HEALTH/PE PLANNED COURSE OUTLINE · Web view1. Students will organize data using frequency distributions 2. Students will be able to represent data in frequency distributions graphically

Centennial School District

Planned Course Outline

Mathematics

Trigonometry & Statistics AHigh School

An educational community committed to student excellencewww.centennialsd.org

June 2006 Office of Curriculum, Instruction, and Assessment

Position Paper on the Use of Technology

Mathematics Curriculum Resource Team

Technology should be integrated into the K-12 mathematics curriculum.

Students in a technological society should be able to use calculators and computers to process information, aid in high level thinking skills, and understand various mathematical processes.

Students should be calculator and computer literate in order to use the technology successfully in their future development. Technology should be used in various ways through activities at each level of schooling. Students need to be introduced to calculators and mathematical relationships and as a computational mathematics check. Students in the middle and high school grades need to further develop their calculator and computer skills problem solving, application and exploration of more sophisticated mathematical understandings. Calculators and computers should be used in math classes and in those disciplines having a mathematical basis. Students should use the appropriate technology in order to make their mathematical task as efficient as possible.

The inclusion of the use of technology in the curriculum does imply the exclusion of the need for students to learn basic arithmetic facts or algorithms. Because calculators and computers are highly symbolic, they cannot be a substitute for manipulatives, pictorial representations, or word processors for writing; they are tools to simplify the process, but they do not accomplish the essential task at hand.

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Centennial School DistrictMathematics Curriculum

Course/Grade: Trigonometry and Statistics Academic

The following Twenty Word List addresses the District Reading/Writing/Speaking/Listening Standard A3 for High School Trigonometry and Statistics A.

1) amplitude

2) arclength

3) asymptote

4) continuous (function)

5) coterminal

6) discontinuous (function)

7) domain

8) function

9) identity

10) interval

11) inverse

12) one-to-one (function)

13) periodic

14) quadrant

15) radian

16) range

17) reflection

18) root

19) symmetry

20) terminal (side of angle)

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Centennial School DistrictMathematics Curriculum

Trigonometry and Statistics A Course Outline

Grade Level: High School

Chapter Title Sections Days

T-9 Sequences, Series and Probability 1-3,5 12

T-P Prerequisites Sections 1-5 should be integrated into Chapters 1-4 0

T-1 Functions 1 to 5 17

T-2 Polynomial and Rational Functions 1 to 7 23

T-3 Exponential and Logarithmic Functions 1 to 5 17

T-4 Trigonometric Functions 1 to 8 26

T-5 Analytic Trigonometry 1 to 3 17

T-6 Additional Topics in Trigonometry 1-3,5 12

Statistics Book

S-1 The Natures of Probability and Statistics 1-8 5

S-2 Frequency Distributions and Graphs 1-5 11

S-3 Data Description 1-6 13

S-4 Probability and Counting Rules 1-7 18

S-10 Correlation and Regression 1,2 4

Totals 62 171

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PLANNED COURSE OUTLINE CENTENNIAL SCHOOL DISTRICTWARMINSTER, PENNSYLVANIA

Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 9 Sequences, Series, and Probability Suggested Number of Days: 12

UNIT QUESTION: 1) Is the sum of an infinite series always infinite?2) Is there a need for probability outside of determining odds in games of chance?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: CONTENT AND SKILLS

1. Students will be able to use sequence, factorial and summation notation to write the terms and sums of sequences.

2. Students will recognize, write, and use arithmetic and geometric sequences.

3. Students will use the binomial Thm and Pascal’s triangle to calculate binomial coefficients and write binomial expansions.

ACTIVITIES AND ASSESSMENTS

1-3a. Students will define and record new terminology.

1-3b. Students will use problem-solving strategies.

1-3c. Students will complete practice problems in skill development sections.

1-3d. Students will use skills to solve situations in: Business Patterns Geometry Life Insurance

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 9, Sections 1-3,5

Student Text

TI-83 Graphing Calculator

http://college.hmco.com

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http://college.hmco.com/


Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: P Prerequisites Suggested Number of Days: Cover as needed

UNIT QUESTION: How can the graph of an equation or an inequality help you see relationships between real-life quantities?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.C.3.1.1, M11.C.3.1.2, M11.D.2.1.1, M11.D.2.1.3; M11.D.2.1.5, M11.D.3.2.1, M11.D.3.2.2, M11.D.3.2.3

CONTENT AND SKILLS

1. Students will be able to plot points in the coordinate plane and use the distance and midpoint formulas.

2. Students will be able to sketch graphs of equations by point plotting or using a graphing utility.

3. Students will be able to find and use the slope of a line to write and graph linear equations.

4. Students will be able to solve linear, quadratic, polynomial, radical, absolute value equations.

5. Students will be able to solve linear, absolute value, polynomial, and rational inequalities.


1-5a Students will define and record new terminology.

1-5b. Students will use problem solving strategies.


1-5d. Students will use skills to solve situations in: Population Finance Education Meteorology

5e. Students will be able to use a graphing utility to find a linear model for the given data.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter P, Sections 1,2,3,4,5

Student Text



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Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 1 Functions and Their Graphs Suggested Number of Days: 17

UNIT QUESTION: 1) What different functions can be used to represent quantities that vary over time?2) What function decreases over time? Increases over time? Remains constant over time?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.D.1.1.2, M11.D.1.1.3, M11.D.2.1.2, M11.D.4.1.1, CONTENT AND SKILLS

1. Students will be able to evaluate functions and find their domains.

2. Students will be able to analyze graphs of functions.

3. Students will be able to identify and graph shifts, reflections, and non rigid transformations of functions.

4. Students will be able to find arithmetic combinations and compositions of functions.

5. Students will be able to find inverses of functions graphically and algebraically.





1-5d. Students will use skills to solve situations in: Communications Business Geometry Transportation

5e. Students will be able to use graphs of functions to decide whether functions have inverses.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 1, Sections 1,2,3,4,5

Student Text



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Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 2 Polynomial and Rational Functions Suggested Number of Days: 23

UNIT QUESTION: 1) How do polynomial functions model quantitative situations including maximums and/or minimums?2) What are the major differences between rational functions and other algebraic functions?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.D.2.1.5, M11.D.2.2.1, M11.D.4.1.1CONTENT AND SKILLS

1. Students will be able to sketch and analyze graphs of quadratic functions.

2. Students will be able to sketch and analyze graphs of polynomial functions.

3. Students will be able to use long and synthetic division to divide polynomial by other polynomials.

4. Students will be able to determine the number of rational and real zeros of polynomial functions and find them.

5. Students will be able to perform operations with complex numbers and plot complex numbers in the complex plane.

6. Students will be able to determine the domain, find asymptotes, and sketch the graphs of rational functions.





1-6d. Students will use skills to solve situations in:

Business Advertising Geometry Data Analysis

2-6e. Students will be able to use rational function to model and solve real life problems.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 2, Sections 1,2,3,4,5,6,7

Student Text



CD Rom

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Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 3 Exponential and Logarithmic Functions Suggested Number of Days: 17

UNIT QUESTION: How do exponential and logarithmic functions illustrate rapid growth in populations and investments?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.A.2.2.1, M11.A.2.2.2, M11.D.1.1.1, M11.D.4.1.1CONTENT AND SKILLS

1. Students will be able to recognize, evaluate, and graph exponential and logarithmic functions.

2. Students will be able to rewrite logarithmic functions with different bases.

3. Students will be able to use properties of logarithms to evaluate, rewrite, expand, or condense logarithmic expressions.

4. Students will be able to solve exponential and logarithmic equations.

5. Students will be able to use exponential growth models, exponential decay models, and logarithmic models to solve real-life problems.





1-5d. Students will use skills to solve situations in: Interest Radioactive Decay Populations Sound Intensity

5e. Students will be able to recognize the five most common types of models involving exponential or logarithmic functions.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 3, Sections 1,2,3,4,5

Student Text



CD Rom

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Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 4 Trigonometric Functions Suggested Number of Days: 26

UNIT QUESTION: 1) What is the origin of trigonometry and its six functions?2) Describe how the graphs of trigonometric functions model repetitive motion such as the movement of a pendulum?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.B.2.1.1, M11.C.1.2.1, M11.C.1.2.2, M11.C.1.2.3CONTENT AND SKILLS

1. Students will be able to describe an angle and convert between degree and radian measures.

2. Students will be able to identify a unit circle and its relationship to real numbers.

3. Students will be able to evaluate trigonometric functions of any angle.

4. Students will be able to use fundamental trigonometric identities.

5. Students will be able to sketch graphs of trigonometric functions.

6. Students will be able to evaluate inverse trigonometric functions.

7. Students will be able to evaluate the composition of trigonometric functions.

8. Students will be able to use trigonometric functions to model and solve real-life problems.





1-8d. Students will use skills to solve situations in: Harmonic Motion Angle of Elevation Distance Ferris Wheel

8e. Students will be able to use trigonometry to solve problems involving right triangles, directional bearings, and harmonic motion.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 4, Sections 1,2,3,4,5,6,7,8

Student Text



CD Rom

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Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 5 Analytic Trigonometry Suggested Number of Days: 17

UNIT QUESTION: 1) How are the six trigonometric functions related?2) How can that relationship be used to generate new mathematical facts?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.A.3.1.1CONTENT AND SKILLS

1. Students will be able to use fundamental trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions.

2. Students will be able to verify trigonometric identities.

3. Students will be able to use standard algebraic techniques and inverse trigonometric functions to solve trigonometric equations.





1-3d. Students will use skills to solve situations in: Projectile Motion Harmonic Motion Data Analysis

1,3e. Students will be able to recognize identities and use standard algebraic techniques to solve trigonometric equations.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 5, Sections 1,2,3

Student Text



CD Rom

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Course: Trigonometry & Statistics Academic GRADE LEVEL(S): High SchoolUNIT: 6 Additional Topics in Trigonometry Suggested Number of Days: 8

UNIT QUESTION: How can trigonometric relationships be used to find angles, sides, and areas of triangles?

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.A.2.1.3, M11.B.2.1.1CONTENT AND SKILLS

1. Students will be able to use the Law of Sines and the Law of Cosines to solve oblique triangles.

2. Students will be able to find areas of oblique triangles.





1-2d. Students will use skills to solve situations in: Engineering Navigation Baseball Altitude

2e. Students will be able to use Law of Cosines and Law of Sines to solve real-life problems.

LEARNING RESOURCES

Precalculus With Limits – A Graphing Approach , Chapter 6, Sections 1,2

Student Text



CD Rom

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Course: Trigonometry & Statistics A Course Outline GRADE LEVEL(S): High School UNIT: S1: The Natures Of Probability & Statistics Suggested Number of Days: 5

UNIT QUESTION: 1. Name and define the two areas of statistics.

2. Identify two ways statistics can be used in everyday life.

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT:

CONTENT AND SKILLS

1. Students will demonstrate knowledge of statistical terms.

2. Students will be able to differentiate between the two branches of statistics.

3. Students will be able to identify data types, sampling techniques, and the measurement level for each variable.

4. Students will be able to explain the difference between an observational and an experimental study.

5. Students will be able to explain how statistics can be used and misused.

6. Students will be able to explain the importance of computers and calculators in statistics



1-6b. Students will discuss and analyze model problems.

1-6c. Students will complete practice problems from the text or worksheets.

1-6d. Students will use the skills acquired to solve problems in mathematics following real world situations: Manufacturing Finance Technology Surveys

1-6e. Unit S1 Assessment and quizzes

LEARNING RESOURCES

Text: Elementary Statistics: A Step by Step Approach, Sixth Edition Chapter 1, sections 1-8

Overhead Panel

Newspaper

Internet

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Course: Trigonometry & Statistics A Course Outline GRADE LEVEL(S): High School UNIT: S2: Frequency Distributions and Graphs Suggested Number of Days: 11

UNIT QUESTION: 1. Identify and describe the different graphs that can be used to represent data.

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.E.1.1.1, M11.E.1.1.2, M11.E.4.1.1

CONTENT AND SKILLS

1. Students will organize data using frequency distributions

2. Students will be able to represent data in frequency distributions graphically using histograms, frequency polygons, and ogives.

3. Students will be able to represent data using Pareto charts, time series, and pie graphs.

4. Students will be able to draw and interpret stem and leaf plots.





1-4d. Students will use the skills acquired to solve problems in mathematics following real world situations: Manufacturing Sports Population Employment Infectious Disease

1-4e. Students will use real world information to construct a data table and analyze data.

1-4f. Students will be able to use technology create and analyze graphs.

1-4g. Unit S2 Assessment and quizzes

LEARNING RESOURCES


Graphing Calculator (TI-83 or TI-84)

Computer (Microsoft Excel & Internet)

Newspaper

Overhead Panel

Graph paper, rulers, protractors

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Course: Trigonometry & Statistics A Course Outline GRADE LEVEL(S): High School UNIT: S3: Data Description Suggested Number of Days: 13

UNIT QUESTION: 1. Given data, find the measures of central tendency, such as mean, median, mode and midrange.

2. Describe the data using range, variance, and standard deviation.

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.E.2.1.1, M11.E.2.1.2, M11.E.2.1.3CONTENT AND SKILLS

1. Students will be able to summarize data using measures of central tendency, such as mean, median, mode, and midrange.

2. Students will be able to describe stat using measures of variation, such as range, variance, and standard deviation.

3. Students will be able to identify the position of a data variable in a data set, using various measures of position, such as percentiles, deciles, and quartiles.

4. Students will use the techniques of exploratory data analysis, including boxplots and five number summaries, to discover various aspects of data.





1-4d. Students will use the skills acquired to solve problems in mathematics following real world situations: Transportation Test Scores Sales Salaries

1-4e. Students will use real world information to construct and analyze data charts.

1-4f. Students will be able to use technology create and analyze graphs.

1-4g. Unit S3 Assessment and quizzes

LEARNING RESOURCES



Computer (Microsoft Excel & Internet)

Newspaper

Overhead Panel

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Course: Trigonometry & Statistics A Course Outline GRADE LEVEL(S): High School UNIT: S4: Probability and Counting Rules Suggested Number of Days: 18

UNIT QUESTION: 1. Identify and give examples of the three types of probability.

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2CONTENT AND SKILLS

1. Students will be able to determine sample spaces and find the probability of an event, using classical probability or empirical probability.

2. Students will be able to find the probability of compound events, using the addition and multiplication rules.

3. Students will be able to find the conditional probability of an event.

4. Students will be able to find the total number of outcomes in a sequence of events, using the fundamental counting rule.

5. Students will be able to find the number of ways that r objects can be selected from n objects, using the permutation rule.

6. Students will be able to find the number of ways that r objects can be selected from n objects without regard to order, using the combination rule.

7. Students will be able to find the probability of an event, using the counting rules.





1-7d. Students will use the skills acquired to solve problems in mathematics following real world situations: Games Manufacturing Elections Education

1-7e. Students will be able to use technology calculate the probability of an event.

1-7f. Unit S4 Assessment and quizzes

LEARNING RESOURCES



Overhead Panel

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Course: Trigonometry & Statistics A Course Outline GRADE LEVEL(S): High School UNIT: S10: Probability and Counting Rules Suggested Number of Days: 4

UNIT QUESTION: 1. Describe when to use a scatter plot. 2. Identify the relationship of the paired data.

PENNSYLVANIA STATE STANDARDS/ ELIGIBLE CONTENT: M11.E.4.2.1, M11.E.4.2.2CONTENT AND SKILLS

1. Students will be able to draw a scatter plot for a set of ordered pairs.

2. Students will be able to determine if a relationship exists between two sets of data.

3. Students will be able to find the line of best fit and use it to predict answers.





1-3d. Students will use the skills acquired to solve problems in mathematics following real world situations: Medicine Education Sports Agriculture

1-3e. Students will be able to use technology to create and analyze scatter plots.

1-3f. Unit S10 Assessment and quizzes

LEARNING RESOURCES

Text: Elementary Statistics: A Step by Step Approach, Sixth Edition Chapter 10, sections 1,2


Computer (Microsoft Excel)

Overhead Panel

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Documents

HEALTH/PE PLANNED COURSE OUTLINE · Web view1. Students will organize data using frequency distributions 2. Students will be able to represent data in frequency distributions graphically