math

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