.A Use equations to solve percent problems and use percents in reallife 3. Use direct and inverse variation and use direct and inverse variation to model reallife situations. Standard: P 4. Simplify a rational expression and use rational expressions to find geometric probability. 5. Multiply and divide rational expressions and use rational expressions as reallife models. 6. Add and subtract rational expressions that have like denominators and unlike denominators. 7. Divide a polynomial by a monomial or by a binomial factor and use polynomial long division. 8. Solve rational equations and graph rational functions. L. Radicals and connections to geometry. 1. Evaluate and graph a square root function and use square root functions to model reallife Anchor: M11.A Add, subtract, multiply, and divide radical expressions and use radical expressions in reallife situations. Anchor: M11.A Solve a radical equation and use radical equations to solve reallife, G 4. Solve a quadratic equation by completing the square and choose a method for solving quadratic equations., G 5. Use the Pythagorean theorem and its converse and use it to solve reallife Standard: B Anchor: M11.C Find the distance and midpoint between two points on the coordinate plane. Standard: G Anchor: M11.C Find the sine, cosine, and tangent of an angle and use trigonometric ratios in reallife Standard: A, B Anchor: M11.C Use logical reasoning to prove a statement is true/false. Standard: A, B, C
7 II. CONTENT OUTLINE AND TIME ALLOCATION A. Make connections to algebra (13 Days) 1. Evaluate a variable expression, and write a variable expression that models a reallive situation. 2. Evaluate expressions containing exponents and use exponents in reallife 3. Use the order of operations to evaluate algebraic expressions and use a calculator to evaluate expressions simulating reallife situations. 4. Check solutions and solve equations using mental math and check solutions of inequalities in a reallife problem. 5. Translate verbal phrases into algebraic expressions and write algebraic equations/inequalities to solve reallife 6. Use tables of organized data and graphs to organize reallife data 7. Identify a function and create an input/output table to represent it. Write equations to represent reallife functions. B. Properties of real numbers (13 Days) 1. Graph and compare real numbers using a number line and find the opposite and the absolute value of a number in reallife applications. 2. Add real numbers using a numbers line or addition rules and use addition of real numbers to solve reallife 3. Subtract real numbers using the subtraction rule and use subtraction of real numbers to solve real life 4. Organize data in a matrix and add and subtract two matrices. 5. Multiply real numbers using properties of multiplication and multiply numbers to solve reallife 6. Use the distributive property and simplify expressions by combining like terms. 7. Divide real numbers and use division to simply algebraic expressions. 8. Find the probability of an event and the odds of an event. C. Solving linear equations (13 Days) 1. Solve linear equations using addition and subtraction and use linear equations to solve reallife 2. Solve linear equations using addition and subtraction and use multiplication and division of equations to solve reallife and geometric 3. Use two or more transformations to solve an equation and use multistep equations to solve reallife 4. Collect variables on one side of an equation and use equations to solve reallife 5. Draw a diagram to help understand reallife problems and use tables and graphs to check answers. 6. Find exact and approximate solutions of equations that contain decimals and solve reallife problems using decimals. 7. Solve a formula or a literal equation for one of its variables and rewrite an equation in function form. 8. Use rates and ratios to solve reallife problems and use percents to model and solve reallife D. Graphing linear equations and functions (15 Days) 1. Plot points on the coordinate plane. Draw a scatter plot and make predictions about reallife situations. 2. Graph a linear equation using a table or a list of values and graph horizontal and vertical lines. 3. Find the intercepts of the graph of a linear equation and use intercepts to make a quick graph of an equation. 4. Find the slope of a line using two points and interpret slope as a rate of change in reallife situations. 5. Write linear equations that represent direct variation and use a ratio to write an equation for direct variation. 6. Graph a linear equation in slope intercept form. Graph and interpret equations in slope intercept form that model reallife situations. 7. Solve a linear equation graphically and use graphs to solve reallife 8. Identify when a relation is a function and use function notation to represent reallife situations.
8 E. Writing linear equations (13 Days) 1. Use the slope intercept form to write and equation of a line and model a reallife situation with a linear function. 2. Use slope and any point on a line to write the equation of the line. Use the linear model to make predictions about a reallife situation. 3. Write an equation of a line given two points on the line and use a linear equation to model a reallife problem. 4. Find a linear equation that approximates a set of data points. Determine whether there is a positive or negative correlation in a set of reallife data. 5. Use the pointslope form to write an equation of a line and use the pointslope form to model a reallife situation. 6. Write a linear equation in standard form and use the standard form to model reallife situations. 7. Determine whether a linear model is appropriate and use a linear model to make a reallife prediction. F. Solving and graphing linear inequalities (13 Days) 1. Graph linear inequalities in one variable and solve onestep linear inequalities. 2. Solve multistep linear inequalities and use linear inequalities to model and solve reallife 3. Write, solve, and graph compound inequalities and model reallife situations with compound inequalities. 4. Solve absolute value equations and inequalities. 5. Graph a linear inequality in two variables and model a reallife situation using a linear inequality in two variables. 6. Make and use a stemandleaf plot to put data in order and find the mean, median, and mode of a set of data. 7. Draw a boxandwhisker plot to organize reallife data and read/interpret boxandwhisker plots. G. Systems of linear equations and inequalities (11 Days) 1. Solve a system of linear equations by graphing and model a reallife problem using a linear system. 2. Use substitution to solve a linear system and model a reallife situation using a linear system. 3. Use linear combinations to solve a system of linear equations and model a reallife problem using a system of linear equations. 4. Choose the best method to solve a system of linear equations and use a system to model reallife 5. Identify linear systems as having one, two or infinitely many solutions. Model a reallife problem using a linear system. 6. Solve a system of linear inequalities by graphing and use a system of linear inequalities to model a reallife situations. H. Exponents and exponential functions (12 Days) 1. Use properties of exponents to multiply exponential expressions and use powers to model reallife 2. Evaluate expressions that have negative or 0 exponents and graph exponential functions. 3. Use the division properties of exponents to evaluate powers and simplify expressions. Use the division properties of exponents to find a probability. 4. Use scientific notation to represent numbers and perform operations with them. Use scientific notation to describe a reallife situation. 5. Write and use models for exponential growth and graph these models. 6. Write and use models foe exponential decay and graph these models. I. Quadratic equations and functions (14 Days) 1. Evaluate and approximate square roots and solve a quadratic equation by finding square roots. 2. Use properties of radicals to simplify radicals and use quadratic equations to model reallife 3. Sketch the graph of a quadratic function and use quadratic models in reallife settings. 4. Solve a quadratic equation graphically and use quadratic models in reallife settings. 5. Use the quadratic formula to solve a quadratic equation and use quadratic models in reallife settings.
9 6. Use the discriminant to find the number of solutions to a quadratic equation and use the discriminat to solve reallife 7. Sketch the graph of a quadratic inequality and use quadratic inequalities as reallife models. 8. Choose a model that best fits a collection of data and use models in reallife settings. J. Polynomials and Factoring (15 Days) 1. Add and subtract polynomials and use polynomials to model reallife situations. 2. Multiply two polynomials and use polynomial multiplication in reallife situations. 3. Use special product patterns for the product of a sum and a difference and for the square of a binomial. Use special product as reallife models. 4. Solve a polynomial equation in factored form and relate factors and xintercepts. 5. Factor a quadratic expression in the form X 2 + bx + c and solve quadratic equations by factoring. 6. Factor a quadratic expression in the form ax 2 + bx + c and solve quadratic equations by factoring. 7. Use special product patterns to factor quadratic polynomials and solve quadratic equations by factoring. 8. Use the distributive property to factor a polynomial and solve polynomial equations by factoring. K. Rational equations and functions (14 Days) 1. Solve proportions and use proportions to solve reallife 2. Use equations to solve percent problems and use percents in reallife 3. Use direct and inverse variation and use direct and inverse variation to model reallife situations. 4. Simplify a rational expression and use rational expressions to find geometric probability. 5. Multiply and divide rational expressions and use rational expressions as reallife models. 6. Add and subtract rational expressions that have like denominators and unlike denominators. 7. Divide a polynomial by a monomial or by a binomial factor and use polynomial long division. 8. Solve rational equations and graph rational functions. L. Radicals and connections to geometry (14 Days) 1. Evaluate and graph a square root function and use square root functions to model reallife 2. Add, subtract, multiply, and divide radical expressions and use radical expressions in reallife situations. 3. Solve a radical equation and use radical equations to solve reallife 4. Solve a quadratic equation by completing the square and choose a method for solving quadratic equations. 5. Use the Pythagorean theorem and its converse and use it to solve reallife 6. Find the distance and midpoint between two points on the coordinate plane. 7. Find the sine, cosine, and tangent of an angle and use trigonometric ratios in reallife 8. Use logical reasoning to prove a statement is true/false. III. TEXTS, MATERIALS, AND MAJOR RESOURCES Algebra I. Evanston, Illinois: McDougal Littell, Other resources published by McDougal Littell: Assessment Book Teacher s Resources for Transfer Students WarmUp Exercises transparencies Using TI81, TI82, TI83 Calculators MultiLanguage Glossary Study Guides Project Book Exploration Lab Manual Skills Bank Problem Bank Activity Bank Practice Bank
10 IV. PROCEDURES FOR ASSESSMENT OF PA ACADEMIC STANDARDS Teacher designed quizzes and tests and/or standard text tests Midterm and cumulative exams as designated by District policy Teacher observation Class participation, group discussions, and teacher conference Teacher, peer, selfassessment of performance Special reports and research Student presentations Opportunity for alternative assessment as deemed appropriate by the teacher V. SPECIAL CONDITIONS OR PREREQUISITES At least a C in prealgebra or a B in advanced Math 7 VI. VII. COURSE EVALUATION PROCEDURE All planned courses will be monitored by the department chair and building administrators and revised according to the District s revision cycle. ACCOMMODATIONS The needs of students in the learning support and gifted programs are met through a variety of adaptations, modifications or enrichments to the planned course. If a student has an IEP or a GIEP (Gifted individual Education Plan), specific strategies and accommodations for that student will be identified in his or her individualized educational plan under the section called specially designed instruction. The learning support and gifted teachers are available to provide classroom teachers with any kind of assistance in providing accommodations.
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