HONORS RESEARCH I / INTRODUCTION TO COMPUTERS · subjects to collect and organize data into logical patterns for presentations. The refinement of presentation skills will be an ongoing

FREEHOLD REGIONAL HIGH SCHOOL DISTRICT

OFFICE OF CURRICULUM AND INSTRUCTION

MEDICAL SCIENCES SPECIALIZED LEARNING CENTER

HONORS RESEARCH I /

INTRODUCTION TO COMPUTERS

COURSE PHILOSOPHY

Students enrolled in this course are provided with an enriched study of advanced mathematical topics spanning algebra, trigonometry, discrete mathematics, computer programming, and mathematical skills needed for scientific research. In addition to mastering these content areas, students will be utilizing these subjects to collect and organize data into logical patterns for presentations.

COURSE DESCRIPTION

Grade Level: 9 Department: Medical Sciences Specialized Learning Center Course Title: Honors Research I/ Introduction to Computers Credits: 5 Course Code: 160240

BOARD OF EDUCATION ADOPTION DATE: AUGUST 31, 2009

FREEHOLD REGIONAL HIGH SCHOOL DISTRICT

Board of Education

Mr. Ronald G. Lawson, President Mr. Christopher Placitella, Vice President

Mr. William Bruno Mr. Tom Caiazza

Mrs. Elizabeth Canario Mr. Barry Hochberg Mrs. Kathie Lavin Mr. Heshy Moses

Mrs. Jennifer Sutera

Mr. James Wasser, Superintendent Ms. Donna M. Evangelista, Assistant Superintendent for Curriculum and

Instruction

Curriculum Writing Committee

Ms. Kimberly Urban Ms. Carol Valosin

Supervisors

Ms. Marion Conrad Ms. Jennifer Seery

Course Philosophy

Students enrolled in this course are provided with an enriched study of advanced mathematical topics spanning algebra, trigonometry, discrete mathematics, computer programming, and mathematical skills needed for scientific research. In addition to mastering these content areas, students will be utilizing these subjects to collect and organize data into logical patterns for presentations. The refinement of presentation skills will be an ongoing process throughout the course. The computer science component provides a venue for the development of logical reasoning, critical thinking, and problem solving techniques.

Course Description

This course will use computer science as a tool to teach critical thinking and problem solving skills. The students will be introduced to fundamental concepts that are used in most computer programming languages: assignments, decision-making, loops, arrays, and strings. Methods of breaking down a complex problem into smaller components are emphasized. The students receive instruction in discrete mathematics related to computer science including computer number systems, recursive functions, bit-string analysis, and Boolean Algebra. Additional subjects addressed are sequences and series, trigonometry, probability, statistics, measurement systems, dimensional analysis, and significant figures. The significance and application of these topics to future math, science, and research courses is stressed. At various times throughout the course, students will be participating in group and/or individual presentations. The inclusion of visual aids produced using technology, such as a Power Point presentation for example, will be necessary.

Freehold Regional High School District Curriculum Map

MS Honors Research I /Introduction to Computers

Assessments Relevant Standards

1 Enduring Understandings

Essential Questions Diagnostic

(before) Formative(during)

Summative (after)

4.1 A3 There are various number systems utilized in addition to the base 10 system used in everyday life.

What other number systems exist besides base 10?

What are the applications of the other number systems? 4.1 B2,4 There are multiple algorithms for finding a

solution. Computational fluency includes understanding the meaning and appropriate use of numerical operations.

What makes a computational strategy both effective and efficient? How do operations affect numbers?

4.2 D1-2 Significant digits and unit of measurement are important descriptors in the accuracy of a value.

What role do significant digits play in the accuracy of a value?

How can units of measurement be used to describe, compare and make sense of phenomena?

4.2 E1 Geometric relationships provide a means to make sense of a variety of phenomena.

How do geometric relationships help to solve problems and/or make sense of phenomena?

What is the difference between direct and indirect measurement?

4.3 A1-2 The symbolic language of algebra and generalization of patterns in mathematics are used to communicate and understand mathematics.

How can patterns, relations and functions be used as tools to best describe and help explain real-life situations?

How can you use a pattern to predict future outcomes?

4.3 B1-4 Patterns, functions, and relationships can be represented graphically, numerically, symbolically or verbally.

What are some algebraic functions and the properties of each? What are the different types of transformations? How can functions be represented?

4.3 C1 Mathematical models can be used to describe and quantify physical relationships.

What are some algebraic models that represent real-life situations?

How can algebraic models be used to make predictions?

4.3 D3 Symbol manipulation can be utilized to analyze the outcome of a computer program.

How can symbol manipulation be used to interpret the output of a computer program?

4.4 A2,4-5 Data can be collected, organized, and analyzed using statistical measures.

How can statistical measures be used to influence an audience? What are some methods of organizing and displaying data?

How can a graphing utility be used to represent and interpret data?

Oral questions/ Discussion Anticipatory set questions

Quizzes Written assignments Class discussion Graphing calculator activity

Unit Test

4

5

Assessments Relevant Standards

1 Enduring Understandings

Essential Questions Diagnostic

(before) Formative(during)

Summative (after)

4.4 B3-5 Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions.

What is the difference between theoretical and experimental probability?

How can probability be used to make predictions or draw conclusions?

4.4 C1-4 Algorithms can effectively and efficiently be used to quantify and interpret discrete information.

What algorithms are used in conjunction with counting principles?

How do you determine which counting principle is used to solve a problem?

4.5 A1-5 Mathematics can be learned through problem solving, inquiry, and discovery.

What are some strategies for problem solving?

What is the difference between inquiry and discovery? 4.5 B1-4 Mathematics can be communicated in an

organized verbal or written form using appropriate mathematical terminology.

How does organization enhance mathematical learning?

What are appropriate means for communicating in math? 4.5 C1-4,6 Mathematics can be applied in practical

situations and in other disciplines. How can connections in mathematics be helpful in the real world?

In what other disciplines is algebra used?

4.5 D4 Mathematical reasoning can be used to evaluate the correctness of solutions.

How can mathematical reasoning be used to evaluate the correctness of a solution?

4.5 E1-3 Mathematical representations can be used to effectively communicate, problem solve and understand mathematics.

What are some mathematical representations?

How can mathematical representations be used to effectively communicate and problem solve?

4.5 F1-4 Technology is a tool to enhance mathematical learning.

How can the use of technology enhance the learning environment?

8.1 B9,11 Computer applications can be used to gather, organize, create and manipulate information and to solve problems.

What computer applications can be used to organize, gather, create and manipulate data?

What is the relevance of computer programs in everyday life?

Freehold Regional High School District

Course Proficiencies and Pacing

MS Honors Research I / Introduction to Computers

Unit Title

Unit Understandings and Goals

Recommended Duration

Unit #1: Presentations Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. 1. The students will be able to develop, organize and present an oral presentation. 2. The students will be able to use a presentation program such as Power Point.

3 weeks

Unit #2: Introduction to Computers

Mathematics can be applied in practical situations and in other disciplines. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. 1. The students will gain an understanding of the history of programming languages and the contributions of some significant people. 2. The students will become familiar with the hardware and software to be utilized throughout the course.

1 week

Unit #3: Programming Format and Simple Commands

Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. 1. The students will be able to write simple programs in QBASIC.

2 weeks

Unit #4: Unconditional and Conditional Statements

Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. 1. The students will be able to implement unconditional and conditional statements in a program.

4 weeks

6

Unit #5: Discrete Math There are various number systems utilized in addition to the base 10 system used in everyday life. Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematics can be learned through problem solving, inquiry, and discovery. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. 1. The students will be able to recognize and apply various discrete math topics, including but not limited to computer-based number systems, truth tables and recursive functions.

1.5 weeks

7

Unit Title



Unit #6: Logical Operators and Loops

Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. 1. The students will be able to write a program using the relationships AND and OR. 2. The students will be able to write code using computer made loops.

4.5 weeks

Unit #7: Arrays Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. 1. The students will be able to develop programs that use arrays to hold large amounts of data.

2 weeks

Unit #8: Strings Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. 1. The students will be able to manipulate character strings and apply conversion and translation statements.

2 weeks

Unit #9: Sequences and Series The symbolic language of algebra and generalization of patterns in mathematics are used to communicate and understand mathematics. Algorithms can effectively and efficiently be used to quantify and interpret discrete information. Mathematics can be learned through problem solving, inquiry, and discovery. Technology is a tool to enhance mathematical learning. 1. The students will be able to identify and apply arithmetic and geometric sequences and series.

2.5 weeks

Unit #10: Triangle Trigonometry

Geometric relationships provide a means to make sense of a variety of phenomena. Mathematical models can be used to describe and quantify physical relationships. Mathematics can be learned through problem solving, inquiry, and discovery. Mathematics can be applied in practical situations and in other disciplines. Technology is a tool to enhance mathematical learning. 1. The students will be able to understand the six trigonometric functions and use them to solve triangles.

3 weeks

8

Unit Title



Unit #11: Trigonometric Graphs and Identities

Patterns, functions, and relationships can be represented graphically, numerically, symbolically or verbally. Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. Technology is a tool to enhance mathematical learning. 1. The students will be able to understand the periodicity and symmetry in graphing trigonometric functions. 2. The students will be able to algebraically manipulate trigonometric identities.

3 weeks

Unit #12: Probability and Statistics

Data can be collected, organized, and analyzed using statistical measures. Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. Algorithms can effectively and efficiently be used to quantify and interpret discrete information. Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. Mathematics can be applied in practical situations and in other disciplines. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Technology is a tool to enhance mathematical learning. 1. The students will be able to display data and use measures of dispersion and central tendency to analyze the data. 2. The students will be able to count the number of ways an event can happen and calculate and use probabilities in real world contexts.

3 weeks

Unit #13: Math for Scientific Research

There are multiple algorithms for finding a solution. Computational fluency includes understanding the meaning and appropriate use of numerical operations. Significant digits and unit of measurement are important descriptors in the accuracy of a value. Data can be collected, organized, and analyzed using statistical measures. Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. Mathematics can be applied in practical situations and in other disciplines. 1. The students will have an understanding of different systems of measurement and the ability to convert among them. 2. The students will be able to represent numbers in a variety of ways including scientific notation and significant figures. 3. The students will be able to have an awareness of how statistical measures can be misleading.

2.5 weeks

9



Unit #1: Presentations

Enduring Understanding: Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. Essential Questions: How does organization enhance mathematical learning?

What are appropriate means for communicating in math? Unit Goals: The students will be able to develop, organize and present an oral presentation. The students will be able to use a presentation program such as Power Point. Duration of Unit: 3 weeks NJCCCS: 4.5 B1-4

Guiding / Topical Questions

Content, Themes, Concepts, and Skills

Instructional Resources and

Materials Teaching Strategies

Assessment Strategies

What visual and auditory qualities are necessary for a good presentation? What are the different parts of a presentation? How can a program such as Power Point enhance a presentation? What is the importance of a visual aid in a presentation? What is the importance of pacing and filling the appropriate amount of time in a speech?

Group project researching various programming languages, history of internet, and significant people in computers. Group project researching and creating a midterm exam review using Power Point. Group project creating a measurement system. Group project researching and creating a final exam review using Power Point.

Power Point Internet Overhead Poster paper Whiteboard VCR/DVD player

Lecture and class discussion Demonstrate and model appropriate presentation skills Cooperative learning activities Student feedback

Group work Presentations

Suggestions on how to differentiate in this unit: • Students with individual learning styles can be assisted through the use of cooperative learning activities, alternative assessments, and mathematical manipulatives.

10



Unit #2: Introduction to Computers

Enduring Understandings: Mathematics can be applied in practical situations and in other disciplines. Computer applications can be used to gather, organize, create and manipulate information and to solve problems. Essential Questions: How can connections in mathematics be helpful in the real world? What computer applications can be used to organize, gather, create and manipulate data?

What is the relevance of computer programs in everyday life? Unit Goals: The students will gain an understanding of the history of programming languages and the contributions of some significant people. The students will become familiar with the hardware and software to be utilized throughout the course. Duration of Unit: 1 week NJCCCS: 4.5 C1-4, 6, 8.1 B9, 11






What is a computer program and how do we write one? What are some of the various computer programming languages? What is the difference between hardware and software? How are computer programs used in everyday life? What is necessary to make a good computer program? What is an algorithm?

Group project to research the history of programming languages and significant people in computers. Worksheet/questionnaire on previous experience and knowledge of computers. Review sheet on equipment and classroom procedures for working in the computer lab.

Computers Internet Flash drives Teacher made worksheets

Lecture and class discussion Demonstrate and model appropriate computer skills Cooperative learning activities

Group work Presentations


11



Unit #3: Programming Format and Simple Commands

Enduring Understandings: Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems.

Essential Questions: How can symbol manipulation be used to interpret the output of a computer program? How can mathematical reasoning be used to evaluate the correctness of a solution?

What are some mathematical representations? How can mathematical representations be used to effectively communicate and problem solve? What computer applications can be used to organize, gather, create and manipulate data?

What is the relevance of computer programs in everyday life? Unit Goal: The students will be able to write simple programs in QBASIC. Duration of Unit: 2 weeks NJCCCS: 4.3 D3, 4.5 D4; E1-3, 8.1 B9, 11






What command can be used to display information on a computer screen? How does the use of the semicolon affect the output of a program? What role does the variable play in computer science? What is the difference between an equation and an assignment statement? How are arithmetic operations performed on data? What is the importance of annotating a computer program?

Discovery activity - copy code, makes modifications, and predict outcomes of variations on the program. Simple programming activity to demonstrate mastery of the print command and arithmetic operations. Write a simple calculator program to demonstrate basic arithmetic operations. Develop a program that accepts input and performs arithmetic computations such as perimeter of a triangle.

Computers Teacher made worksheets

Lecture and class discussion Demonstrate and model appropriate skills Cooperative learning activities

Computer programs Quiz


12



Unit #4: Unconditional and Conditional Statements

Enduring Understandings: Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematical reasoning can be used to evaluate the correctness of solutions.

Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Computer applications can be used to gather, organize, create and manipulate information and to solve problems.



What is the relevance of computer programs in everyday life? Unit Goal: The students will be able to implement unconditional and conditional statements in a program. Duration of Unit: 4 weeks NJCCCS: 4.3 D3, 4.5 D4; E1-3, 8.1 B9, 11



Instructional Resources

and Materials Teaching Strategies


How does an unconditional branch make code repeat? What is the difference between an unconditional and conditional statement? What is the difference between a simple IF and block IF statement? How do you determine which type of conditional statement to use in a program?

Worksheet on tracing code that uses the read command. Determine the value of the variables at each line number. As a class, develop a simple program such as calculating the area of a rectangle and use it to demonstrate the following: an endless loop, INPUT with decision-making statement, and READ/DATA commands. Have students write a simple program such as calculating the volume of a box, given the length, width, and height. Have them modify the program to incorporate each of the following: an endless loop, INPUT with decision-making statement, and READ/DATA commands. Develop a program to calculate the slope, midpoint and distance between two points on a line. Write a program that utilizes the IF/THEN/ELSE command. (Count number of Positives/Negatives/Zeros)



Computer programs Quiz Unit Test


13



Unit #5: Discrete Math

Enduring Understandings: There are various number systems utilized in addition to the base 10 system used in everyday life. Symbol manipulation can be utilized to analyze the outcome of a computer program. Mathematics can be learned through problem solving, inquiry, and discovery. Mathematical reasoning can be used to evaluate the correctness of solutions. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics.

Essential Questions: What other number systems exist besides base 10? What are the applications of the other number systems? How can symbol manipulation be used to interpret the output of a computer program? What are some strategies for problem solving?

What is the difference between inquiry and discovery? How can mathematical reasoning be used to evaluate the correctness of a solution? What are some mathematical representations?

How can mathematical representations be used to effectively communicate and problem solve? Unit Goal: The students will be able to recognize and apply various discrete math topics, including but not limited to computer-based number systems, truth tables and recursive functions. Duration of Unit: 1.5 weeks NJCCCS: 4.1 A3, 4.3 D3, 4.5 A1-5; D4; E1-3






How can equations that involve multiple number systems be solved? How can a recursive function be evaluated? How do you trace code in a computer program? How are truth tables used to organize information in discrete math? What operations can be performed using bit string analysis?

Solve an equation that involves multiple number systems. Evaluate a recursive function. Given a segment of a program, trace the code and write the output. Create truth tables to explore the properties of the logical operators AND/OR.

Current resource binders Teacher created worksheets Computer software

Lecture and class discussion Demonstrate and model appropriate skills Cooperative learning activities Guided and independent practice

Written tests and quizzes Worksheets Responses to class discussion Do now activity Closure questions Open ended questions


14



Unit #6: Logical Operators and Loops





What is the relevance of computer programs in everyday life? Unit Goals: The students will be able to write a program using the relationships AND and OR. The students will be able to write code using computer made loops. Duration of Unit: 4.5 weeks NJCCCS: 4.3 D3, 4.5 D4; E1-3, 8.1 B9, 11

15






What is the difference between the AND and OR operators? What are the different types of loops? How do you determine which type of loop to use in a program?

Write a program to determine whether three side lengths can form a triangle, and if so, classify it as scalene, isosceles, or equilateral. Be sure to check for bad data (negative # or cannot form a triangle). Determine if it is a right triangle as well. Write a program on paper that receives three side lengths for a triangle and determines if it is acute, right, or obtuse. Modify a previously written program to count from any number to any number by any increment. Ongoing activity to match the parts of a loop from a segment of code to the flow chart of parts of a loop. (FOR/NEXT, DO WHILE, etc) Discovery activity where students are given segments of code, predict the output and check results on computer.







Unit #7: Arrays





What is the relevance of computer programs in everyday life? Unit Goal: The students will be able to develop programs that use arrays to hold large amounts of data. Duration of Unit: 2 weeks NJCCCS: 4.3 D3, 4.5 D4; E1-3, 8.1 B9, 11






What is an array? When is it appropriate to use an array? How do you sort a list of numbers from least to greatest? How is this different from how a computer sorts numbers? What is the significance of generating unique random numbers? How is a flag array used to generate unique random numbers?

Discovery activity to determine importance of arrays in programming. Students write a program that will accept 7 grades, calculate the average grade, and print the number of grades above the average. Rewrite and modify previous program using an array and dimension statement. Visual demonstration of sorting, using students as examples followed by examples of code on overhead. Write a program using the random number generator and selection sort technique. Write a program using a flag array that generates unique random numbers, stores them in an array, sorts them, and prints them.





16



Unit #8: Strings





What is the relevance of computer programs in everyday life? Unit Goal: The students will be able to manipulate character strings and apply conversion and translation statements. Duration of Unit: 2 weeks NJCCCS: 4.3 D3, 4.5 D4; E1-3, 8.1 B9, 11






What is the difference between strings and numeric data? What operations can be performed on strings? What is the difference between LEFT$ and RIGHT$ functions? What is meant by parsing a string? How are strings sorted?

Handout for students to try writing a program utilizing functions to manipulate strings. Worksheet on tracing code utilizing strings and writing down the output of the code. Students verify the output on the computer. Partner activity – practice problems involving parsing, conversion and translation of strings. Write a program involving string manipulation.





17



Unit #9: Sequences and Series

Enduring Understandings: The symbolic language of algebra and generalization of patterns in mathematics are used to communicate and understand mathematics. Algorithms can effectively and efficiently be used to quantify and interpret discrete information. Mathematics can be learned through problem solving, inquiry, and discovery. Technology is a tool to enhance mathematical learning. Essential Questions: How can patterns, relations and functions be used as tools to best describe and help explain real-life situations? How can you use a pattern to predict future outcomes? What algorithms are used in conjunction with counting principles? How do you determine which counting principle is used to solve a problem? What are some strategies for problem solving? How can the use of technology enhance the learning environment? Unit Goal: The students will be able to identify and apply arithmetic and geometric sequences and series. Duration of Unit: 2.5 weeks NJCCCS: 4.3 A1-2, 4.4 C4, 4.5 A1-5; F4






What is the difference between an arithmetic and geometric sequence? How can sigma notation be used in determining the sum of a series? How can the formulas for finding the next term of an arithmetic and geometric sequence be derived? What information is necessary to create the formula for finding the sum of an arithmetic series? How is the formula for finding the sum of an infinite geometric series related to that of a finite geometric series? What are some examples of sequences and series in everyday life? How and when can Pascal’s Triangle be used to expand powers of a binomial?

HSPA style open ended questions to find the next term in a pattern and explain. Demonstrate the derivation of the formulas for finding the general term (and later, the sum) of an arithmetic and geometric sequence (series). Word problem activity to apply the formulas for arithmetic and geometric series and sequences. Use summation notation to represent a series and find the sum of that series. Bouncing ball problem to demonstrate an infinite geometric series. Koch’s Snowflake and Curve activities to demonstrate an infinite series. Binomial expansion activity to derive Pascal’s Triangle. Use combinations to determine the coefficient of any term in binomial expansion.

Current text and resource binders Teacher created worksheets HSPA resources Graphing calculators Graphing calculator software for the computer

Lecture and class discussion Guided and independent practice Demonstrate and model vocabulary and example problems using the board and overhead Cooperative learning activities Guided discovery

Written tests and quizzes Worksheets Responses to discussion questions Do now activity Closure questions Open ended questions Projects


18

Freehold Regional High School District MS Honors Research I / Introduction to Computers

Unit #10: Triangle Trigonometry

Enduring Understandings: Geometric relationships provide a means to make sense of a variety of phenomena. Mathematical models can be used to describe and quantify physical relationships.

Mathematics can be learned through problem solving, inquiry, and discovery. Mathematics can be applied in practical situations and in other disciplines. Technology is a tool to enhance mathematical learning.

Essential Questions: How do geometric relationships help to solve problems and/or make sense of phenomena? What is the difference between direct and indirect measurement?

What are some algebraic models that represent real-life situations? What are some strategies for problem solving?

How can connections in mathematics be helpful in the real world? In what other disciplines is algebra used? How can the use of technology enhance the learning environment? Unit Goal: The students will be able to understand the six trigonometric functions and use them to solve triangles. Duration of Unit: 3 weeks NJCCCS: 4.2 E1, 4.3 C1, 4.5 A1-5; C1-4, 6; F1, 4






How do angles in trigonometry differ from angles in geometry? What are the six trigonometric functions of an angle? How would you determine which trigonometric ratios should be used to solve a problem? How are reference angles used to find the trigonometric functions of any angle? How can you determine the missing measures in a right or oblique triangle? How can the area of an oblique triangle be determined? How can trigonometric functions be used to model real life phenomena?

Activity to review the special right triangles (45-45-90) and (30-60-90). Calculator activity to evaluate all six trigonometric functions of an angle measure. Calculator activity to use the inverse trig keys to find an angle measure. Word problems to demonstrate the use of the Law of Sines and Law of Cosines. Worksheet of problems in which the students need to identify the given information, draw a diagram, and determine which trigonometric formula to apply.



Written tests and quizzes Worksheets Responses to discussion questions Do now activity Closure questions Open ended questions Projects


19



Unit #11: Trigonometric Graphs and Identities

Enduring Understandings: Patterns, functions, and relationships can be represented graphically, numerically, symbolically or verbally. Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology.

Technology is a tool to enhance mathematical learning. Essential Questions: What are some algebraic functions and the properties of each?

What are the different types of transformations? How can functions be represented?

How does organization enhance mathematical learning? What are appropriate means for communicating in math?

How can the use of technology enhance the learning environment? Unit Goals: The students will be able to understand the periodicity and symmetry in graphing trigonometric functions.

The students will be able to algebraically manipulate trigonometric identities. Duration of Unit: 3 weeks NJCCCS: 4.3 B1-4, 4.5 B1-4; F1-4






What are radians and how are they used? How is it determined whether a function is even, odd or neither? What do the parent graphs of trigonometric functions look like? How can periodicity, amplitude and symmetry be used to graph trigonometric functions? How can sine and cosine functions be used to model real life phenomena? How are fundamental trigonometric identities used to simplify expressions and to prove other identities?

Problem solving activity to apply formulas for arc length and area of a sector. Make a table of values and hand graph sine and cosine waves. Graphing activity using amplitude, period and phase shift for sine and cosine functions. Graphing calculator activity to verify the graphs previously done by hand. Partner activity to prove trigonometric identities.

Current text and resource binders Teacher created worksheets Graphing calculators Graphing calculator software for the computer


Written tests and quizzes Worksheets Responses to discussion questions Do now activity Closure questions Open ended questions


20

Freehold Regional High School District MS Honors Research I / Introduction to Computers

Unit #12: Probability and Statistics

Enduring Understandings: Data can be collected, organized, and analyzed using statistical measures. Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. Algorithms can effectively and efficiently be used to quantify and interpret discrete information. Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. Mathematics can be applied in practical situations and in other disciplines. Mathematical representations can be used to effectively communicate, problem solve and understand mathematics. Technology is a tool to enhance mathematical learning.

Essential Questions: What are some methods of organizing and displaying data? How can a graphing utility be used to represent and interpret data? What is the difference between theoretical and experimental probability? How can probability be used to make predictions or draw conclusions?

What algorithms are used in conjunction with counting principles? How do you determine which counting principle is used to solve a problem? How does organization enhance mathematical learning? How can connections in mathematics be helpful in the real world? How can mathematical representations be used to effectively communicate and problem solve? How can the use of technology enhance the learning environment? Unit Goals: The students will be able to display data and use measures of dispersion and central tendency to analyze the data. The students will be able to count the number of ways an event can happen and calculate and use probabilities in real world contexts. Duration of Unit: 3 weeks NJCCCS: 4.4 A4-5; B3-5; C1-4, 4.5 B1-4; C1-4, 6; E1-3; F1-4






What are some methods to display data? What are the measures of central tendency and dispersion, and how are they used to analyze data? What constitutes a normal distribution? What does a correlation coefficient determine about a set of data? What are the different methods to calculate the number of ways an event can happen? How do you find the probability of a single event, mutually exclusive events, and independent events?

HSPA open ended packets involving methods of displaying data. HSPA open ended packets utilizing the measures of central tendency and dispersion. Graphing calculator activity to display data in various methods. Calculator activity to determine probability of events.


Lecture and class discussion Guided and independent practice Demonstrate and model vocabulary and example problems using the board and overhead Cooperative learning activities



21

22



Unit #13: Math for Scientific Research

Enduring Understandings: There are multiple algorithms for finding a solution. Computational fluency includes understanding the meaning and appropriate use of numerical operations. Significant digits and unit of measurement are important descriptors in the accuracy of a value. Data can be collected, organized, and analyzed using statistical measures. Mathematics can be communicated in an organized verbal or written form using appropriate mathematical terminology. Mathematics can be applied in practical situations and in other disciplines. Essential Questions: What makes a computational strategy both effective and efficient? How do operations affect numbers? What role do significant digits play in the accuracy of a value? How can units of measurement be used to describe, compare and make sense of phenomena? How can statistical measures be used to influence an audience? How does organization enhance mathematical learning? What are appropriate means for communicating in math? How can connections in mathematics be helpful in the real world? Unit Goals: The students will have an understanding of different systems of measurement and the ability to convert among them. The students will be able to represent numbers in a variety of ways including scientific notation and significant figures. The students will be able to have an awareness of how statistical measures can be misleading. Duration of Unit: 2.5 weeks NJCCCS: 4.1 B2, 4, 4.2 D1-2, 4.4 A2, 4.5 B1-4; C1-4, 6






What are some different systems of measurement? How are conversion factors used to convert within a system and between different systems of measurement? What is the benefit of representing numbers in scientific notation? How do you determine the correct number of significant figures to be used in a problem? Are all statistics reliable? How are statistics used to market a product?

Cooperative learning activity to discuss history of measurement systems. Independent activity to practice applying dimensional analysis. Worksheet for scientific notation, exponents and significant figures. Video “Junk Science” to be viewed in class. Students will discuss reaction to how statistics are utilized in marketing. Students gain an understanding of how statistics are not always reliable.

Resource binders Teacher created worksheets Video

Lecture and class discussion Guided and independent practice Demonstrate and model vocabulary and example problems using the board and overhead Cooperative learning activities



Documents

HONORS RESEARCH I / INTRODUCTION TO COMPUTERS · subjects to collect and organize data into logical patterns for presentations. The refinement of presentation skills will be an ongoing