Algebra 1
Curriculum Map
Table of Contents
Unit 1: Expressions and Equations
Unit 6: Polynomials
Unit 2: Linear Equations
Unit 7: Factoring and Quadratics
Unit 3: Representing Linear Equations
Unit 8: Rational Equations
Unit 4: Linear Inequalities
Unit 9: Applying Fractions
Unit 5: Systems of Linear Equations
Unit 10: Radical Equations
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.
Unit 1: 1: Expressions & Equations Approximate Duration of Study: 1 weeks CCS A.SSE.1.a A.SSE.1.b
Essential Question Why do we use variables?
Why are “the order of operations” and other properties of mathematics important?
Concept Variables and Expressions
Order of Operations
Distributive Property
Equations
Skills 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 Solve equations with two variables given a domain
When to Study: Aug Assessments
Helpful Strategies and Resources
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 2.4-2.6 Quiz 2.6-2.8
Vocabulary: Variable, Expression, Order of Operations, Distributive Property, Equations, Domain
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 1 and accompanying resources McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 2 and accompanying resources Algeblocks Labs o Labs 3-1, 3-2, 3-3, 3-4, 3-5, 3-6 Labs 5-2, 5-3, 5-1, 5-4, 5-5, 5-6 o Math Words Jigsaw Activity Writing a Story Problem Project Rubric Distributive Property (pdf) Combining Like Terms (pdf) Evaluating Expressions (pdf) Order of Operations (pdf)
Unit 2: Linear Equations Approximate Duration of Study: 2 weeks CCS A.CED. 1
A.REI.1 A.REI.3
Essential Question Why is advantageous to use and solve equations algebraically for realworld problems?
Concept Writing Equations
One-step equations
A.REI.1 A.REI.3
Multi-Step Equations
A.REI.1 A.REI.3
Equations with the variable on each side
A.REI.1
A.CED. 4
When would we want to use the absolute value of numbers?
Absolute Value Equations Literal Equations
Skills
When to Study: Aug/ Sept Assessments
Translate sentences into equations 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
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 3 and accompanying resources McDougal Littell/ Houghton Mifflin – “Algebra: 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 Equations (pdf) Two-Step Equations (pdf) Multi-Step Equations (pdf) Absolute Value Equations (pdf)
A.N. Chap. 3 Quiz A.N. Chap. 3 Quiz #2 A.N. Chap. 3 Quiz #3 Chap. 3.3-4.1
Vocabulary: Formula, Equation, Equivalent, Consecutive Integers, Integers, Identity, Cost, Value, Income, Literal Equation, Absolute Value
Unit 3: Representing Linear Linear Equations Approximate Duration of Study: 3 – 4 weeks CCS
Essential Question
A.REI.10
Concept Graphing Linear Equations
Skills
When to Study: September Assessments
Identify linear equations, intercepts, and zeros
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 8 and accompanying resources 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 Equations (pdf)
Graph linear equations A.REI.10
How does the slope affect direct variation?
Solving linear equations by graphing
Solve equations by graphing and identifying the root Estimate solutions to an equation by graphing
Rate of Change and Slope
Use rate of change to solve problems Find the slope of a line
Direct Variation
Write and graph direct variation equations Solve problems involving direct variation
A.REI.10
A.CED.2
What does the slope-intercept form of an equation tell us?
Graphing Equations in Slope-Intercept Form
Write and graph linear equations in slopeintercept form
Writing equations in slope-intercept form
Write an equation of a line in slope-intercept form given the slope and one point
Model real-world data with equations in slopeintercept form
Write an equation of a line in slope-intercept form given two points
Helpful Strategies and Resources
A.N. Chap. 8 Quiz A.N. Chap. 8 Quiz #2 A.N. Chap. 8 Quiz #3 A.N. Chap. 8 Quiz #4
ACED.2 A.REI.1 0
Why should we know different forms of linear equations?
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
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
Write equations of lines passing through a given point and either parallel or perpendicular to a given line
Lines of Fit
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 Perpendicular Lines, Scatter Plot, Line of Fit
Unit 4: Linear Inequalities Approximate Duration of Study: 2 weeks CCS A.REI.3
Essential Question -How are inequalit ies and equations alike? How are they different?
How do the words “and” and “or” affect the outcome of an inequality?
A.REI.1 2
Concept Inequalities Involving Addition and Subtraction Inequalities Involving Multiplication and Division Solving MultiStep Inequalities
Solving Compound Inequalities
Inequalities involving Absolute Value Inequalities in Two Variables
Skills
When to Study: Assessments
Solving linear inequalities by using addition and subtraction
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 10 and accompanying resources 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)
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 graph “and” and their solution set Solve compound inequalities containing the word and graph their “or” and 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
Helpful Strategies and Resources
Chapter 10 Test Chapter 10 Test(2) Chapter 10 Test(3)
Unit 5: Systems of Linear Equations and Inequalities Approximate Duration of Study: 2 weeks CCS A.REI.6 A.REI.1 1
Essential Question How might one determine the most efficient method for solving a system of equations?
Concept Graphing Systems of Equations
A.REI.5 A.REI.6
Substitution
A.REI.5 A.REI.6
Elimination
A.REI.6
Applying Systems of Linear Equations
A.REI.8
Why would using a matrix to solve a system of equations be useful?
Matrix equations
Skills
When to Study: October/November Assessments
Determine the number of solutions a system of 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
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 9 and accompanying resources Systems of Equations Graphing (pdf) Systems of Equations Substitution (pdf) Systems of Equations Elimination (pdf) Systems of Equations Word Problems (pdf)
A.N. Chap. 9 Quiz #1 A.N. Chap. 9 Quiz #2 A.N. Chap. 9 Quiz #3 A.N. Chap. 9 Quiz #4
Vocabulary: System of Equations, Consistent, Independent, Dependent, Inconsistent, Substitution, Elimination, Elimination, Matrix, Augmented Matrix, Row Reduction
Unit 6: Polynomials Approximate Duration of Study: 3 – 4 weeks CCS A.APR.1
Essential Question How might we classify polynomials?
A.APR.1
A.APR.1
A.APR.1
A.APR.1
How can we use the polynomial operations of addition, subtraction, and multiplication multiplication in real life?
Concept Multiplying Monomials
Skills
When to Study: November Assessments
Base and Exponent Power of product Power of a power
Dividing Monomials
Find the quotient of two monomials
Polynomial Identification
Simplify expressions containing negative and zero exponents Find the degree of a polynomial Write polynomials in standard form Identify “like terms”
Adding/ Subtracting Polynomials
Quiz 4.3-4.4
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 4 and accompanying resources Algeblocks Labs o Labs 6-1, 6-2, 6-3 Multiplying Polynomials by Monomials Exponents Intro PowerPoin PowerPointt More Properties of Exponents (pdf) Naming Polynomial Polynomialss (pdf) Adding & Subtracting Polynomials (pdf) Multiplying Polynomial Polynomialss (pdf) Multiplying Special Cases (pdf) Properties of Exponents (pdf)
Add/ subtract polynomials
Multiplying a Polynomial by a Monomial
Use the Distributive Property to multiply a monomial by a polynomial
Multiplying Polynomials
Use the Distributive Property to multiply a polynomial by another polynomial
Special Products
Find the squares of sums and differences Find the product of a sum and difference
Quiz 4.6-4.8
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, Monomial, Constant, Zero Exponents, Negative Exponents, Like Terms, Polynomial, Binomial, Trinomial, Degree of a Monomial, Monomial, Degree of a Polynomial, Standard Form of a Polynomial, Polynomial, Leading Coefficient, Quadratic Expression
Unit 7: Factoring and Quadratic Equations Approximate Duration of Study: 4 – 5 weeks CCS
Essential Question How does finding greatest common factors in factoring polynomials?
Concept Factoring Monomials
Monomial Factors of Polynomials Zero Product Property A.REI.2 A.REI.4b A.SSE.3a
Why do we factor polynomials?
Factoring Quadratic Equations
Skills
Assessments
Write a monomial in factored form Find the Greatest Common Factors (GCF) of monomials Divide out the GCF of the terms
How can we identify a difference of squares?
Special Products
A-REI.4b
When might it be a good idea to not factor and use a different method for solving quadratic equations?
Square Root Property
F.IF.7a F.IF.8a
Solve a quadratic equation using the zero product property Factor quadratic equations of the form: 2
x bx c 0 Factor quadratic equations of the form: ax 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
Solving Quadratic Equations by
Quiz 5.1-5.3
Factor a polynomial by grouping
2
A-REI.4b A-REI.2
When to Study: January
2
n
Analyze the characteristics of the graphs of quadratic equations
Quiz 5.4-5.6
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 5 and accompanying resources 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 5.1- 5.3.notebook 5.4-5.7.notebook
Graphing
A-REI.4b A-REI.4a
Completing the Square
A-REI.4b
Quadratic Formula
Vocabulary:
Estimate solutions of quadratic equations by graphing Solve quadratic equations by completing the square Use the Discriminant to determine the number of solutions to a quadratic equations Solve quadratic equations by using the Quadratic Formula
Chapter 5d Test
Unit 8: Rational Expressions Expressions Approximate Duration of Study: 3 – 4 weeks CCS
Essential Question How is factoring used to simplify a rational expression?
Concept Simplifying Rational Expression
A.APR.6 A.APR.7
How are reciprocals used to divide rational expressions?
Multiplying and Dividing Rational Expressions
A.APR.7
How do we add/subtract fractions?
Adding and Subtracting Rational Expressions
A.CED.3
A.APR.7
Vocabulary:
Mixed Expressions
Skills
When to Study: February Assessments
Simplify rational expressions using common factors to reduce 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
Quiz 6.1 Ch 6.1 Quiz Ch 6.1-6.2 Quiz
Simplify mixed expressions Simplify and use complex fractions to solve problems
Chapter 6 Test Chapter 6 Test #2
Ch 6.2-6.3 Quiz Ch 6.3-6.4 Quiz Ch 6.7 Quiz
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 6 and accompanying resources 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 Polynomial Polynomialss (pdf) SmartBoard 6.1 - 6.3.notebook 6.4 - 6.5.notebook
Unit 9: Applying Fractions Fractions Approximate Duration of Study: 3 weeks CCS A.CED.1
A.CED.1
Essential Question How can proportions be used to solve problems? How are percents and fractions related?
A.APR.1 A.REI.2
A.SSE.3c
Concept Ratios and Proportions
Percents
Fractional Equations
How is a problem simplified with a negative exponent?
Negative Exponents
Skills Setup and simplify ratios Setup and solve proportions 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
When to Study: March Assessments Quiz 7.1 Quiz 7.1-7.3
Chapter 7 Test Chapter 7 Test #2
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 7 and accompanying resources 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 7.1-7.3.notebook 7.4-7.6.notebook
Vocabulary: Ratio, Proportion, Percent, Percent of Change, Fractional Equations, Mixture, Negative Exponents, Scientific Notation
Unit 10: Radical Functions Approximate Duration of Study: 3 weeks CCS
A.SSE.3C
Essential Question What makes a number a rational number?
What are your essential rules when performing basic operations and simplification simplification of square roots?
Concept
Skills
Properties of Rational Numbers
Identify a rational number Convert a number in fractional form to decimal form and vice versa Find the value of a rational square root
Rational and Irrational Square Roots
A.SSE.2
Operations on Square Roots
A.REI.2
Radical Equations
G.SRT.8
Pythagorean’s Theorem
Vocabulary:
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
When to Study: April/May Assessments Quiz 11.1 - 11.3
Quiz 11.4 Quiz 11.5 – 11.6 Quiz 11.1 - 11.3 Quiz 11.1 –11.3 (2) Quiz 11.1-11.3 (3) Quiz 11.7-11.9
Helpful Strategies and Resources
McDougal Littell/ Houghton Mifflin – “Algebra: Stucture and Method Book 1” – Chapter 11 and accompanying resources Study Guide for 11-5 to 11-6 Study Guide for 11-7 to 11-9 Radical Equations 1 (pdf) Radical Equations 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 11.1 - 11.3