Integrated Algebra

Scope and Sequence

Schenectady High School Department of Mathematics

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Chapter 1

Foundations for Algebra

 1-1

Writing Mathematical Expressions

1-2,1-3

Operations with Integers

1-4

Powers and Exponents

1-5

Square Roots and Real Numbers

1-6

Order of Operations

1-7

Simplifying Expressions

1-8

The Coordinate Plane

Sup

Number Properties & Absolute Value

0-2, p. 52, Sup

Basic Area & Perimeter

Chapter 2

Equations

2-1,2-2

Solving One-Step Equations

2-3

Solving Two-Step and Multi-Step Equations

2-4

Solving Equations with Variables on Both Sides

2-5

Solving for a Variable

Extension

Solving Absolute Value Equations p. 148 & Supplement

Sup

Writing & Solving Linear Equations

2-6

Rates, Ratios and Proportions

2-7

Applications of Proportions

2-8

Percents

2-9

Applications of Percents

2-10

Percent of Increase and Decrease

Sup

Relative Error

Chapter 3

Inequalities

3-1,3-2

Graphing, Writing & Solving Inequalities (Adding & Subtracting)

3-3,3-4

Solving Inequalities (Multiplying & Dividing), Two-Step, Multi-Step

3-5

Solving Inequalities with Variables on Both Sides

3-6

Solving Compound Inequalities

Chapter 4

Functions

4-1, 4-2

Graphing Relationships/Relations & Functions

p. 243

Vertical Line Test Lab

4-3 & Sup

Writing Functions

4-5, A-5 p. 939

Scatter Plots and Trend Lines

Sup, p. 270

Scatter Plots on Graphing Calculator

Quarter 1 Exam

First Week of November

Chapter 5

Linear Functions

5-2

Using Intercepts

5-3, 5-4

Rate of Change/ The Slope Formula

Sup

Writing Equations in y=mx+b form and Graph

5-6 & Sup

Slope-Intercept Form

5-7 & Sup

Writing the Equation of a line given the Slope and one point or given two points

5-5

Direct Variation (Note:  Emphasis b = 0)

Sup

Lab on Families of Linear Functions

5-8

Slopes of Parallel and Perpendicular Lines

Extension

Absolute Value Functions p. 366 & Supplement

Chapter 6

Systems of Equations and Inequalities

6-1 & Sup

Solving Linear Systems by Graphing

6-2

Solving Systems by Substitution

6-3 & Sup

Solving Systems by Elimination (Note: Emphasize word problems)

6-4

Solving Special Systems (no solution or infinite solutions)

6-5

Solving Linear Inequalities

6-6

Solving Systems of Linear Inequalities

Sup

Graphing Systems of Linear Inequalities on the Graphing Calculator

Sup

Graphing Linear Inequalities on the Graphing Calculator

Chapter 7

Exponents and Polynomials

7-1 & Sup

Integer Exponents

7-2

Powers of Ten and Scientific Notation

p.458-9

Properties of Exponents

7-3,7-4

Properties of Exponents when Multiplying and Dividing

7-5

Polynomials

7-6 & p.482-3

Adding and Subtracting Polynomials

7-7 & Sup

Multiplying & Dividing Polynomials by a Monomial

7-7, 7-8 & Sup

Multiplying Two Binomials by FOIL (Special Products)

p.500 & Sup

Volume and Surface Area & Review Basic Formulas (Area of Shaded Regions)

Midterm Exam

Week of January 18th

(75% Quarter 2 Material, 25% Quarter 1 Material)

Chapter 8

Factoring Polynomials

8-1

Factors and Greatest Common Factors

8-2

Factor by Greatest Common Factor

8-3

Factoring x2+bx+c

8-5 & Sup

Factoring Special Products

8-6

Choosing a Factoring Method

8-4

OPTIONAL Factoring ax2+bx+c when a > 1

Chapter 9

Quadratic Functions and Equations

9-1,9-4

Identifying and Transforming Quadratic Functions

Sup

Families of Quadratic Functions on the Graphing Calculator

Sup & p. 598

Axis of Symmetry & Vertex

9-2 & Sup

Characteristics of Quadratic Functions

9-3 & Sup

Graphing Quadratic Functions (using a table)

9-6

Solving Quadratic Equations by Factoring

9-6 Sup

Writing & Solving Quadratic Equations

9-5

Solving Quadratic Equations by Graphing

Sup

Solving Linear-Quadratic Systems by Graphing

9-7

OPTIONAL Solving Quadratic Equations by Using Square Roots

9-8

OPTIONAL Completing the Square

Chapter 12

Rational Functions and Equations

12-1,12-2

Undefined Fractions

12-3

Simplifying Rational Expressions

12-4, 12-6

Multiplying and Dividing Rational Expressions

12-5

Adding and Subtracting Rational Expressions

12-7

Solving Rational Equations (choose cross products only)

Quarter 3 Exam

Week of March 29th

Chapter π

Introduction to Geometry & Trigonometry

p.642

The Distance Formula

Sup

Pythagorean Theorem (p.S71 Skills Bank)

Extension

Trig Ratios p. 908 & Supplement

Extension

Inverse Trig Functions p. 908 & Supplement

Sup

Distinguishing between Trig and the Pythagorean Theorem

Chapter 10

Data Analysis and Probability

10-1, A-1 p. 925

Organizing and Displaying Data (Quantitative vs. Qualitative)

10-2, A-2 p. 926

Frequency and Histograms (Include Cumulative) & Univariate/Bivariate

10-3, A-4 p. 936

Measures of Central Tendency (Box & Whisker Plots)

10-4 & p.708,944

Misleading Graphs and Statistics (Sample Methods/Bias)

10-5, 10-6

Experimental & Theoretical Probability

10-7 & p.734

Independent and Dependent Events

Sup

Tree Diagrams & Sample Space

10-8

Combinations and Permutations

p.746

Set Theory: Notation, Subset, Venn Diagrams

Sup

Set Theory: Union, Intersection, Complement

Sup

Histograms on the Graphing Calculator

p.712

Simulations

Sup

Simulations on the Graphing Calculator (if time allows)

Chapter 11

Exponential and Radical Functions

11-1 & Sup

Arithmetic Sequence/Geometric Sequence Recognize and Identify

11-2 & Sup

Evaluate, Recognize and Identify Basic Exponential Functions

5-1 & Sup

Identifying Functions (Linear, Quadratic, Exponential, Conic, Absolute Value)

11-4

Linear, Quadratic and Exponential Models

11-3

Exponential Growth and Decay

11-6

Radical Expressions

11-7

Adding and Subtracting Radical Expressions

11-8

Multiplying and Dividing Radical Expressions

11-9

Solving Radical Equations (if time allows)

11-5

OPTIONAL Square Root Functions

Extension

OPTIONAL Rational Exponents