Georgia Mathematics 1 Text Alignment to Georgia …math.uga.edu/~azoff/wkshop/txtalign.pdfGeorgia...

xviii ■ Alignment to the Georgia Performance Standards Georgia Mathematics 1

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Georgia Mathematics 1Text Alignment to Georgia Standards

Chapter # Chapter / Section Title Georgia Standard

1st SEMESTER

GEORGIA PERFORMANCE STANDARDS UNIT 1 AND UNIT 2 (ALGEBRA)

Chapter 1 Linear Functions, Equations, and Inequalities

1.1 Introduction to Linear Functions MM1A1b

1.2 Solving Linear Equations and Linear

Inequalities in One Variable MM1P1, P3, P4, P5

1.3 Slope Intercept Form of Linear Functions MM1A1b

1.4 General Form of Linear Functions MM1P1, P3, P4, P5

1.5 Parent Functions and Linear Transformations MM1A1b

MM1A1c

1.6 Finding the Equations of Linear Functions MM1P1, P3, P4, P5

1.7 Absolute Value in Equations and Inequalities MM1A1b

in One and Two Variables MM1A1d

MM1A1e

1.8 Functional Notation, Inverses, and Piecewise MM1A1a (and throughout)

Functions

1.9 Arithmetic Sequences MM1A1f

Chapter 2 Polynomial Expressions

2.1 Adding and Subtracting Polynomials MM1A2c

2.2 Multiplying and Dividing Polynomials MM1A2c

MM1A2g

2.3 Multiplying Binomials MM1A2c

2.4 Factoring Polynomials MM1A2f

Chapter 3 Quadratic Functions

3.1 Introduction to Quadratic Functions MM1A1b

3.2 Parabolas MM1A1b

MM1A1d

MM1A1e

3.3 Comparing Linear and Quadratic Functions MM1A1b

MM1A1g

3.4 Square Roots and Radicals MM1A2a

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3.5 Solving by Factoring and Extracting MM1A3a

Square Roots MM1A3c

3.6 Using the Quadratic Formula to Solve

Quadratic Equations MM1A3c

3.7 Using a Vertical Motion Model MM1A1b

MM1A1d

MM1A1e

MM1A1i

3.8 Using Quadratic Functions MM1A1b

Chapter 4 Polynomial Functions

4.1 Introduction to Polynomial Functions MM1A1b

MM1A1d

4.2 Solving Polynomial Equations and Inequalities:

Factoring MM1P1, P3, P4, P5

4.3 Solving Polynomial Equations and Inequalities: MM1A1b

Graphing MM1A1i

4.4 Extrema and End Behavior MM1A1b

MM1A1d

MM1A1e

MM1A1h

GEORGIA PERFORMANCE STANDARDS UNIT 3 (GEOMETRY)

Chapter 5 Parallel Lines and Triangles

5.1 Transversals and Parallel Lines MM1P1, P3, P4, P5

5.2 Introduction to Proofs MM1G2a

5.3 Parallel Lines and Proofs MM1G2a

5.4 The Triangle Inequality MM1G3b

5.5 Angle and Line Segment Bisectors MM1P1, P3, P4, P5

5.6 Points of Concurrency in Triangles MM1G3e

Chapter 6 Similarity

6.1 Ratio and Proportion MM1P1, P3, P4, P5

6.2 Similar and Congruent Figures MM1P1, P3, P4, P5

6.3 Similar Triangles MM1G2a

6.4 Indirect Measurement MM1P1, P3, P4, P5

6.5 Similar Solids MM1P1, P3, P4, P5

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Chapter 7 Congruence

7.1 Introduction to Congruence MM1G3c

7.2 Proving Triangles Congruent: SSS and SAS MM1G3c

MM1G2a

7.3 Proving Triangles Congruent: ASA and AAS MM1G3c

MM1G2a

7.4 Proving Triangles Congruent: HL MM1G3c

MM1G2a

7.5 Fractals MM1G3c

Chapter 8 Quadrilaterals

8.1 Introduction to Quadrilaterals MM1G3d

8.2 Kites and Trapezoids MM1G3d

8.3 Parallelograms and Rhombi MM1G3d

8.4 Rectangles and Squares MM1G3d

8.5 Sum of the Interior Angle Measures in a Polygon MM1G3a

8.6 Sum of the Exterior Angle Measures in a Polygon MM1G3a

2nd SEMESTER

GEORGIA PERFORMANCE STANDARDS UNIT 4 (PROBABILITY)

Chapter 9 Counting Methods and Probability

9.1 Simple Probability and Sample Spaces MM1P1, P3, P4, P5

9.2 Compound Probability MM1D2a

MM1D2b

MM1D2c

9.3 Permutations and Combinations MM1D1a

MM1D1b

9.4 Pascal’s Triangle and the Binomial Theorem MM1A1d

9.5 Experimental Probability MM1D2d

Chapter 10 Statistical Analysis

10.1 Measures of Central Tendency MM1D3a

MM1D3b

10.2 Collecting and Analyzing Data MM1D3a

MM1D3c

10.3 Quartiles and Box-and-Whisker Plots MM1D3a

10.4 Sample Variance and Standard Deviation MM1D4

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GEORGIA PERFORMANCE STANDARDS UNIT 5 (ALGEBRA)

Chapter 11 Rational Equations and Functions

11.1 Introduction to Rational Functions MM1P1, P3, P4, P5

11.2 Simplifying, Adding, and Subtracting MM1A2e

of Rational Expressions

11.3 Multiplying and Dividing of Rational MM1A2e

Expressions

11.4 Solving Rational Equations and Inequalities MM1A3d

11.5 Graphing Rational Functions and MM1A1b

Discontinuities MM1A1d

MM1A1e

11.6 Work and Mixture Problems MM1A3d

Chapter 12 Radical Equations and Functions

12.1 Introduction to Radicals MM1P1, P3, P4, P5

12.2 Simplifying Radical Expressions MM1A2a

MM1A2b

12.3 Solving Radical Equations MM1A3b

12.4 Graphing Radical Functions MM1A1b

MM1A1d

MM1A1e

GEORGIA PERFORMANCE STANDARDS UNIT 6 (GEOMETRY)

Chapter 13 Coordinate Geometry

13.1 The Distance Formula MM1G1a

MM1G1d

13.2 The Midpoint Formula MM1G1c

13.3 Parallel and Perpendicular Lines in the

Coordinate Plane MM1P1, P3, P4, P5

13.4 Exploring Triangles in the Coordinate Plane MM1G1c

MM1G1e

13.5 Rectangles and Parallelograms in the MM1G1a

Coordinate Plane MM1G1e

MM1G3d

Georgia Mathematics I Standards covered in Supplemental Software:

• MM1G2b – Understand and use the relationships among a statement and its converse, inverse, and

contrapositive

• MM1G1b – Determine the distance between a point and a line

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Georgia Mathematics 2

Text Alignment to Georgia Standards

Unit Chapter Section Title Standard(s)

1

0

Functions, Relations, & Inverses

1 Functions and Relations

2 Evaluating Functions: Functional Notation, Domain and Range

3 Linear Functions

4 Inverses of Linear Functions

1

Quadratic Functions

1 Introduction

2 Parabolas

3 Increase, Decrease, and Rates of Change

4 Roots and Zeros

5 Vertex

6 Vertex Form of Equation

7 Graphing and Transformations

2

Quadratic Formula, Equations, and Inequalities

1 Proof of Quadratic Formula

2 Calculating roots and Zeros

3 Discriminant

4 Complex Numbers

5 Complex Roots and Zeros

6 Quadratic Inequalities

7 Arithmetic Sequences and Partial Sums

8 Modeling Partial Sums

2

3

Right Triangles

1 Pythagorean Theorem

2 Distance and Midpoint Formulas

3 Special Triangles

4 Properties of Special Triangles

4

Trigonometric Ratios

1 Similar and Congruent Polygons

2 Tangent Ratio

3 Sine Ratio

4 Cosine Ratio

5 Angles of Elevation and Depression

3 5

Circles

1 Introduction

2 Central and Inscribed Angles and Intercepted Arcs

3 Angles Inside and Outside of Circles

4 Chords and Circles

5 Tangents and Circles

6 Arc Length

7 Areas of Parts of Circles

8 Circle Measurements and Relationships

6

Spheres

1 Properties of Spheres

2 Volume of a Sphere

3 Surface Area of a Sphere

4 Applications

4 7

Data Analysis

1 Variance

2 Effect of Sample Size

3 Sampling Techniques

4 Bias and Experiment Design

5 Experimental Analysis

5

8

Exponential Functions

1 Integral Exponents

2 Domain, Range, Intercepts

3 Increase, Decrease, Asymptotes, End Behavior

4 Transformations

5 Solving Exponential Equations

9

Exponential Modeling

1 Growth, Decay, and Interest

2 Geometric Sequences and Partial Sums

3 Geometric Sequences and Series as Exponential Functions

4 Modeling with Exponential Functions

10

Other Functions and Inverses

1 Absolute Value as Piecewise

2 Graphs of Absolute Value Functions

3 Properties of Piecewise Functions

4 Solving Absolute Value Equations and Inequalities

5 Power Functions and Inverses

6 Inverses

6

11

Modeling with Linear Functions

1 Drawing Line of Best Fit

2 Performing an Experiment

3 Median-Median Line of Best Fit

4 Least Squares

5 Regression Equation Via Technology

6

7 Causation versus Correlation

12

Mathematical Modeling

1 Modeling with Quadratic Functions

2 & 3 Using Functions to Model Data

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Georgia Mathematics 3Text Alignment to Georgia Standards


Chapter 1 Matrix Operations and Equations

1.1 Introduction to Matrices and Matrix Operations MM3A4a

MM3A4c

1.2 Matrix Multiplication MM3A4a

1.3 Number Properties and Matrices MM3A4b

MM3A4c

1.4 Multiplicative Inverses MM3A4b

MM3A4c

1.5 Matrix Equations MM3A5a

MM3A5b

MM3A5c

1.6 Determinants MM3A4a

Chapter 2 Matrices and Applications

2.1 Matrices and Problem Solving MM3A6a

MM3A6b

2.2 Introduction to Linear Programming MM3A6a

MM3A6b

2.3 Linear Programming and Problem Solving MM3A6a

MM3A6b

2.4 Vertex-Edge Graphs, Part I MM3A7a

MM3A7b

2.5 Vertex-Edge Graphs, Part II MM3A7a

MM3A7b

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20 ● Alignment to the Georgia Performance Standards Georgia Mathematics 3


Chapter 3 Power Functions and Polynomial Functions

3.1 Power Functions MM3A1a

3.2 Polynomial Functions MM3A1a

3.3 Graphs of Polynomial Functions MM3A1a

3.4 Symmetry MM3A1c

3.5 Zeros and Multiplicity MM3A1b

MM3A1d

3.6 Extrema, Domain & Range, and End Behavior MM3A1b

MM3A1d

3.7 Graphs and Properties of Polynomial Functions MM3A1a

MM3A1b

MM3A1c

MM3A1d

Chapter 4 Polynomial Functions and Data Modeling

4.1 Polynomial Function Operations and

Composition MM3A1

4.2 Piecewise Polynomial Functions MM3A1d

4.3 Polynomial Functions and Data, Part I MM3A1d

4.4 Polynomial Functions and Data, Part II MM3A1d

Chapter 5 Three-Dimensional Coordinates

5.1 Point Plotting in Three Dimensions MM3G3a

5.2 Equations of Planes MM3G3b

5.3 Distance in Three Dimensions MM3G3b

5.4 Models and Volume MM3A1a

MM3A1b

MM3A1c

MM3A1d



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Chapter 6 Exponential Functions

6.1 Inverses of Functions REVIEW

6.2 Rational Exponents, Part I MM3A2a

MM3A2b

6.3 Rational Exponents, Part II MM3A2a

MM3A2b

6.4 Graphs of Exponential Functions MM3A2e

6.5 Transformations of Exponential Functions MM3A2f

6.6 Exponential Functions and Problem Solving,

Part I MM3A2g

6.7 Exponential Functions and Problem Solving,

Part II MM3A2g

Chapter 7 Logarithmic Functions

7.1 Logarithmic Functions as Inverses MM3A2c

MM3A2e

7.2 Exponential and Logarithmic Forms MM3A2c

7.3 Graphs of Logarithmic Functions MM3A2e

7.4 Transformations of Logarithmic Functions MM3A2f

Chapter 8 Exponential and Logarithmic Functions

8.1 Exponential and Logarithmic Equations, Part I MM3A2c

MM3A2g

8.2 Exponential and Logarithmic Equations, Part II MM3A2c

MM3A2g

8.3 Exponential and Logarithmic Problem Solving,

Part I MM3A2g

8.4 Exponential and Logarithmic Problem Solving,

Part II MM3A2g



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Chapter 9 Exponential and Logarithmic Equations

9.1 Properties of Logarithms MM3A2d

9.2 Exponential and Logarithmic Equations MM3A3b

MM3A3c

MM3A3d

9.3 Exponential Functions and Data MM3A3b

MM3A3c

MM3A3d

9.4 Exponential and Logarithmic Problem Solving MM3A3b

MM3A3c

MM3A3d

Chapter 10 Polynomial Equations

10.1 Polynomial Equation Solving by Factoring MM3A3

10.2 Polynomial Inequality Solving by Factoring MM3A3

10.3 The Fundamental Theorem of Algebra MM3A3

10.4 Synthetic Division MM3A3

10.5 The Remainder Theorem MM3A3

10.6 The Factor Theorem MM3A3

10.7 Polynomial Equations, Part I MM3A3

10.8 Polynomial Equations, Part II MM3A3

Chapter 11 Introduction to Conics and Circles

11.1 Conics as Cross Sections MM3G2b

11.2 Equations of Conic Sections MM3G2b

11.3 Circles MM3G1a

MM3G1b

11.4 Intersections of Circles and Lines MM3G1d

11.5 Tangent Lines MM3G1c

11.6 Intersections of Two Circles MM3G1e

11.7 Circles and Problem Solving MM3G1



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Supplemental

Software


Chapter 12 Ellipses

12.1 Ellipses Centered at the Origin MM3G2a

MM3G2b

MM3G2c

12.2 Ellipses not Centered at the Origin MM3G2a

MM3G2b

MM3G2c

12.3 Forms of Ellipses MM3G2a

MM3G2b

MM3G2c

12.4 Ellipses and Problem Solving MM3G2a

MM3G2b

MM3G2c

Chapter 13 Hyperbolas

13.1 Hyperbolas Centered at the Origin MM3G2a

MM3G2b

MM3G2c

13.2 Hyperbolas not Centered at the Origin MM3G2a

MM3G2b

MM3G2c

13.3 Forms of Hyperbolas MM3G2a

MM3G2b

MM3G2c

13.4 Hyperbolas and Problem Solving MM3G2a

MM3G2b

MM3G2c

Chapter 14 Parabolas

14.1 Parabolas Centered at the Origin MM3G2a

MM3G2b

MM3G2c

14.2 Parabolas not Centered at the Origin MM3G2a

MM3G2b

MM3G2c

14.3 Forms of Parabolas MM3G2a

MM3G2b

MM3G2c

14.4 Parabolas and Problem Solving MM3G2a

MM3G2b

MM3G2c



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Chapter 15 Conics and Problem Solving

15.1 Forms of Conics MM3G2a

MM3G2b

MM3G2c

15.2 Applications of Conics, Part I MM3G2a

MM3G2b

MM3G2c

15.3 Applications of Conics, Part II MM3G2a

MM3G2b

MM3G2c

15.4 Spheres and Planes MM3G3c

Chapter 16 Distributions of Discrete Data

16.1 Sampling Methods and Bias MM3D3

16.2 Observational Studies and Experiments MM3D3

16.3 Study Design MM3D3

16.4 Probability Histograms MM3D1

16.5 Binomial Distributions MM3D1

16.6 Reports of Studies MM3D3

Chapter 17 Distributions of Continuous Data

17.1 Normal Distributions MM3D2

17.2 Mean and Standard Deviation MM3D2

17.3 Introduction to z-scores MM3D2

17.4 More with z-scores MM3D2

17.5 Distributions and Problem Solving MM3D2

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