Algebra 1. Curriculum Map

Transcription

1 Algebra 1 Curriculum Map

2 Table of Contents Unit 1: Expressions and Unit 2: Linear Unit 3: Representing Linear Unit 4: Linear Inequalities Unit 5: Systems of Linear Unit 6: Polynomials Unit 7: Factoring and Quadratics Unit 8: Rational Unit 9: Applying Fractions Unit 10: Radical

3 Purpose of a Curriculum Map The purpose of a curriculum map is to document the intended relationship between components of the curriculum. Used as an analysis tool, a curriculum map allows instructors to review the curriculum to check for unnecessary redundancies, inconsistencies, misalignments, weaknesses and gaps. Ultimately, a curriculum map will be the bridge between the state standards and state-mandated curriculum and the taught and learned curriculum.

4 Unit 1: Expressions & Approximate Duration of Study: 1 weeks When to Study: Aug A.SSE.1.a Why do we use Variables and A.SSE.1.b variables? Expressions Why are the order of operations and other properties of mathematics important? Order of Operations Distributive Property Write verbal expressions for algebraic expressions Write algebraic expressions for verbal expressions Evaluate numerical and algebraic expressions by using the order of operations Use the Distributive Property to simplify and evaluate expressions A.N. Chap. 1 Quiz A.N. Chap. 1 Quiz #2 A.N. Chap. 1 Quiz #3 A.N. Chap. 2 Quiz A.N. Chap. 2 Quiz #2 A.N. Chap. 2 Quiz #3 A.N. Chap. 2 Quiz #4 Chap. 1.7 Story Problem Quiz Quiz Quiz Solve equations with two variables given a domain Vocabulary: Variable, Expression, Order of Operations, Distributive Property,, Domain Stucture and Method Book 1 Chapter 1 and Stucture and Method Book 1 Chapter 2 and Algeblocks Labs o Labs 3-1, 3-2, 3-3, 3-4, 3-5, 3-6 o Labs 5-2, 5-3, 5-1, 5-4, 5-5, 5-6 Math Words Jigsaw Activity Writing a Story Problem Project Rubric Distributive Property (pdf) Combining Like Terms (pdf) Evaluating Expressions (pdf) Order of Operations (pdf)

5 Unit 2: Linear Approximate Duration of Study: 2 weeks When to Study: Aug/ Sept A.CED. Writing Translate sentences 1 into equations A.REI.1 A.REI.3 A.REI.1 A.REI.3 A.REI.1 A.REI.3 A.REI.1 Why is advantageous to use and solve equations algebraically for realworld problems? When would we want to use the absolute value of numbers? One-step equations Multi-Step with the variable on each side Absolute Value Solve equations by using addition or subtraction Solve equations by using multiplication or division Solve equations involving more than one operation Solve equations with the variable on each side Solve equations involving grouping symbols Evaluate absolute value expressions Solve absolute value equations Solve equations for given variables Stucture and Method Book 1 Chapter 3 and Stucture and Method Book 1 Chapter 1, Sec. 9 (Absolute Value of Expressions) Algeblocks Labs o Labs 9-2, 9-3, 9-4, 9-5, 9-6, 9-7, 9-8 Cost, Value, Income Worksheet Chapter 3 Review Worksheet One-Step (pdf) Two-Step (pdf) Multi-Step (pdf) Absolute Value (pdf) A.CED. 4 Literal A.N. Chap. 3 Quiz A.N. Chap. 3 Quiz #2 A.N. Chap. 3 Quiz #3 Chap Vocabulary: Formula, Equation, Equivalent, Consecutive Integers, Identity, Cost, Value, Income, Literal Equation, Absolute Value

6 Unit 3: Representing Linear Approximate Duration of Study: 3 4 weeks When to Study: September A.REI.10 Graphing Linear Identify linear equations, intercepts, and zeros A.REI.10 A.REI.10 How does the slope affect direct variation? What does the slope-intercept form of an equation tell us? Solving linear equations by graphing Rate of Change and Slope Direct Variation Graphing in Slope-Intercept Form Graph linear equations Solve equations by graphing and identifying the root Estimate solutions to an equation by graphing Use rate of change to solve problems Find the slope of a line Write and graph direct variation equations Solve problems involving direct variation Write and graph linear equations in slopeintercept form Model real-world data with equations in slopeintercept form Stucture and Method Book 1 Chapter 8 and Graphing Lines Activity (Using Geogebra) Graphing Lines Activity on Graphing Calculators Rate of Change Activity Plotting Points Activity (Excel) y=mx+b slider (GeoGebra) Line of best Fit Project o Chapter 8 Project Cover Sheet o Sample Datasets for Ch. 8 Project.xlsx Slope From a Graph (pdf) Slope From Two Points (pdf) Slope From an Equation (pdf) Graphing Lines in Slope-Intercept Form (pdf) Graphing Lines in Standard Form (pdf) Writing Linear (pdf) A.CED.2 Writing equations in slope-intercept form Write an equation of a line in slope-intercept form given the slope and one point A.N. Chap. 8 Quiz A.N. Chap. 8 Quiz #2 A.N. Chap. 8 Quiz #3 A.N. Chap. 8 Quiz #4 Write an equation of a line in slope-intercept form given two points

7 Why should we know different forms of linear equations? in different forms Write equations of lines in standard form Write equations of lines in point-slope form Write linear equations in different forms A- CED.2 A.REI.1 0 How do we write the equations of parallel and perpendicular lines? How do we use real-world data to write the equation of a line? Parallel and Perpendicular Lines Lines of Fit Write equations of lines passing through a given point and either parallel or perpendicular to a given line Investigate relationships between quantities by using points on scatter plots Use lines of fit to make and evaluate predictions Vocabulary: Linear Equation, x-intercept, y-intercept, Rate of Change, Slope, Direct Variation, Slope-Intercept Form, Point-Slope Form, Parallel Lines, Perpendicular Lines, Scatter Plot, Line of Fit

8 Unit 4: Linear Inequalities Approximate Duration of Study: 2 weeks When to Study: A.REI.3 -How are inequalities and equations alike? Inequalities Involving Solving linear inequalities by using How are they Addition and addition and different? Subtraction subtraction A.REI.1 2 How do the words and and or affect the outcome of an inequality? Inequalities Involving Multiplication and Division Solving Multi- Step Inequalities Solving Compound Inequalities Inequalities involving Absolute Value Inequalities in Two Variables Solving linear inequalities by using multiplication and division Solve linear inequalities involving more than one operation Solve inequalities involving the Distributive Prop. Solve compound inequalities containing the word and and graph their solution set Solve compound inequalities containing the word or and graph their solution set Solve and graph absolute value inequalities Graph linear inequalities on the coordinate plane Solve inequalities by graphing Vocabulary: Inequality, Compound Inequality, Boundary, Half-Plane Chapter 10 Test Chapter 10 Test(2) Chapter 10 Test(3) Stucture and Method Book 1 Chapter 10 and HW Set #16 HW Set #17 Inequality Problem Solving Multi-Step Inequalities (pdf) One-Step Inequalities (pdf) Two-Step Inequalities (pdf) Compound Inequalities (pdf) Absolute Value Inequalities (pdf) Graphing Linear Inequalities (pdf)

9 Unit 5: Systems of Linear and Inequalities Approximate Duration of Study: 2 weeks When to Study: October/November A.REI.6 A.REI.1 1 Graphing Systems of Determine the number of solutions a system of A.REI.5 A.REI.6 A.REI.5 A.REI.6 A.REI.6 A.REI.8 How might one determine the most efficient method for solving a system of equations? Why would using a matrix to solve a system of equations be useful? Substitution Elimination Applying Systems of Linear Matrix equations equations has, if any Solve systems of linear equations by graphing Solve systems of equations by using substitution Solve systems of equations by using elimination with addition Solve systems of equations by using elimination with subtraction systems of equations by using elimination with multiplication Determine the best method for solving systems of equations Apply systems of equations to solve real-world problems Represent and solve systems of equations in reduced-row echelon form A.N. Chap. 9 Quiz #1 A.N. Chap. 9 Quiz #2 A.N. Chap. 9 Quiz #3 A.N. Chap. 9 Quiz #4 Stucture and Method Book 1 Chapter 9 and Systems of Graphing (pdf) Systems of Substitution (pdf) Systems of Elimination (pdf) Systems of Word Problems (pdf) Vocabulary: System of, Consistent, Independent, Dependent, Inconsistent, Substitution, Elimination, Matrix, Augmented Matrix, Row Reduction

10 Unit 6: Polynomials Approximate Duration of Study: 3 4 weeks When to Study: November A.APR.1 How might we classify polynomials? Multiplying Monomials Base and Exponent Power of product Power of a power A.APR.1 A.APR.1 A.APR.1 How can we use the polynomial operations of addition, subtraction, and multiplication in real life? Dividing Monomials Polynomial Identification Adding/ Subtracting Polynomials Multiplying a Polynomial by a Monomial Find the quotient of two monomials Simplify expressions containing negative and zero exponents Find the degree of a polynomial Write polynomials in standard form Identify like terms Quiz Add/ subtract polynomials Use the Distributive Property to multiply a monomial by a polynomial Quiz Stucture and Method Book 1 Chapter 4 and Algeblocks Labs o Labs 6-1, 6-2, 6-3 Multiplying Polynomials by Monomials Exponents Intro PowerPoint More Properties of Exponents (pdf) Naming Polynomials (pdf) Adding & Subtracting Polynomials (pdf) Multiplying Polynomials (pdf) Multiplying Special Cases (pdf) Properties of Exponents (pdf) A.APR.1 Multiplying Polynomials Special Products Use the Distributive Property to multiply a polynomial by another polynomial Find the squares of sums and differences Find the product of a sum and difference A.N. Chap. 4 Quiz #1 A.N. Chap. 4 Quiz #2 A.N. Chap. 4 Quiz #3 A.N. Chap. 4 Quiz #4 Vocabulary: Monomial, Constant, Zero Exponents, Negative Exponents, Like Terms, Polynomial, Binomial, Trinomial, Degree of a Monomial, Degree of a Polynomial, Standard Form of a Polynomial, Leading Coefficient, Quadratic Expression

11 Unit 7: Factoring and Quadratic Approximate Duration of Study: 4 5 weeks When to Study: January How does finding greatest common factors in factoring polynomials? Factoring Monomials Write a monomial in factored form Find the Greatest Common Factors (GCF) Quiz A.REI.2 A.REI.4b A.SSE.3a A-REI.4b A-REI.2 A-REI.4b F.IF.7a F.IF.8a Why do we factor polynomials? How can we identify a difference of squares? When might it be a good idea to not factor and use a different method for solving quadratic equations? Monomial Factors of Polynomials Zero Product Property Factoring Quadratic Special Products Square Root Property Solving Quadratic by of monomials Divide out the GCF of the terms Factor a polynomial by grouping Solve a quadratic equation using the zero product property Factor quadratic equations of the form: x 2 bx c 0 Factor quadratic equations of the form: ax 2 bx c 0 Factor quadratic equations that are the differences of squares Factor quadratic equations that are perfect squares Solve a quadratic equation in the form x 2 n Analyze the characteristics of the graphs of quadratic equations Quiz Stucture and Method Book 1 Chapter 5 and HW Set #1 HW Set #2 HW Set #3 HW Set #4 HW Set #5 HW Set #6 HW Set #7 Chapter 5 Review Factoring Review Worksheet Chapter 5 Practice Test Factoring 1 (pdf) Factoring 2 (pdf) Factoring Special Cases (pdf) Factoring By Grouping (pdf) Solving Quadratic Factoring (pdf) Complete the Square (pdf) Solving Completing Square (pdf) Quadratic Formula (pdf) Solving Quadratic Roots (pdf) SmartBoard Presentations notebook notebook

12 A-REI.4b A-REI.4a Graphing Estimate solutions of quadratic equations by graphing Completing the Square Solve quadratic equations by completing the square A-REI.4b Vocabulary: Quadratic Formula Use the Discriminant to determine the number of solutions to a quadratic equations Solve quadratic equations by using the Quadratic Formula Chapter 5d Test

13 Unit 8: Rational Expressions Approximate Duration of Study: 3 4 weeks When to Study: February A.CED.3 How is factoring Simplifying Simplify rational Quiz 6.1 used to simplify a Rational expressions using Ch 6.1 Quiz rational Expression common factors to Ch Quiz expression? reduce A.APR.6 A.APR.7 A.APR.7 A.APR.7 Vocabulary: How are reciprocals used to divide rational expressions? How do we add/subtract fractions? Multiplying and Dividing Rational Expressions Adding and Subtracting Rational Expressions Mixed Expressions Identify excluded values that would make the expression impossible (i.e. the denominator equal to 0) Multiply rational expressions, as we would common fractions, and reduce by common factors Divide rational expressions and reduce by common factors Divide rational expressions using polynomial long division Determine the Least Common Denominator of two or more fractions Add/ subtract rational expression with and without common denominators Simplify mixed expressions Simplify and use complex fractions to solve problems Ch Quiz Ch Quiz Ch 6.7 Quiz Chapter 6 Test Chapter 6 Test #2 Stucture and Method Book 1 Chapter 6 and HW Set #8 (Hanner) HW Set #9 (Hanner) HW Set #10 (Hanner) Fractions Review (Hanner) Adding Fractions Worksheet (Hanner) Chapter 6 Review Simplifying Rational Expressions (pdf) Multiplying Rational Expressions (pdf) Adding & Subtracting Rational Expressions (pdf) Dividing Rational Expressions (pdf) Dividing Polynomials (pdf) SmartBoard notebook notebook

14 Unit 9: Applying Fractions Approximate Duration of Study: 3 weeks When to Study: March A.CED.1 How can Ratios and Setup and simplify ratios Quiz 7.1 proportions be Proportions Quiz Setup and solve used to solve proportions problems? A.CED.1 A.APR.1 A.REI.2 A.SSE.3c How are percents and fractions related? How is a problem simplified with a negative exponent? Percents Fractional Negative Exponents Write a percent in decimal and fractional form Setup and solve percent proportions Find the percent of change and solve problems involving percent of change Solve equations with fractional coefficients Solve equations involving variables in the denominator of fractions Setup and solve problems involving mixture Simplify an expression involving negative exponents Simplify expressions in scientific notation Chapter 7 Test Chapter 7 Test #2 Stucture and Method Book 1 Chapter 7 and HW Set 11 HW Set 12 HW Set 13 HW Set 14 HW Set 15 Proportion Worksheet Proportion Problem Solving More Proportion Problem Solving Mixture and Work Problems Chapter 7 Review Solving Proportions (pdf) Percent Problems (pdf) Percent of Change (pdf) Mixture Word Problems (pdf) Work Word Problems (pdf) Writing Scientific Notation (pdf) Operations Scientific Notation (pdf) SmartBoard Lessons notebook notebook Vocabulary: Ratio, Proportion, Percent, Percent of Change, Fractional, Mixture, Negative Exponents, Scientific Notation

15 Unit 10: Radical Functions Approximate Duration of Study: 3 weeks When to Study: April/May CCS A.SSE.3C A.SSE.2 A.REI.2 G.SRT.8 Essential Question What makes a number a rational number? What are your essential rules when performing basic operations and simplification of square roots? Concept Skills Assessments Helpful Strategies and Resources Properties of Rational Numbers Rational and Irrational Square Roots Operations on Square Roots Radical Pythagorean s Theorem Identify a rational number Convert a number in fractional form to decimal form and vice versa Find the value of a rational square root Simplify an irrational square root expression Simplify a square root expression involving variables Multiply and divide square root expression Use conjugates to rationalize the denominator Add and subtract square root expressions Use the Power Property of Equality to solve equations Checking for extraneous solutions Use Pythagorean s Theorem to solve problem involving right triangles Quiz Quiz 11.4 Quiz Quiz Quiz (2) Quiz (3) Quiz Stucture and Method Book 1 Chapter 11 and Study Guide for 11-5 to 11-6 Study Guide for 11-7 to 11-9 Radical 1 (pdf) Radical 2 (pdf) Simplifying Radicals (pdf) Adding & Subtracting Radical Expressions (pdf) Multiplying Radical Expressions (pdf) Dividing Radical Expressions (pdf) HW Set #19 HW Set #20 SmartBoard Presentations Vocabulary: