KY Advanced Mathematical Concepts - Glencoedev.glencoe.com/sites/correlations/pdf/KYAMC04.pdf · Kentucky Core Content 2 Glencoe/McGraw-Hill Advanced Mathematical Concepts: Precalculus

KENTUCKY

Correlation with Kentucky Core Content for Mathematics Assessment and Responses to Standards for Mathematics Evaluation Instrument

Adoption Group IV Commonwealth of Kentucky 2003-2009

Kentucky Core Content 1 Glencoe/McGraw-Hill Advanced Mathematical Concepts: Precalculus with Applications

Number/Computation

Concepts

OBJECTIVES PAGE REFERENCES MA-H-1.1.1 Students will describe properties of, define, give examples of, and apply real numbers to both real-world and mathematical situations, and understand that irrational numbers cannot be represented by terminating or repeating decimals.

SE: 8, 46, 206, 362, 421, 448, 493, 556, 665, 705 Graphing Calculator Exploration 86

TWE: GE 86

MA-H-1.1.2 Students will recognize, define, give examples of, and apply to both real-world and mathematical situations finite arithmetic and geometric sequences and series.

SE: Sample Demonstrator: 759 759-765, 766-773, 830, A48 TWE: TM 758c

MA-H-1.1.3 Students will understand how matrices are used to represent real-world data.

SE: 78-85, 120, A28 TWE: A 86 MC 88

See page 27 for a list of codes used for TWE pages.


Sample Demonstrator Number/Computation: Concepts

MA-H-1.1.1 to MA-H-1.1.3


Number/Computation

Skills OBJECTIVES PAGE REFERENCES

MA-H-1.2.1 Students will perform addition, subtraction, multiplication, and division with real numbers in problem-solving situations to specified accuracy.

SE: 284-290, 299-304, 305-311, 336, 337, A34

SAT & ACT Preparation 64-65 TWE: MC 291

MA-H-1.2.2 Students will simplify real number expressions such as those containing opposites, reciprocals, absolute values, exponents (integer), roots (square, cube), and factorials.

SE: 7, 10-11, 191, 797-799, 803-805

MA-H-1.2.3 Students will use matrix addition, subtraction, multiplication (no larger than 2 by 2), and scalar multiplication to solve real-world problems.

SE: Sample Demonstrator: 78 78-85, 98-104, 120, A28, A29 TWE: A 86

MC 88

MA-H-1.2.4 Students will determine a specific term of a sequence given an explicit formula and write an explicit rule for the nth term of arithmetic and geometric sequences.

SE: 759-765, 766-773, 830, A48 TWE: TM 758c

MA-H-1.2.5 Students will use simple combinations and permutations to count discrete quantities.

SE: 837-845, 882, 885, A51 TWE: MC 846


Sample Demonstrator Number/Computation: Skills MA-H-1.2.1 to MA-H-1.2.5


Number/Computation

Relationships OBJECTIVES PAGE REFERENCES

MA-H-1.3.1 Students will understand how the following subsets of real numbers relate to each other: natural, whole, integers, rational, irrational, reals.

See Algebra 2.

MA-H-1.3.2 Students will understand how real number properties (identity, inverse, commutative, associative, distributive, closure) are used to simplify expressions and solve equations.

SE: 8, 46, 206, 362, 421, 448, 493, 556, 665, 705 Graphing Calculator Exploration 86

TWE: GE 86

MA-H-1.3.3 Students will understand how to use equivalence relations (reflexive, symmetric, transitive) and order relations (less than, greater than, equal to) to solve problems using real numbers.

SE: SAT & ACT Preparation 202-203 Also see Algebra 2.

MA-H-1.3.4 Students will understand how ratio and proportion can be used in a variety of mathematical contexts and to solve real-world problems.

SE: Sample Demonstrator: 692 141, 191-196, 200, 284-290, 294,

345 SAT & ACT Preparation 692-693

TWE: MC 291 IE 192


Sample Demonstrator Number/Computation: Relationships

MA-H-1.3.1 to MA-H-1.3.4


Geometry/Measurement

Concepts OBJECTIVES PAGE REFERENCES

MA-H-2.1.1 Students will describe properties of and give examples of geometric transformations and apply geometric transformations (translations, rotations, reflections, dilations), with and without a coordinate plane, to both real-world and mathematical situations.

SE: 88-95, 121, 670-677, A28 TWE: A 96

MC 98

MA-H-2.1.2 Students will define, describe properties of, give examples of, and apply to both real-world and mathematical situations spatial relationships such as betweenness, parallelism, and perpendicularity.

SE: Sample Demonstrator: 34 34-37, 59, A27 TWE: MC 38

MA-H-2.1.3 Students will define, describe properties of, give examples of, and apply to both real-world and mathematical situations angle relationships such as linear pairs, vertical, complementary, supplementary, corresponding, and alternate interior angles.

SE: 277-283 Also see Geometry.

MA-H-2.1.4 Students will describe properties of, define, give examples of, and apply to both real-world and mathematical situations ratio measures including slope and rate.

SE: 20-25, 59, A26 TWE: IE 21

MA-H-2.1.5 Students will describe properties of, define, give examples of, and apply to both real-world and mathematical situations right triangle trigonometric measures (sine, cosine, tangent).

SE: 285-290, 299-304, 320-326, 327-332, 336, 337, A34

Graphing Calculator Exploration 333-334

TWE: MC 291


Sample Demonstrator Geometry/Measurement: Concepts

MA-H-2.1.1 to MA-H-2.1.5




MA-H-2.2.1 Students will perform transformations (reflections, translations, rotations, dilations) on figures.

SE: 88-95, 121, A28 TWE: A 96

MC 98

MA-H-2.2.2 Students will classify two-dimensional and three-dimensional geometric figures according to their characteristics such as lengths of sides; angle measures; and number of sides, faces, edges, and vertices. Students will describe the intersection of a plane with a three-dimensional geometric figure.

SE: SAT & ACT Preparation 482-483 Also see Geometry.

MA-H-2.2.3 Students will determine height and distance using methods of indirect measurement such as similar triangles (including shadow or mirror method) and right triangle relationships (including trigonometric ratios).

SE: 285-290, 299-304, 336, 337, A34 TWE: MC 291

MA-H-2.2.4 Students will use Pythagorean relationships to solve problems in real-world and mathematical situations.

SE: Sample Demonstrator: 615 421-429, 615-616, 624

SAT & ACT Preparation 340-341 TWE: EC 341

MA-H-2.2.5 Students will apply the concepts of congruence and similarity to solve real-world and mathematical problems (not including proofs).

SE: 92-95, 284-285 TWE: GC 285 Also see Geometry.


OBJECTIVES PAGE REFERENCES

MA-H-2.2.6 Students will calculate surface area and volume of rectangular prisms, pyramids, cylinders, cones, and spheres in problem settings using given formulas.

SE: 178, 186, 187, 192-193, 233, 318, 701, 975

MA-H-2.2.7 Students will apply formulas for the slope of a line, distance between two points, and midpoint of a segment to solve problems.

SE: Sample Demonstrator: 615 20-25, 615-621, 688, A44 SAT & ACT Preparation 272-273 TWE: IE 616

MC 623


Sample Demonstrator Geometry/Measurement: Skills

MA-H-2.2.1 to MA-H-2.2.7




MA-H-2.3.1 Students will solve real-world geometry problems by using algebra.

SE: Sample Demonstrator: 88 88-95, 121, 615-621, 688, A28,

A44 TWE: A 96 IE 616

MC 98, 623

MA-H-2.3.2 Students will apply algebra to solve problems involving geometric figures in a coordinate plane.

SE: Sample Demonstrator: 88 88-95, 121, 615-621, 688, A28,

A44 TWE: A 96 IE 616

MC 98, 623

MA-H-2.3.3 Students will understand how figures in a coordinate plane and their resulting images under a transformation are algebraically and geometrically related. Students will describe elements that change and elements that do not change under these transformations.

SE: Sample Demonstrator: 88 88-95, 121, A28 TWE: A 96

MC 98

MA-H-2.3.4 Students will understand how a change in one or more dimensions of a geometric shape affects perimeter, area, volume, or surface area.

See Geometry.


Sample Demonstrator Geometry/Measurement: Relationships

MA-H-2.3.1 to MA-H-2.3.4


Probability/Statistics


MA-H-3.1.1 Students will understand how standard deviation measures the scatter of a discrete set of real-world data.

SE: 911-917, 921-925, 935, A54 TWE: MC 918, 927

MA-M-3.1.2 Students will recognize that curve fitting (linear, quadratic, exponential) can be used as a method of describing and predicting from a set of data or scatter plot. Students will recognize the appropriate curve for a particular set of data.

SE: Sample Demonstrator: 38 38-44, 60, 740-747, A27 TWE: MC 45

MA-M-3.1.3 Students will describe and give examples of various sampling techniques and biases in data collection.

SE: 927-932, 936, A54 TWE: AN 929 ML 927

MA-H-3.1.4 Students will understand the differences between combinations and permutations.

SE: 837-845, 846-851, 882, 885, A51 TWE: MC 846

MA-H-3.1.5 Students will understand differences between theoretical and experimental probability.

SE: 852-857, 859-867, 868-874, 875-880, 883, 884, A51, A52

TWE: GC 877


Sample Demonstrator Probability/Statistics: Concepts

MA-H-3.1.1 to MA-H-3.1.5




MA-H-3.2.1 Students will analyze, interpret results, make decisions, and draw conclusions based on a set of data.

SE: 908-917, 918-925, 927-932, 935, 936, A54 SAT & ACT Preparation 938-939

TWE: AP 836c

MA-H-3.2.2 Students will plot a set of bivariate data and select an appropriate curve (linear, quadratic, exponential) of best fit.

SE: 38-44, 60, 740-747, A27 TWE: MC 45

MA-H-3.2.3 Students will organize, display and interpret statistical models (tables, graphs) of bivariate data.

SE: 38-44, 60, 740-747, 889-896, 908-917, 918-925, 927-932, 935, 936, A27, A54

SAT & ACT Preparation 938-939 TWE: AP 836c MC 45

MA-H-3.2.4 Students will interpret the results of a probability simulation, draw conclusions, and make predictions.

SE: 875-880, 884, A52 TWE: GC 877

MA-H-3.2.5 Students will represent probabilities in multiple ways such as fractions, decimals, percentages, and geometric area models.

SE: Sample Demonstrator: 859 852-857, 859-867, 868-874, 875-

880, 883, 884, A51, A52 TWE: GC 877

MA-H-3.2.6 Students will determine probabilities in situations involving replacement and non-replacement.

SE: Sample Demonstrator: 859 859-867, 884, 885, A52 TWE: MC 868


Sample Demonstrator Probability/Statistics: Skills MA-H-3.2.1 to MA-H-3.2.6




MA-H-3.3.1 Students will understand how outliers affect measures of central tendency.

SE: Sample Demonstrator: 897 897-907, 934, A53 TWE: MC 908

MA-H-3.3.2 Students will describe how sampling techniques can influence results.

SE: 927-932, 936, A54 TWE: AN 929 ML 927

MA-H-3.3.3 Students will understand and reason about the use and misuse of statistics and statistical representations such as type of graph and choice of scale.

SE: 927-932, 936, A54 TWE: AN 929 ML 927

MA-H-3.3.4 Students will use data and curve of best fit to make and defend predictions.

SE: 38-44, 60, 740-747, A27 TWE: MC 45


Sample Demonstrator Probability/Statistics: Relationships

MA-H-3.3.1 to MA-H-3.3.4


Algebraic Ideas


MA-M-4.1.1 Students will understand the concept of a function and roles of independent and dependent variables.

SE: 5-11, 58, 704-711, A26 TWE: A 12

MA-H-4.1.2 Students will describe, give examples of, and recognize differences among expressions, equations, and inequalities.

SE: SAT & ACT Preparation 124-125, 202-203

Also see Algebra 1.

MA-H-4.1.3 Students will understand systems of linear equations (2 equations in 2 variables) and representations of linear systems.

SE: 67-72, 120, A28 TWE: MC 73

MA-H-4.1.4 Students will identify linear, quadratic, absolute value, and exponential functions from graphs and equations.

SE: 20-25, 59, 137-145, 198, 704-710, 750, A26, A30, A46

TWE: MC 27, 146

MA-H-4.1.5 Students will apply direct and inverse variation to both real-world and mathematical problems.

SE: 189-196, 200, A31 TWE: IE 190, 191 TM 126c

MA-H-4.1.6 Students will recognize, give examples of, and apply the laws of exponents.

SE: Sample Demonstrator: 695 695-702, 750, A46 TWE: A 703 MC 704


Sample Demonstrator Algebraic Ideas: Concepts MA-H-4.1.1 to MA-H-4.1.6


Algebraic Ideas


MA-H-4.2.1 Students will solve linear equations and linear inequalities.

See Algebra 2.

MA-H-4.2.2 Students will graph the equation of a line.

SE: 20-25, 59, A26 TWE: MC 27

MA-H-4.2.3 Students will solve systems of linear equations (2 equations in 2 variables) including systems that arise from real-world problems.

SE: 67-72, 100-104, 120, 122, A28, A29

TWE: A 105 MC 73

MA-H-4.2.4 Students will create tables of numerical values of functions including linear, quadratic, absolute value, exponential, and simple piecewise such as some long distance phone rates.

SE: 20-25, 59, 137-145, 198, 704-710, 750, A26, A30, A46

TWE: MC 27, 146

MA-H-4.2.5 Students will determine the domain and range of a function, the slope and intercepts of a linear function, and the maximum/minimum and intercepts of a quadratic function.

SE: 20-25, 59, 140-145, 704-711, A26, A30

TWE: MC 27, 146

MA-H-4.2.6 Students will determine approximate solutions to quadratic equations.

SE: 213-220, 268, A32 TWE: MC 222


OBJECTIVES PAGE REFERENCES

MA-H-4.2.7 Students will add, subtract, and multiply polynomial expressions, and students will factor polynomial expressions using the greatest common monomial factor.

SE: 646, 656 Also see Algebra 2.

MA-H-4.2.8 Students will use direct and inverse variation to solve real-world problems.

SE: Sample Demonstrator: 189 189-196, 200, A31 TWE: IE 190, 191 TM 126c


Sample Demonstrator Algebraic Ideas: Skills

MA-H-4.2.1 to MA-H-4.2.8


Algebraic Ideas


MA-H-4.3.1 Students will write and solve linear equations describing real-world situations.

SE: 27-31, 32-37, 38-44, 59, 60, A26, A27

TWE: MC 45

MA-H-4.3.2 Students will understand how formulas, tables, graphs, and equations of functions relate to each other.

SE: Sample Demonstrator: 137 20-25, 59, 137-145, 198, 704-710,

750, A26, A30, A46 TWE: MC 27, 146

MA-H-4.3.3 Students will demonstrate how slope shows rate of change in linear functions arising from real-world situations.

SE: 20-25, 61 TWE: A 25 IE 21

MA-H-4.3.4 Students will show how changes in parameters affect graphs of functions [e.g., compare the graphs y = x2, y = 2x2, y = (x – 4)2, and y = x2 + 3].

SE: Sample Demonstrator: 137 137-145, 198, A30 Graphing Calculator Exploration

26 TWE: MC 146

MA-H-4.3.5 Students will show how equations and graphs are models of the relationship between two real-world quantities (e.g., the relationship between degrees Celsius and degrees Fahrenheit).

SE: Sample Demonstrator: 137 20-25, 61, 137-145, 201, 704-710,

753 TWE: A 25


Sample Demonstrator Algebraic Ideas: Relationships

MA-H-4.3.1 to MA-H-4.1.5


Codes Used for TWE Pages

A Assess AN Addressing Individual Needs AP Applications EC Extra Credit GE Graphing Calculator Exploration IE In-Class Examples MC 5-Minute Check ML Motivating the Lesson TM Technology/Multimedia


LESSON PLAN CORRELATIONS


Chapter 1 Reasoning in Geometry

LESSON KENTUCKY OBJECTIVES 1-1 Relations and Functions

MA-H-1.1.1, MA-H-1.2.2, MA-H-1.3.2, MA-H-4.1.1

1-2 Composition of Functions

Supports Kentucky and National Math Standards and Objectives

1-3 Graphing Linear Equations

MA-H-2.1.4, MA-H-2.2.7, MA-H-4.1.4, MA-H-4.2.2, MA-H-4.2.4, MA-H-4.2.5, MA-H-4.3.2, MA-H-4.3.3, MA-H-4.3.5

1-4 Writing Linear Equations

MA-H-4.3.1

1-5 Writing Equations of Parallel and Perpendicular Lines

MA-H-2.1.2, MA-H-4.3.1

1-6 Modeling Real-World Data With Linear Functions

MA-H-3.1.2, MA-H-3.2.2, MA-H-3.2.36, MA-H-3.3.4, MA-H-4.3.1

1-7 Piecewise Functions

MA-H-1.1.1, MA-H-1.3.2

1-8 Graphing Linear Inequalities



Chapter 2 Systems of Linear Equations and Inequalities

LESSON KENTUCKY OBJECTIVES 2-1 Solving Systems of Equations in Two Variables

MA-H- 4.1.3, MA-H-4.2.3

2-2 Solving Systems of Equations in Three Variables


2-3 Modeling Real-World Data with Matrices

MA-H-1.1.3, MA-H-1.2.3

2-4 Modeling Motion with Matrices

MA-H-2.1.1, MA-H-2.2.1, MA-H-2.2.5, MA-H-2.3.1, MA-H-2.3.2, MA-H-2.3.3

2-5 Determinates and Multiplicative Inverses of Matrices

MA-H-1.2.5, MA-H-4.2.3

2-6 Solving Systems of Linear Inequalities


2-7 Linear Programming



Chapter 3 The Nature of Graphs

LESSON KENTUCKY OBJECTIVES 3-1 Symmetry and Coordinate Graphs


3-2 Families of Graphs

MA-H-1.3.4, MA-H-4.1.4, MA-H-4.2.4, MA-H-4.2.5, MA-H-4.3.2, MA-H-4.3.4, MA-H-4.3.5

3-3 Graphs of Nonlinear Inequalities


3-4 Inverse Functions and Relations


3-5 Continuity and End Behavior


3-6 Critical Points and Extrema

MA-H-2.2.6

3-7 Graphs of Rational Functions

MA-H-2.2.6

3-8 Direct, Inverse, and Joint Variation



Chapter 4 Polynomials and Rational Functions

LESSON KENTUCKY OBJECTIVES 4-1 Polynomial Functions

MA-H-1.1.1, MA-H-1.3.2

4-2 Quadratic Equations

MA-H- 4.2.6

4-3 The Remainder and Factor Theorems


4-4 The Rational Root Theorem

MA-H-2.2.6

4-5 Locating Zeros of a Polynomial Function


4-6 Rational Equations and Partial Fractions


4-7 Radical Equations and Inequalities


4-8 Modeling Real-World Data with Polynomial Functions



Chapter 5 The Trigonometric Functions

LESSON KENTUCKY OBJECTIVES 5-1 Angles and Degree Measure

MA-H-2.1.3

5-2 Trigonometric Ratios in Right Triangles

MA-H-1.3.4, MA-H-2.1.5, MA-H-2.2.3, MA-H-2.2.5

5-3 Trigonometric Functions on the Unit Circle

MA-H-1.3.4

5-4 Applying Trigonometric Functions

MA-H-2.1.5, MA-H-2.2.3

5-5 Solving Right Triangles

MA-H-1.2.1

5-6 The Law of Sines

MA-H-2.2.6

5-7 The Ambiguous Case for the Law of Sines

MA-H-2.1.5

5-8 The Law of Cosines

MA-H-2.1.5


Chapter 6 More about Triangles

LESSON KENTUCKY OBJECTIVES 6-1 Angles and Radian Measure

MA-H-1.3.4

6-2 Linear and Angular Velocity


6-3 Graphing Sine and Cosine Functions

MA-H-1.1.1, MA-H-1.3.2

6-4 Amplitude and Period of Sine and Cosine Functions


6-5 Translations of Sine and Cosine Functions


6-6 Modeling Real-World Data with Sinusoidal Functions


6-7 Graphing Other Trigonometric Functions


6-8 Trigonometric Inverses and Their Graphs



Chapter 7 Triangle Inequalities

LESSON KENTUCKY OBJECTIVES 7-1 Basic Trigonometric Identities

MA-H-1.1.1, MA-H-1.3.2, MA-H-2.2.4

7-2 Verifying Trigonometric Identities


7-3 Sum and Difference Identities


7-4 Double-Angle and Half-Angle Identities

MA-H-1.1.1, MA-H-1.3.2

7-5 Solving Trigonometric Equations


7-6 Normal Form of a Linear Equation


7-7 Distance From a Point to a Line



Chapter 8 Quadrilaterals

LESSON KENTUCKY OBJECTIVES 8-1 Geometric Vectors


8-2 Algebraic Vectors

MA-H-1.1.1

8-3 Vectors in Three-Dimensional Space


8-4 Perpendicular Vectors


8-5 Applications with Vectors


8-6 Vectors and Parametric Equations


8-7 Modeling Motion Using Parametric Equations


8-8 Transformational Matrices in Three-Dimensional Space



Chapter 9 Proportions and Similarity

LESSON KENTUCKY OBJECTIVES 9-1 Polar Coordinates

MA-H-1.1.1, MA-H-1.3.2

9-2 Graphs of Polar Equations


9-3 Polar and Rectangular Coordinates


9-4 Polar Form of a Linear Equation


9-5 Simplifying Complex Numbers


9-6 The Complex Plane and Polar Form of Complex Numbers


9-7 Products and Quotients of Complex Numbers in Polar Form


9-8 Powers and Roots of Complex Numbers



Chapter 10 Polygons and Area

LESSON KENTUCKY OBJECTIVES 10-1 Introduction to Analytic Geometry

MA-H-2.2.4, MA-H-2.2.7, MA-H-2.3.1, MA-H-2.3.2

10-2 Circles

MA-H-2.2.4

10-3 Ellipses


10-4 Hyperbolas

MA-H-4.2.7

10-5 Parabolas

MA-H-4.2.7

10-6 Rectangular and Parametric Forms of Conic Sections

MA-H-1.1.1, MA-H-1.3.2

10-7 Transformations of Conics

MA-H-2.1.1

10-8 Systems of Second-Degree Equations and Inequalities



Chapter 11 Circles

LESSON KENTUCKY OBJECTIVES 11-1 Real Exponents

MA-H-2.2.6, MA-H-4.1.6

11-2 Exponential Functions

MA-H-1.1.1, MA-H-1.3.2, MA-H-4.1.1, MA-H-4.1.4, MA-H-4.2.4, MA-H-4.2.5, MA-H-4.3.2, MA-H-4.3.5

11-3 The Number e


11-4 Logarithmic Functions


11-5 Common Logarithms


11-6 Natural Logarithms


11-7 Modeling Real-World Data with Exponential and Logarithmic Functions

MA-H-3.1.2, MA-H-3.2.2, MA-H-3.2.3, MA-H-3.3.4


Chapter 12 Surface Area and Volume

LESSON KENTUCKY OBJECTIVES 12-1 Arithmetic Sequences and Series

MA-H-1.1.2, MA-H-1.2.4

12-2 Geometric Sequences and Series

MA-H-1.1.2, MA-H-1.2.4

12-3 Infinite Sequences and Series


12-4 Convergent and Divergent Series


12-5 Sigma Notation and the nth Term

MA-H-1.2.2

12-6 The Binomial Theorem

MA-H-1.2.2

12-7 Special Sequences and Series


12-8 Sequences and Iteration


12-9 Mathematical Induction



Chapter 13 Right Triangles and Trigonometry

LESSON KENTUCKY OBJECTIVES 13-1 Permutations and Combinations

MA-H-1.2.5, MA-H-3.1.4

13-2 Permutations with Repetitions and Circular Permutations

MA-H-3.1.4

13-3 Probability and Odds

MA-H-3.1.5, MA-H-3.2.5

13-4 Probabilities of Compound Events

MA-H-3.1.5, MA-H-3.2.5, MA-H-3.2.6

13-5 Conditional Probability

MA-H-3.1.5, MA-H-3.2.5

13-6 The Binomial Theorem and Probability

MA-H-3.1.5, MA-H-3.2.4, MA-H-3.2.5

Chapter 14 Circle Relationships LESSON KENTUCKY OBJECTIVES

14-1 The Frequency Distribution

MA-H-3.2.3

14-2 Measures of Central Tendency

MA-H-3.3.1

14-3 Measures of Variability

MA-H-3.1.1, MA-H-3.2.1, MA-H-3.2.3

14-4 The Normal Distribution

MA-H-3.1.1, MA-H-3.2.1, MA-H-3.2.3

14-5 Sample Sets of Data



Chapter 15 Formalizing Proof

LESSON KENTUCKY OBJECTIVES 15-1 Limits


15-2 Derivatives and Antiderivatives


15-3 Area Under a Curve


15-4 The Fundamental Theorem of Calculus

MA-H-2.2.6


STANDARDS FOR MATHEMATICS EVALUATION INSTRUMENT


Content/Process

Comments

1. Material is comprehensive and includes content emphasized in Kentucky’s Learning Goals and Academic Expectations and supported by the Core Content for Assessment, Program of Studies, and relevant National Standards.

Content emphasized in Kentucky’s Learning Goals and Academic Expectations is covered in Core Content statements MA-H-1.1.2, MA-H-1.2.4, MA-H-1.2.5, MA-H-1.3.4, MA-H-2.1.1, MA-H-2.1.2, MA-H-2.1.3, MA-H-2.1.5, MA-H-2.2.2, MA-H-2.2.3, MA-H-2.2.4, MA-H-2.2.5, MA-H-2.2.6, MA-H-2.2.7, MA-H-2.3.1, MA-H-2.3.2, MA-H-2.3.3, MA-H-2.3.4, MA-H-3.1.2, MA-H-3.1.4, MA-H-3.2.4, MA-H-4.1.2, MA-H-4.1.5, MA-H-4.2.1, MA-H-4.2.5, MA-H-4.2.6, MA-H-4.2.8, MA-H-4.3.1, and MA-H-4.3.4. A correlation to NCTM standards can be found in the Teacher’s Wraparound Edition (TWE) on pages T14 and T15.

2. Content appears to be free from factual errors.

Advanced Mathematical Concepts: Precalculus with Applications is the product of ongoing classroom-oriented research that involves students, teachers, curriculum supervisors, administrators, parents, and college-level mathematics educators. Prior to publication of any Glencoe program, typical research activities include a review of educational research and recommendations made by groups such as NCTM; mail surveys of mathematics educators, discussion groups involving mathematics teachers, department heads, and supervisors; focus groups involving mathematics educators; face-to-face interviews with mathematics educators; telephone surveys of mathematics educators; in-depth analysis of manuscript by a wide range of reviewers and consultants; and field tests in which students and teachers use pre-publication manuscript in the classroom.


Content/Process

Comments

3. Content makes connections to other content areas across the curriculum.

There is an emphasis on integrating number and operations, algebra, measurement, data analysis and probability.

4. Concepts and application of skills to real-life situations are introduced when appropriate.

Relevant, real-life applications are a part of every lesson. Practical problem solving is linked to students’ real-life interests. Internet Projects appear before each unit and enable students to become more deeply engaged in a problem situation.

5. Content appears to be free of social, ethnic, racial, religious, gender, and geographical bias.

Relevant, real-life applications are a part of every lesson. Practical problem solving is linked to students’ real-life interests.

6. Material is flexible and accommodates various learning styles, interest/ability levels, and intelligences, including adaptations and accommodations for students with special needs.

Advanced Mathematical Concepts: Precalculus with Applications introduces new concepts in a variety of ways to meet the needs of all learners. In addition to more traditional instructional experiences, Advanced Mathematical Concepts: Precalculus with Applications encourages students to do mathematics. The Addressing Individual Needs feature found throughout the TWE is just one example of how needs of all students are met.

7. Reading level is appropriate for interest and ability level of intended student group; level remains consistent throughout.

The readability level is 11.2 Dale Chall.


Content/Process

Comments

8. Content reflects research-based practices (e.g., hands-on activities, technology, problem-solving situations).

Graphing Calculator Exploration features give students hands-on experience, with a partner or group, in discovering mathematical concepts for themselves and taking responsibility for their own learning. Practical problem solving is linked to students’ real-life interests. Internet Projects appear before each unit and enable students to become more deeply engaged in a problem situation. The use of technology tools throughout the program encourage investigation and problem solving. Online support provides additional practice for each lesson.

9. Concepts are explored in depth and reinforced throughout.

The content addresses relations, functions, and graphs; trigonometry; advanced functions and graphing; discrete mathematics; and an introduction to calculus.


Assessment

Comments

1. Student assessment is aligned with the instructional program. Assessment activities are similar to learning activities.

The curriculum alignment to Kentucky Core Content Standards promotes the ability of students to perform well on CATS tests and other standardized tests. The student edition has a Mid-Chapter Quiz in each chapter as well as a Study Guide and Assessment that includes vocabulary exercises, review exercises for each objective, applications and problem solving, and alternative assessment. Also included for each chapter are a Chapter Test (in the back of the text) and a 2-page SAT and ACT Preparation.

2. Assessment activities examine the extent to which students have internalized and made sense of mathematical concepts and whether they can use mathematics to communicate their ideas.

Every chapter has a Study Guide and Assessment that includes Vocabulary, Understanding and Using the Vocabulary, Examples and Review Exercises for each objective, Applications and Problem Solving, and an Alternative Assessment, which includes a Portfolio suggestion.

3. Assessment activities provide opportunities for students to demonstrate knowledge and skills in real-life situations and interdisciplinary applications.

Every chapter has a Study Guide and Assessment, Applications and Problem Solving, an Alternative Assessment, which includes a Portfolio suggestion. Every lesson has a Closing Activity in the Teacher’s Wraparound Edition that involves writing, speaking, or modeling.


Assessment

Comments

4. A variety of assessments (e.g., diagnostic, formative, summative, open response, multiple choice, individual, small group, oral, demonstrations, presentations, self and peer, performance, portfolio prompts) is included.

In the Student Edition, every lesson has a Mixed Review that includes a test practice item. Every chapter has Math Journals, a Unit Project, a Mid-Chapter Quiz, SAT and ACT Preparation, a Chapter Test, a Study Guide and Assessment, Applications and Problem Solving, and an Alternative Assessment, which includes a Portfolio suggestion. In the Teacher’s Wraparound Edition, every lesson includes a 5-Minute Check that covers the previous lesson or chapter, and a Closing Activity that involves writing, speaking, or modeling. The Assessment and Evaluation Masters include multiple-choice tests, free-response tests, a calculator-based test, a performance assessment, a mid-chapter test, quizzes, cumulative review, and mathematics learning assessment items. The TestCheck and Worksheet Builder CD-ROM, correlated to the Kentucky Core Content Standards for Pre-Calculus and Advanced Math Topics in Math, allows teachers to create customized tests and quizzes with any combination of free-response, multiple-choice, short-answer, and open-ended items. Advanced Mathematical Concepts: Precalculus with Applications provides integrated and ongoing test preparation throughout the year to help reduce student anxiety and improve student performance. The Standardized Test Preparation CD-ROM contains blocks of test items from state proficiency tests, the SAT, the ACT, TIMSS, and NAEP.


Assessment

Comments

5. Assessment activities provide opportunities for student integration of technology in the assessment process.

The Advanced MathPASS CD-ROM reviews and reinforces important concepts through a unique Pretest-Tutorial-Guided Practice-Posttest format. Self-paced and easy-to-use, it is also an excellent tool for standardized test preparation.


Organization and Structure

Comments

1. Organization is logical and allows for spiraling of content.

Advanced Mathematical Concepts: Precalculus with Applications is composed of 15 chapters, each having 4 to 9 lessons. Each lesson follows a straight forward format. The lesson begins with What you’ll learn and When am I ever going to use this?, which provides the objective of the lesson and a relevant benefit of learning the concept. Completely worked-out examples with clear explanations parallel the exercises in the Guided Practice and Practice sections. Check for Understanding exercises ensure that all students are engaged in the lesson and understand the concepts. In the Communicating Mathematics exercises, students define, describe, and explain mathematical concepts. The Guided Practice exercises present a representative sample of the exercises in the Practice exercises. The Practice exercises are separatged into A, B, and C sections, indicated only in the TWE. Each lesson contains a Critical Thinking exercise in which students explain, justify, and prove mathematical relationships. Applications and Problem Solving exercises apply geometric concepts to both real-life and mathematical problem situations. The Mixed Review exercises are spiraled and cumulative. Each chapter concludes with a comprehensive Study Guide and Assessment review section.

2. Language is clear and concise with correct grammar and sentence structure.

Prior to publication of any Glencoe program, an in-depth analysis of manuscript by a wide range of reviewers and consultants is conducted. Field tests in which students and teachers use pre-publication manuscript in the classroom also helps ensure accuracy.



Comments

3. Vocabulary and key terms are clearly defined and easily accessible within each lesson.

Vocabulary words are found in highlighted, boldface type where they are defined in the lesson.

4. Visual illustrations (e.g., graphs, charts, models) and examples are clearly presented and content-related.

Graphs, charts, and models are used throughout the book to illustrate concepts. Completely worked-out examples with clear explanations parallel the exercises in the Guided Practice and Practice sections.

5. Illustrations and language reflect diversity (e.g., racial, ethnic, culture, age, gender, disabilities).

Relevant, real-life applications are a part of every lesson. Practical problem solving is linked to students’ real-life interests.

6. Legible type, length of lines, spacing, page layout, and width of margins contribute to overall appearance and use.

Prior to publication of any Glencoe program, an in-depth analysis of manuscript by a wide range of reviewers and consultants is conducted. Field tests in which students and teachers use pre-publication manuscript in the classroom also helps ensure accuracy.

7. Student materials seem durable and conducive to daily student use (e.g., size, weight).

The very best materials are used in all Glencoe products. The materials are easy for students to use, both in school and at home.

8. Textbook includes appropriate and sufficient glossary, index, and appendices.

The Student Handbook can be found on pp. A2-A206. It contains a Graphing Calculator Appendix and sections on Extra Practice, Chapter Tests, Glossary, Selected Answers, and the Index. Symbols and Formulas can be found on the inside back cover.



Comments

9. Materials are organized into units of study (or similar structures) with daily lessons that include worthwhile, real-world tasks.

Advanced Mathematical Concepts: Precalculus with Applications is composed of 15 chapters, each having 4 to 9 lessons. Each lesson follows a straight forward format. The lesson begins with What you’ll learn and When am I ever going to use this?, which provides the objective of the lesson and a relevant benefit of learning the concept. Completely worked-out examples with clear explanations parallel the exercises in the Guided Practice and Practice sections. Check for Understanding exercises ensure that all students are engaged in the lesson and understand the concepts. In the Communicating Mathematics exercises, students define, describe, and explain mathematical concepts. The Guided Practice exercises present a representative sample of the exercises in the Practice exercises. The Practice exercises are separated into A, B, and C sections, indicated only in the TWE. Each lesson contains a Critical Thinking exercise in which students explain, justify, and prove mathematical relationships. Applications and Problem Solving exercises apply geometric concepts to both real-life and mathematical problem situations.

10. Materials can be easily understood by students and parents.

The reading level of Advanced Mathematical Concepts: Precalculus with Applications is on target at 11.2 Dale Chall. In addition, the material presented is interesting and related to students’ lives. The Glencoe Math Website helps parents get involved with their child’s learning by providing challenging activities such as problems of the week and group activities.


Student Experiences

Comments

1. The program emphasizes students doing mathematics rather than memorizing mathematics.

Doing mathematics is so much more effective than memorizing mathematics! That is why Advanced Mathematical Concepts: Precalculus with Applications gives teachers and students several opportunities to engage in projects of varying lengths that put mathematics in motion. These opportunities include Internet Projects and Graphing Calculator Explorations found throughout the book.

2. Both group and individual activities are included.

Advanced Mathematical Concepts: Precalculus with Applications offers multiple opportunities for students to learn cooperatively as well as individually. In addition to more traditional instructional experiences, Graphing Calculator Explorations features give students hands-on experience, with a partner or group, in discovering mathematical concepts.

3. Materials and activities provide authentic applications that allow students to make meaningful connections across the curriculum, to real-world situations, and to interrelated mathematical concepts.

Practical problem solving is linked to students’ real-life interests. There is an emphasis on integrating algebra, geometry, measurement, proportional reasoning, statistics, probability, technology, and problem solving. In addition, interdisciplinary connections are a part of every lesson.

4. Materials and activities encourage students to explore and investigate mathematical ideas through various problem-solving techniques.

Practical problem solving is linked to students’ real-life interests. Internet Projects and Graphing Calculator Explorations are found throughout the book. are found throughout the book.


Student Experiences

Comments

5. Materials and activities ask students to read, write, and discuss mathematics.

In the Communicating Mathematics exercises found in each lesson, students define, describe, and explain mathematical concepts. Special activities found in these exercises include writing in a Math Journal.

6. Materials and activities ask students to reflect upon, clarify, justify, and generalize their mathematical ideas.

Each lesson contains a Critical Thinking exercise in which students explain, justify, and prove mathematical relationships.


Technology

Comments

1. In order for students to focus on decision-making, reflection, reasoning, and problem solving, instructional activities incorporate the use of technology (e.g., calculators, probes, computers) and include instructions on how to use the technology tools.

Students have multiple opportunities to use technology-graphing calculator and the internet-to explore and understand graphing and other mathematical concepts.

2. Various forms of media are included (e.g., CDs, videos, computer software)

The TestCheck and Worksheet Builder CD-ROM, correlated to the Kentucky Core Content Standards for Pre-Calculus and Advanced Math Topics in Math, allows teachers to create customized tests and quizzes with any combination of free-response, multiple-choice, short-answer, and open-ended items. Advanced Mathematical Concepts: Precalculus with Applications provides integrated and ongoing test preparation throughout the year to help reduce student anxiety and improve student performance. The Advanced MathPASS CD-ROM reviews and reinforces important concepts through a unique Pretest-Tutorial-Guided Practice-Posttest format. Self-paced and easy-to-use, it is also an excellent tool for standardized test preparation. The TeacherWorks All-in-One Lesson Planner and Resource Center CD-ROM contains all of the blackline masters and transparencies available for Advanced Mathematical Concepts: Precalculus with Applications. It also includes a lesson planner and interactive Teacher Edition, so teachers can customize lesson plans and reproduce classroom resources quickly and easily just about anywhere.

3. Student materials are available online. Free access to Glencoe Math Website and On-line Study Tools is provided with the program.


Resource Materials

Comments

1. Teacher materials coordinate easily with student materials (e.g., additional resources included at point of need, student pages shown, manipulatives appropriate for indicated lesson, instructional technology indicated).

Each lesson in the Teacher’s Wraparound Edition (TWE) begins with Resource Manager, which includes instructional technology. A list of blackline masters and manipulatives for each lesson is included at the beginning of each chapter. Each student page is shown in the TWE on the same pages as related teacher’s materials.

2. Activities are included that adapt to the various learning styles, intelligences, and interest/ability levels.

In the TWE, ideas for Extra Credit are provided for each lesson. Also found in the TWE are frequent suggestions of ways to accommodate students with Addressing Individual Needs.

3. Extension activities including adaptations and accommodations for students with special needs.

In the TWE, ideas for Extra Credit are provided for each lesson. Also found in the TWE are frequent suggestions of ways to accommodate students with Addressing Individual Needs.

4. Resources provide objectives, background information, common student errors, hints, advice for lesson implementation and real-world connections, connections within mathematics, and references (e.g., solutions manuals, study guides).

The following features are provided throughout the TWE: Motivating the Lesson, Teaching Tip, Addressing Individual Needs, and Error Analysis. Ancillary materials include Solutions Manual, Answer Key Transparencies, Graphing Calculator Keystrokes Masters, and Study Guide and Practice Masters.


Resource Materials

Comments

5. Suggestions are made for integration of themes and/or interdisciplinary instruction.

The SE and TWE include features such as Career Choices. Ancillary materials include Problem Solving and Applications Masters.

6. Suggestions are made for family and community involvement and school/home communication.

The Glencoe Math Website helps parents get involved with their child’s learning by providing challenging activities such as problems of the week and group activities.

7. The included media are durable, easy to use, and have technical merit.

All included media are made to last and can be easily incorporated into lessons.

8. Teacher resources are available online. Free access to the Glencoe Math Website and On-line Study Tools, as well as is provided with the program.

Marcia L. Rieder South Central Region Kentucky Sales Representative 6510 Jimmy Carter Boulevard 2005 Crooked Creek Court Norcross, GA 30071 Crestwood, Kentucky 40014 Tel 770 613 0281 Tel 502 241 6701 Toll Free 800 731 2365 Fax 502 243 9769 [email protected]

Documents

KY Advanced Mathematical Concepts - Glencoedev.glencoe.com/sites/correlations/pdf/KYAMC04.pdf · Kentucky Core Content 2 Glencoe/McGraw-Hill Advanced Mathematical Concepts: Precalculus