Grand Canyon Middle School-Level I (Math 01) Mathematics Course Outline

2006- 2007

Name of Course: Math 6-01

Teacher and Contact Information:                    Cynthia SauvÈ

School Phone: 928/ 638-6421 x502

Email: cynthias@grandcanyonschool.org

Course Description:

The curriculum for Math 6-01 is aligned with the Arizona State Standards and the MYP Aims and Objectives. The curriculum encompasses a hands-on, performance-based, interdisciplinary program which fosters the development of a positive "can-do" attitude toward mathematics. The framework for 6-1 Math includes the following areas of mathematics; Numeracy & Rational Numbers, Fractions, Decimals & Percents, Probability & Statistics, Euclidean & Non-Euclidean Geometry, Data Analysis, Discrete Math and Logic. Students in this course are expected to master arithmetic skills and establish a solid knowledge base in the mathematical areas listed above.

In Math 6-01, students will understand that math is embedded within all cultures. It is a universal language and a vital intellectual tool in our post-industrial Information Age. It is for that reason; students will need to go beyond the basics in order to develop mathematical reasoning and strategies to think critically, to problem solve, and make logical decisions. Students, in this course, will be exposed to diverse mathematical applications and will be expected to analyze mathematical models of natural phenomena, human behavior, and social systems.

1^st Semester :    "Why do we do what we do?"

-Number Sense: It Makes a Whole Lot of Sense!

• What would our world be like without numbers?
• AOI: Approaches to Learning- students will coherently organize and present the characteristics, numeration, and theory of a chosen number.   

•       Place Value and Number Concepts

•       Number Theory: factors, multiples, prime numbers, divisibility tests, GCF, LCM

•       Number Operations and Properties: addition, subtraction, multiplication, and division

•       Powers of Ten and Standard Form

•       "Multiplication Olympics"

   Throughout these units, students will explore of the history of natural numbers and what our world would be like without them. Topics may include: The Babylonians - and how they developed a powerful place value system; the Egyptians- and how they had all the powers of 10 up to one million; the Hindu-Arabic place-valued decimal system; and the beginning roots of the concept of zero.  Students will also participate in the "Multiplication Olympics", linking Social Studies and Physical Education to these math units. 

-Fractions, Decimals and Percent: Falling into Pieces!

• Why is it said, the whole is more than the sum of its parts?

• AOI: Homo Faber- Recognizing man's creativity and ability to transform componential objects into a greater whole. For example, a painted picture carries a different and altogether greater meaning than its individual components: paint, canvas, and a brush.

•       Fractions: concepts and operations

•       Decimals: concepts and operations

•       Percents: compute and convert between decimals and fractions

•       Ratios and Proportions

•       Percent Circles/ Pie Chart

•       Discrete Math: Systems Theory

   Throughout these units, students will reflect on the general principle of Holism with an overview of Aristotle's Metaphysics and Max Wertheimer's Gestalt psychology. Discussion will be lead up to the introduction of Discrete Math through Systems Theory. These units will integrate Technology & Design and Language Arts.

2^nd Semester:  "So this is why we did what we did!"

-Data Analysis, Probability & Statistics: Your Goal- Do You Stand a Chance?

• How would the probability for having a healthy population be affected if we were all aware of important world statistics?
• AOI: Health and Social Education- discrete math provides students with different forms of representation to illustrate ideas, issues and data. Students will create various forms of graphs, tables and charts to represent health trends within our culturally diverse student body.

•       Probability: Experimental/theoretical probability and dependent/independent events

•       Statistics: Sampling, scatter plots, stem and leaf diagrams, box and whisker plots

•       Data Analysis: Graph construction and interpretation

•       "Walk Across the Wild West" 

   Throughout these units, students will be examining the national state of adolescent health, safety, and well-being through the CDC's National Initiative to Improve Adolescent Health by the Year 2010. Students will participate in the "Walk Across the Wild West" competition and will collect, compute and analyze data from their own student body then compare these results with the national statistics.

   Students will also read David Smith's book, If the World Were a Village, to graph the world's demographics. These units will integrate Technology & Design, Social Studies, Physical Education and Health.

-Geometry: Let's Get Into Shape!           

• It has been stated that Phi is the harmony and glue that holds the unity of the universe. If Phi did not exist, how would our world change?
• AOI: Environment- Students will examine historical and natural phenomena of geometry; the Golden Ratio: Fibonacci Series & Nature, and ancient architecture.

•       Area and Volume

•       Euclidean Geometry

•       Transformation of Shapes

•       Coordinate Geometry

•       Measurement

   Throughout these units, students will explore Leonardo Pisano Fibonacci and the Golden Ratio and its frequent appearance in geometry, Ancient Greek Architecture and nature. These units will integrate Social Studies, Art, and Science.

  -Discrete Math and Logic:  Let's Be DiscreteÖ

• Why is the art of proposing a question worth more than the value of solving it?
• AOI: Environment- Students will examine historical and natural phenomena of geometry; the Golden Ratio: Fibonacci Numbers & Nature, and ancient architecture. 

Discrete Math: Sudoku, mazes, and dot-to-dot and Rubik's Cubes!

Logic: Set Theory

   In Discrete Math, students will investigate the history of Soduko through ancient Islamic Magic Squares and Graeco-Latin Squares. With Logic, students will look into the works of the Russian mathematician Georg Cantor and his Set Theory. Science, Social Studies, Art, and Language Arts will be integrated throughout these units.

Teaching and Assessment

Math 6-01 requires energetic, relevant instruction not solely based on lecture and rote learning. Instead the role of the teacher in this class is to instruct, guide and facilitate experiential learning in a student-centered classroom while maintaining a balance in developing mathematical skills through rote learning.

Assessment is two-fold: it is an ongoing, integrated, multidimensional process to identify students' strengths and weaknesses as well as valuable tool to improve teaching effectiveness. The assessment criteria for Mathematics are categorized into four areas: Knowledge & Understanding, Application & Reasoning, Communication, and Reflection & Evaluation. Math 6-01 has clear, explicitly stated objectives which authentically relate to the assessment criteria and reflect real-world application.

 In this course, evidence of competency is assessed both formatively and summatively with criterion based evaluations. Some of the formative examples include: "After-Math", "Exit Cards", "Quick Quizzes", "Pre-tests", as well as classroom observation and guided whole class discussions. Some of the summative assessments include: comprehensive broad-based unit tests, relevant projects with reflection, oral presentations, written reports, and uses of technology. All assessments are continually followed up with appropriate feedback.

 Resources:

…       Connected Mathematics: Prentice Hall

…       Middle School Math: Scott Foresman- Addison Wesley

Grand Canyon Middle School- Level I Mathematics Course Outline

2006- 2007

Name of Course:  Level I Math

Teacher and Contact Information:                    Cynthia SauvÈ

School Phone: 928/ 638-6421 x502

Email: cynthias@grandcanyonschool.org

Course Description:

The curriculum for Level I Math is aligned with the Arizona State Standards and the MYP Aims and Objectives. The curriculum encompasses a hands-on, performance-based, interdisciplinary program which fosters the development of a positive "can-do" attitude toward mathematics. The framework for 6-1 Math includes the following areas of mathematics; Numeracy & Rational Numbers, Fractions, Decimals & Percents, Probability & Statistics, Euclidean & Non-Euclidean Geometry, Data Analysis, Discrete Math & Logic, and Algebra & Functions. Students in this course are expected to master arithmetic skills and establish a solid knowledge base in the mathematical areas listed above.

In Level I Math, students will understand that math is embedded within all cultures. It is a universal language and a vital intellectual tool in our post-industrial Information Age. It is for this reason that students need to go beyond the basics. Students must develop mathematical reasoning and strategies in order to think critically, to problem solve, and make logical decisions. This course will examine diverse mathematical applications and analyze mathematical models of natural phenomena, human behavior, and social systems.

1^st Semester :    "Why do we do what we do?"

-Number Sense: It Makes a Whole Lot of Sense!

• What would our world be like without numbers?
• AOI: Approaches to Learning- students will coherently organize and present the characteristics, numeration, and theory of a chosen number.   

•       Place Value and Number Concepts

•       Number Theory: factors, multiples, prime numbers, divisibility tests, GCF, LCM

•       Number Operations and Properties: addition, subtraction, multiplication, and division

•       Powers of Ten and Standard Form

•       "Multiplication Olympics"

   Throughout these units, students will explore of the history of natural numbers and what our world would be like without them. Topics may include: The Babylonians - and how they developed a powerful place value system; the Egyptians- and how they had all the powers of 10 up to one million; the Hindu-Arabic place-valued decimal system; and the beginning roots of the concept of zero.  Students will also participate in the "Multiplication Olympics", linking Social Studies and Physical Education to these math units. 

-Fractions, Decimals and Percent: Falling into Pieces!

• Why is the whole more than the sum of its parts?

• AOI: Homo Faber- Recognizing man's creativity and ability to transform componential objects into a greater whole. For example, a painted picture carries a different and altogether greater meaning than its individual components: paint, canvas, and a brush.

•       Fractions: concepts and operations

•       Decimals: concepts and operations

•       Percents: compute and convert between decimals and fractions

•       Ratios and Proportions

•       Percent Circles/ Pie Chart

•       Discrete Math: Systems Theory

   Throughout these units, students will reflect on the general principle of Holism with an overview of Aristotle's Metaphysics and Max Wertheimer's Gestalt psychology. Discussion will be lead up to the introduction of Discrete Math through Systems Theory. These units will integrate Technology & Design and Language Arts.

2^nd Semester:  "So this is why we did what we did!"

-Data Analysis, Probability & Statistics: Your Goal- Do You Stand a Chance?

• How would the probability change for having a healthy global population if we were all aware of the world's health statistics?
• AOI: Health and Social Education- discrete math provides students with different forms of representation to illustrate ideas, issues and data. Students will create various forms of graphs, tables and charts to represent health trends within our culturally diverse student body.

•       Probability:        Experimental/theoretical probability and dependent/independent events

•       Statistics:           Sampling, scatter plots, stem and leaf diagrams, box and whisker plots

•       Data Analysis: Graph construction and interpretation

•       "Walk Across the Wild West" 

   Throughout these units, students will be examining the national state of adolescent health, safety, and well-being through the CDC's National Initiative to Improve Adolescent Health by the Year 2010. Students will participate in the "Walk Across the Wild West" competition and will collect, compute and analyze data from their own student body then compare these results with the national statistics.

   Students will also read David Smith's book, If the World Were a Village, to graph the world's demographics. These units will integrate Technology & Design, Social Studies, Physical Education and Health.

-Geometry: Let's Get Into Shape!           

•  It has been stated that Phi is the harmony and glue that holds the unity of the universe. If Phi did not exist, how would our world change?
• AOI: Environment- Students will examine historical and natural phenomena of geometry; the Golden Ratio: Fibonacci Series & Nature, and ancient architecture.

•       Area and Volume

•       Euclidean Geometry

•       Transformation of Shapes

•       Coordinate Geometry

•       Measurement

   Throughout these units, students will explore Leonardo Pisano Fibonacci and the Golden Ratio and its frequent appearance in geometry, Ancient Greek Architecture and nature. These units will integrate Social Studies, Art, and Science.

-Discrete Math and Logic:  Let's Be Discrete.

• Why is the art of proposing a question worth more than the value of solving it?
• AOI: Environment- Students will examine historical and natural phenomena of geometry; the Golden Ratio: Fibonacci Numbers & Nature, and ancient architecture. 

•       Discrete Math: Sudoku, mazes, and dot-to-dot and Rubik's Cubes!

•       Logic: Set Theory

   In Discrete Math, students will investigate the history of Soduko through ancient Islamic Magic Squares and Graeco-Latin Squares. With Logic, students will look into the works of the Russian mathematician Georg Cantor and his Set Theory. Science, Social Studies, Art, and Language Arts will be integrated throughout these units.

-Algebra and Functions: It's all about balance!

•       expanding & factorizing

•       simplifying & substituting

•       solving equations

Teaching and Assessment

   Level I Math requires energetic, relevant instruction not solely based on lecture and rote learning. Instead the role of the teacher in this class is to instruct, guide and facilitate experiential learning in a student-centered classroom while maintaining a balance in developing mathematical skills through rote learning.

   Assessment is two-fold: it is an ongoing, integrated, multidimensional process to identify students' strengths and weaknesses as well as valuable tool to improve teaching effectiveness. The assessment criteria for Mathematics are categorized into four areas: Knowledge & Understanding, Application & Reasoning, Communication, and Reflection & Evaluation. Math 6-1 has clear, explicitly stated objectives which authentically relate to the assessment criteria and reflect real-world application.

   In this course, evidence of competency is assessed both formatively and summatively with criterion based evaluations. Some of the formative examples include: "After-Math", "Exit Cards", "Quick Quizzes", "Pre-tests", as well as classroom observation and guided whole class discussions. Some of the summative assessments include: comprehensive broad-based unit tests, relevant projects with reflection, oral presentations, written reports, and uses of technology..

Resources:

Connected Mathematics: Prentice Hall

Middle School Math: Scott Foresman- Addison Wesley

Level II Course Outline

Name Of Course:  Level II Math (6^th grade honors and 7^th grade standard mathematics)

I.  Course Description:

This course is designed as an extension of the topics explored in 6th grade math and to prepare students for success in Pre-Algebra and beyond.  Students will develop positive attitudes toward the continued learning of math, appreciate its history and recognize its applications to everyday life.

Approaches to learning will be used throughout the year as students develop problem solving skills through the investigation of relationships, patterns, and applications.  Students will also be introduced to intercultural connections as they explore number systems, use the abacus, and study the metric system.  Through exploration of historical topics, students will look at mathematics through the lens of Homo Faber.

Process and communication will be emphasized as students will share ideas, provide written explanations, and reflect upon their work.

II. Topics:

Semester I:

• Number Sense
• Fractions, Decimals, & Percents
• Integers
• Algebra & Functions

First semester will include an extensive study of fractions, decimals, and percents.  Applications including discounts, sales tax, and tips will be explored which will lead students into computational techniques that make sense.  Integer arithmetic is introduced using the number line.  This will give students a visual connection to the rules for addition and subtraction.  They will extend these rules to all rational numbers.  Number sense will be a focus throughout the semester in all areas of study.  A look at different number systems, arithmetic in different bases, and use of the abacus will reinforce place value and decimal arithmetic.  Hands-on equations prepare students for a unit on solving equations.

Semester II:

• Geometry, Transformations, & Measurement
• Discrete Math & Logic
• Data Analysis, Statistics, & Probability

During this semester there will be an emphasis on terminology, notation, and hands-on activities involving polygons, area and perimeter, and transformations.  Students will use graphing and measurement throughout the semester as they apply ratios and proportions and use the metric system.  Students will collect and analyze data and study probability and other discrete math topics through experimentation.

III.        Teaching and Assessment:

Students in this course will be expected to learn in a variety of ways.  Through questioning and problem solving techniques students will investigate and conjecture.  They will be expected to explain their reasoning in class or cooperative group discussions and in writing.  Explorations will include experiments and applications using manipulatives, geometric constructions, computer investigations, calculator-based labs, and hands-on equations.

Formative and summative assessments will be based on the following criteria:

Criterion A         Knowledge & Understanding

Criterion B         Application & Reasoning

Criterion C         Communication

Criterion D         Reflection & Evaluation

IV.  Resources:

Connected Math.  Pearson, Prentice Hall

Middle School Math Course 2.  Scott Foresman

Quantitative Literacy Series.  Dale Seymour

Geometer's Sketchpad

Texas Instruments CBL's

Numerous other handouts

Teacher:  Jane Halverson  jane@grandcanyonschool.org

Pre-Algebra Course Outline

Name of Course:  Pre-Algebra (Level II Honors, Level III Standard and Level IV Basic Math)

I.  Course Description:

This course is intended to continue the mathematical educational process to prepare students for Algebra I and develop a positive attitude toward the continued learning of mathematics.  It is intended to foster the appreciation of the usefulness, power and beauty of mathematics, and recognize its relationship with other disciplines and with everyday life.  The purpose of the course is gaining a foundation of the fundamental concepts and vocabulary of Algebra.  It is intended to enhance student appreciation, development and knowledge-base of mathematical concepts.  The application of skills is the central focus of the course and students will develop the ability to reflect upon and evaluate the significance of their work and the work of others.

The relevancy of mathematics applications outside the classroom will be an important component of the course.  Intercultural connections will be woven throughout the lessons to facilitate the appreciation for international dimensions of mathematics and its varied cultural and historical perspectives.  Summative and formative assessments will center around the prescribed assessment tasks of broad-based classroom tests and examinations, reasoned pieces of work in which the student has the opportunity to apply mathematics in an everyday situation and to reflect upon and evaluate findings, and written reports in which the student reflects upon methods and processes and evaluates findings of an investigation.

II. Topics:

Integers- Comparing and ordering, adding and subtracting, multiplying and dividing (Approaches to Learning)

Variables and Expressions- Evaluating expressions, order of operations, properties of numbers formulas (Approaches to Learning))

Equations and Problem Solving-  Solving equations and inequalities, adding, subtracting, multiplying and dividing equations, inverse operations, translating work expressions (Homo Faber)

Number Theory- Factors and Multiples, divisibility, prime and composite numbers, LCM and GCF (Homo Faber)

Fractions- Equivalent fractions, adding, subtracting, multiplying and dividing fractions and mixed numbers (Approaches to Learning)

Probability-  Ratio and proportion, ratio and measurement, collecting data, recording data, independent and dependent events, permutations (Health and Social)

Decimals- Rational numbers and expressions, decimals and fractions, repeating decimals, scientific notation, metric system product and quotient of decimals (Homo Faber and Approaches to Learning)

Percent- Interchanging fractions, decimals and percents, percent of a number, interest, discounts (Approaches to Learning)

Analyzing Data- Misleading graphs, presenting data, measures of central tendency, stem-n-leaf plots, box-n-whisker plots, situational graphs (Environment)

Number Line and Inequalities- Properties of inequalities, solving inequalities, conjunctions and disjunctions (Approaches to Learning)

Coordinate Plane- coordinate graphs, graphing linear equations, standard form, slope, non-linear equations, graphing inequalities (Approaches to Learning)

Throughout the year students will compare and contrast various international cultures through currencies, populations, weights and measure, history of math and manipulatives.  The areas of interaction listed will be used as the focus of the study of the unit.

III. Teaching and Assessment

Students in this course will be expected to learn in a variety of ways.  They will learn through investigation, questioning techniques, and direct instruction.  Process is emphasized and students will show how to solve a problem and/or write an explanation of their reasoning. They will be expected to explain their reasoning in class or cooperative group discussions and in writing.

Formative assessments will include teacher generated and student-generated questioning, quizzes, tests, board work, group work and group activities.  Summative assessments will measure knowledge and understanding with class tests and open-ended investigations, application and reasoning through reasoned pieces of work (which include open-ended investigations set in a variety of contexts), communication through tasks allowing students to communicate effectively when using concepts and skills and reflection and evaluation by reporting on investigations undertaking using concepts and skills.

IV. Resources

Connected Math.  Pearson, Prentice Hall

Transition Mathematics.  Scott Foresman, Addison Wesley

Cord Algebra.   South-Western Educational Publishing

Numerous other handouts.

Teacher:  Nancy Hunter

Algebra I Course Outline

Name of Course:  Algebra I (Level III Honors or Level IV Standard Math)

I.  Course Description:

This course is designed to build a comprehensive mathematical knowledge base that will enable students to be successful in higher-level math courses.  The skills learned in this course can be the foundation to succeed in a wide range of careers.  Students will continue to develop positive attitudes toward the learning of math.  Approaches to learning will be used throughout the course.  The analysis of real-world data and the graphical modeling of equations will allow students to connect math to the environment and health and social applications.  Homo Faber will used throughout the course as well as the history of mathematical ideas are explored and students see mathematics as an international language.

II. Topics

Semester I:

Real Number System

Expressions & Formulas

Equations & Inequalities

Proportions

Students will build on the knowledge obtained in Pre-Algebra.  In this semester students will use a Venn diagram to illustrate the relationships among classes of numbers in the Real Number System and use a number line to explain and use the rules for operations on rational numbers and absolute value equations and inequalities.  Students will use the ideas of balance, inverse operations, and number sense to solve equations.  A study of proportional reasoning will be based on investigations involving real-world data.

Semester II:

Graphs & Functions

Systems of Equations & Inequalities

Exponents & Radicals

Polynomial (Quadratic Equations)

Data Analysis & Probability

In this semester students will use graphical methods to make predictions, solve systems, and model real-world situations.  Computational techniques involving exponents & radicals will aid in graphing & solving quadratics.  A study of probability will be included in which theoretical and experimental results are compared and used to make predictions and solve problems.

III. Teaching & Assessment

Students will be expected to learn in a variety of ways.  They will learn through investigation, questioning techniques, and direct instruction.  Process is emphasized and students will show how to solve a problem and/or write an explanation of their reasoning.  They will explain orally or in writing the connections between concepts.  Students will work individually and in cooperative groups using the graphing calculator and calculator-based labs to investigate.

Formative and summative assessments will be based on the following criteria:

Criterion A         Knowledge & Understanding