Math Descriptions

MATHEMATICS

All courses are designed to integrate math topics across the curriculum, and each topic will be presented numerically, graphically, and algebraically. We will make significant use of technology, particularly graphing calculators. Students may check out a graphing calculator for the year on contract, but we highly recommend that students purchase graphing calculators if possible. See individual course descriptions. Ask the course instructor for details before purchasing.

Math Support: The high school has developed a program to provide out of class math support for students taking Algebra I, IA, IB or Geometry. If at progress report time or at the end of the quarter, a student’s math grade is a C- or lower, the student will be assigned two periods of math support each week in addition to his or her regular math course. These math support classes are organized and taught by the MHS math teachers; attendance is required for a minimum of four weeks. Failure to attend an assigned math support class will result in detention.

209 INTEGRATED MATH I (G)

SUMMARY:

Integrated Math is designed to strengthen students’ skills in mathematical reasoning and application. Topics are chosen to engage the student in hands-on learning and to minimize the need to perform repetitive pencil and paper arithmetic calculations. Some computation is performed to strengthen or maintain students’ arithmetic skills. However, the emphasis is on students investigating and making connections individually and through group work in areas such as: patterns, reflections, symmetry, graphs, charts and tables, probability, statistics, newspaper math, visual thinking, problem solving, tessellations, and algebra. Working within small cooperative groups and completing individual projects will be stressed. This course could lead to Algebra Prob/Stat IA, Applied Business Math and Integrated Math II.

EXPECTATIONS FOR STUDENTS:

Students are expected to work independently and in small groups in order to master to their own ability the material presented. This will incorporate the need for students to function well with all other students and to use the teacher as a resource. Most work will be individually paced. It is expected that all students, while continuing their study of math, will learn to treat each other respectfully, will be polite listeners and participants, will willingly help anyone in class, will grow to limit their own distracting behaviors and will focus on their own work.

ASSESSMENT:

Assessment is done on a daily basis as determined by the quality and amount of work accomplished and the ability to work in a group. Projects will be graded based on completeness, quality and how closely the student has followed directions. Infrequent quizzes and tests will be given. Self-evaluation is done quarterly.

KEY STANDARDS:

· Vital Results: 3.10 Teamwork, 3.11 Interactions, 3.12 Conflict Resolution, 3.13 Roles and Responsibilities, 4.4 Effects of Prejudice, 1.20 Communication of Data, 1.18 Research

· Fields of Knowledge: 7.6 Arithmetic, Number, and Operation Concepts, 7.7 Geometric and Measurement Concepts, 7.8 Function and Algebra Concepts, 7.9 Statistic and Probability Concepts, 7.10 Mathematical Problem Solving and Reasoning

0.5 Credit – Semester

210 INTEGRATED MATH II (G)

SUMMARY:

Integrated Math II is designed to strengthen students’ skills in mathematical reasoning and application through exposure to hands-on learning and problem solving. Independent, ability-paced work along with cooperative work in groups is stressed. Topics will focus on geometric and algebraic learning through manipulative-based units. Manipulatives will include tangrams, pattern blocks, compasses and protractors, algebra tiles, pentominos, cards, dominos, dices, games and “Hands-on” algebra. An additional focus will be a school-to-work initiative. Students will be “on site” in the community to gain exposure to math in the work place and will follow-up on this with project work in class. Computational skills will continue to be developed. However, the emphasis is on students investigating problems and making connections in many mathematical areas. Working within small cooperative groups and completing individual projects will be stressed. The student who successfully completes Integrated Math I and Integrated Math II will have gained exposure to all Math Standards in the Vermont Framework.

EXPECTATIONS FOR STUDENTS:

Students are expected to work independently and in small groups in order to master, to their own ability, the material presented. This will incorporate the need for students to function well with others and to use the teacher as a resource. Most work will be individually paced. It is expected that all students will continue their study of math, learn to treat each other respectfully, be polite listeners and participants, willingly help anyone in class, grow to limit their own distracting behaviors and focus on their own work. While “on-site”, students will be expected to demonstrate those behaviors appropriate for the work place.

ASSESSMENT:

On-going assessment will be based on the quality and quantity of work and projects done on a daily basis. Appropriate work-relationships within groups will be stressed and evaluated. Self-evaluation will occur quarterly. Assessment also will occur through occasional quizzes and tests. Assessment for learning while involved with the school-to-work component will be completed by the teacher and supervisor. It will also incorporate project work specific to school-to-work.

KEY STANDARDS:

· Vital Results: 3.10 Teamwork, 3.11 Interactions, 3.12 Conflict Resolution, 3.13 Roles and Responsibilities, 4.4 Effects of Prejudice, 1.20 Communication of Data, 1.18 Research

0.5 Credit - Semester

624 APPLIED BUSINESS MATH (G) (Fall and/or Spring)

SUMMARY:

This course is designed to strengthen the student's math skills needed for the world of business and personal finance. The course will cover areas such as: banking, personal money management,

budgeting, investments, and insurance.

EXPECTATIONS FOR STUDENTS:

Students will be expected to work as individuals as well as in groups. Work will be completed both in and out of the classroom. Major expectations revolve around comprehension of mathematical formulas, basic use of the calculator, an in-depth investments project, and completion of a financial simulation.

ASSESSMENT:

Assessment is based on individual and team performance of work, participation, mathematical comprehension and mathematical computation. The students are expected to prepare large and small projects. Assessment will also be determined through traditional methods that measure content and comprehension.

KEY STANDARDS:

· Vital Results: 2.8 Approach (Taking Risks), 2.12 Abstract and Creative Thinking (Flexibility), 3.7 Making Informed Decisions, 3.8 Personal Economics

· Fields of Knowledge: 7.2 Inquiry, Experimentation, and Theory, 7.6 Arithmetic, Number, and Operation Concepts

0.5 Credit – Semester

212 ALGEBRA, PROBABILITY, AND STATISTICS IA (G)

SUMMARY:

This course is the first year of a two year math sequence covering the same topics as Algebra I with Probability and Statistics (see below). The course is paced in order to cover the topics at a slower rate. The course is designed for the student who does not meet the prerequisite for Algebra 1with Probability and Statistics, but who wishes to meet the requirements for college entrance.

Prerequisite: Teacher recommendation from 8th grade math or Integrated Math I. Graphing calculator

required (TI-83).

EXPECTATIONS FOR STUDENTS:

Students are expected to complete daily homework assignments and should have graph paper for this purpose. A pencil or pen, paper, three-ring binder, textbook, and graphing calculator are required everyday! There will also be frequent quizzes on the homework as well as unit tests. In addition, there will be occasional projects and portfolio problems that are graded as tests. There will be a midterm in January and a final exam in June. Each exam will be 1 ½ hours long and will be cumulative.

Students are also expected to do a substantial amount of graphing calculator work.

ASSESSMENT:

A variety of assessments are used: individual student class work, homework, quizzes, tests, written responses to open-ended questions (Vermont Portfolio pieces), group work, projects.

KEY STANDARDS:

· Vital Results: 1.20 & 1.21 Information Technology, 2.2 & 2.3 Problem Solving, 2.5 Mathematics Dimensions

· Fields of Knowledge: 7.6 Mathematical Understanding - Arithmetic, Number and Operation Concepts, 7.8 Function and Algebra Concepts, 7.9 Statistics and Probability Concepts, 7.10 Mathematical Problem Solving and Reasoning - Applications

1.0 Credit - Year

213 ALGEBRA PROBABILITY AND STATISTICS IB (G)

SUMMARY:

The second year of a two-year math sequence covering Algebra I with Probability and Statistics topics. This course can be taken concurrently with Geometry with Trig.

Prerequisite: Must have passed Algebra Prob/Stat IA. Graphing calculator required (TI-83).

EXPECTATIONS FOR STUDENTS:

Homework: Homework will be assigned daily and will need to be completed on time. Homework must be maintained in a notebook. A pencil or pen, paper, three-ring binder, textbook and graphing calculator are required everyday! Quizzes: Frequent quizzes (both announced and unannounced) covering recent work will be given. Questions will be based on homework or recently covered material. Tests: Tests will generally cover individual chapters. Problem-solving skills will be emphasized. Cumulative material will be included on tests. Portfolios/Projects: There will be two portfolios assigned per quarter. In addition we may do projects or problem-solving activities based on materials covered in class. Midterm and final exams: There will be a midterm in January and a final exam in June. Each exam will be 1 ½ hours long and will be cumulative.

ASSESSMENT:

Assessment is based on individual student class work and homework, quizzes and tests, Vermont Portfolio pieces, and individual and group projects.

KEY STANDARDS:

· Vital Results: 1.20 & 1.21 Information Technology, 2.2 & 2.3 Problem Solving 2.5 Mathematics Dimension

· Field of Knowledge: 7.6 Mathematical Understanding - Arithmetic, Number and Operation Concepts, 7.8 Function and Algebra Concepts, 7.9 Statistics and Probability Concepts, 7.10 Mathematical Problem Solving & Reasoning

1.0 Credit – Year

211 ALGEBRA, PROBABILITY, AND STATISTICS I (C)

SUMMARY:

Algebra Prob/Stat I is designed to introduce the student to the power of generalizing math through algebra. An integrated approach will include topics in algebra, statistics, graphs, probability, graphs, functions and the real number systems. Emphasis will be on individual and group problem solving which includes portfolio work. At all times making connections among the algebraic, the numerical and the graphical representations will be stressed.

Prerequisite: Minimum "B" average in 8th grade math. Graphing calculator required. (TI 83)

EXPECTATIONS OF STUDENTS

Students are expected to complete daily homework, one or two portfolio problems per quarter, two chapter tests per quarter, and projects. A pencil or pen, paper, three-ring binder, textbook and graphing calculator are required everyday! There is a mid-term exam and a final exam.

ASSESSMENT:

Assessment is done through tests, quizzes, portfolios, projects and self-evaluation.

KEY STANDARDS:

· Vital Results: 1.20 Communication of Data, 1.21 Selection, 2.2 Problem solving process, 2.3 Types of problems, 2.5 Mathematical dimensions, 3.1 Teamwork, 3.11 Interactions

· Fields of Knowledge: 7.6 Arithmetic, Number and operation concepts, 7.7 Geometric and Measurement Concepts, 7.8 Functions and Algebra Concepts, 7.9 Statistics and Probability Concepts

1.0 Credit – Year

221 GEOMETRY WITH TRIGONOMETRY (C)

SUMMARY:

This course is designed to introduce geometric and trigonometric concepts through a discovery approach. While emphasizing comprehensive coverage of formal geometric topics, the course also shows a connection to everyday life and integrates algebra skills. Geometry topics are explored with hands on activities and graphing calculator projects. In addition there are problem solving activities through open-ended portfolio problems that require multiple steps.

Prerequisite: Minimum "C" in Algebra Prob/Stat I or Algebra Prob/Stat IA/IB

Graphing calculator required. (TI 83)

EXPECTATIONS FOR STUDENTS:

Students are expected to complete a daily homework assignment and occasional longer term assignments (small projects). In addition, portfolio problems are given once or twice per quarter. These problems are completed outside the classroom. There is a two-week time period between the time they are assigned and the time they are due. They are graded as a test. Students are also expected to become familiar with Geometer’s Sketchpad software and use it for some assignments.

In the spring, each student must complete a major project. The focus of the project is to incorporate the geometry they have learned with something that is not necessarily thought of in geometric terms. The project includes a hands-on component, written component, oral presentation, and concludes with a display in the school.

ASSESSMENT:

Assessment is based on individual and group work, portfolio problems, projects, and tests and quizzes.

KEY STANDARDS:

· Vital Results: 1.17 Notation and Representation, 2.5 Mathematics Dimensions-Understanding, Approach, Reasoning, Observations and Extensions, Language, Presentation, 3.10 Teamwork

· Field of Knowledge: 7.3 Mathematical Theory, 7.7 Geometric and Measurement Concepts, 7.8 Function and Algebra Concepts, and 7.10 Problem Solving and Reasoning - Applications

1.0 Credit – Year

224 ADVANCED GEOMETRY WITH TRIGONOMETRY (A)

SUMMARY:

This course is an accelerated course covering the same topics as Geometry with Trigonometry. In addition, more emphasis is placed on student’s understanding of formal proof through deductive reasoning.

Prerequisite: Minimum "B" in Algebra Prob/Stat I. Graphing calculator required. (TI 83)

EXPECTATIONS FOR STUDENTS:

Students are expected to complete a daily homework assignment and occasional longer term assignments (small projects). In addition, portfolio problems are given twice per quarter. These problems are completed outside the classroom. There is a two-week time period between the time they are assigned and the time they are due.

ASSESSMENT:

Assessment is based on individual and group classroom work and homework, portfolio problems, small and large projects, tests and quizzes. Midterm and final exams: There will be a midterm in January and a final exam in June. Each exam will be 1 ½ hours long and will be cumulative.

KEY STANDARDS:

· Vital Results: 1.17 Notation and Representation, 2.5 Mathematics Dimensions

· Field of Knowledge: 7.3 Mathematical Theory, 7.7 Geometric and Measurement Concepts, 7.8 Algebra and Functions Concepts, and 7.10 Problem Solving and Reasoning

1.0 Credit - Year

232 ALGEBRA II (C)

SUMMARY:

Algebra II is a continuation of the study of concepts introduced in Algebra I with Probability and Statistics and Geometry and has a goal of both developing greater algebraic conceptual understanding and manipulation skills and adding new concepts and skills not covered in Algebra I with Prob/Stat or Geometry. An integrated approach brings in topics from across the math curriculum, as well as real life applications. Portfolio problem work will continue. Graphing calculators are required (TI 83 recommended).

Prerequisite: Minimum "C" average in Geometry with Trig or Advanced Geometry with Trig and Algebra

Prob/Stat I

EXPECTATIONS FOR STUDENTS:

Homework: Homework will be assigned daily and will need to be completed on time. Homework must be maintained in a notebook. A pencil or pen, paper, three-ring binder, and textbook are required everyday! Quizzes: Frequent quizzes (both announced and unannounced) covering recent work will be given. Questions will be based on homework or recently covered material. Tests: Tests will generally cover several lessons within a chapter. Problem-solving skills will be emphasized. Cumulative material will be included on tests. Portfolios/Projects: there will be one or two portfolios assigned per quarter. In addition we may do projects or problem-solving activities based on material covered in class.

ASSESSMENT:

Assessment is based on individual homework, portfolio problems, projects, tests and quizzes. Midterm and final exams: There will be a midterm in January and a final exam in June. Each exam will be 1 ½ hours long and will be cumulative.

KEY STANDARDS:

· Vital Results: 2.2 Problem Solving Process, 2.3 Types of Problem - Increasing Complexity,

3.10 Teamwork

· Field of Knowledge: 7.10 Problem Solving and Reasoning, 7.6 Mathematical Understanding-Arithmetic, Number, and Operation Concepts, 7.7 Geometric and Measurement Concepts, 7.8 Function and Algebra Concepts, 7.9 Statistics and Probability Concepts

1.0 Credit – Year

231 ADVANCED ALGEBRA II (A)

SUMMARY:

This course is an accelerated, more rigorous Algebra II course and also includes monthly participation in New England Math League competitions. This course is designed to broaden the students’ skills in algebra, geometry, statistics and probability through the use of problem solving, reasoning, real life applications, and technology. Scientific or graphing calculators are required (T-83 recommended).

Prerequisite: Minimum “B” in Algebra Prob/Stat I AND

Minimum "B" in Geometry with Trig or Advanced Geometry with Trig

EXPECTATIONS FOR STUDENTS:

Homework: Homework will be assigned daily and will need to be completed on time. Homework must be maintained in a notebook. A pencil or pen, paper, three-ring binder, and textbook are required everyday! Quizzes: Frequent quizzes (both announced and unannounced) covering recent work will be given. Questions will be based on homework or recently covered material. Tests: Tests will generally cover several lessons within a chapter. Problem-solving skills will be emphasized. Cumulative material will be included on tests. Portfolios/Projects: There will be two portfolios assigned per quarter. In addition we may do projects or problem-solving activities based on material covered in class. Midterm and final exams: There will be a midterm in January and a final exam in June. Each exam will be 1 ½ hours long and will be cumulative.

ASSESSMENT:

A variety of assessments are used for this course. These assessments include daily homework assignments, quizzes, tests, portfolio problems, group work and classroom participation.

KEY STANDARDS:

Vital Results: 2.2 & 2.3 Solving problems of increasing complexity, 2.5 Mathematics Dimensions

Fields of Knowledge: 7.10 Problem Solving and Reasoning, 7.6 Mathematical Understanding-Arithmetic, Number, and Operation Concepts, 7.7 Geometric and Measurement Concepts, 7.8 Function and Algebra Concepts, 7.9 Statistics and Probability Concepts

1.0 Credit – Year

240 FUNCTIONS, STATISTICS AND TRIGONOMETRY (A)

SUMMARY:

This is a full year course for students who have completed Algebra II or Algebra II/Trig. A student cannot take Pre-Calculus prior to this course. It gives strong attention to statistics as well as functions and trigonometry, and requires students to integrate technology into their learning. This course explores relations among equations, their numerical solutions, and their representative graphs. It promotes a student’s ability to visualize functions, to carry out experiments, and to generalize and analyze data. Reading and problem solving are emphasized in reality-oriented situations.

Prerequisite: Minimum "C" average in Algebra II, Advanced Algebra II

Graphing calculator is required (TI-83 recommended).

EXPECTATIONS FOR STUDENTS:

Homework: Homework will be assigned daily and needs to be completed on time. Homework must be maintained in a notebook. Quizzes: Frequent unannounced quizzes covering recent work will be given. Questions may be asked which require problem solving skills and written answers, and which demonstrate understanding of homework. Tests: Tests will cover individual chapters. Cumulative information will be included on tests. Projects/Problem Solving: There will be at least one project or problem solving activity per chapter which will based on work covered in class. This activity will have real-world application. Midterm and final exams: there will be a midterm in January and a final in June. Each exam will be 1 ½ hours long and will be cumulative. The final exam will concentrate on the second half of the year.

ASSESSMENT:

Assessment is based on tests, quizzes, homework completion, written problem solving, projects, and self-evaluation.

KEY STANDARDS:

· Vital Results: 1.20 Communications of Data, 1.21 Selection, 1.22 Simulation of Modeling,

2.2 Problem Solving Process, 2.3 Types of Problems, 2.5 Mathematics Dimensions

· Fields of Knowledge: 7.6 Arithmetic, Number, and Operation Concepts, 7.8 Function and Algebra Concepts, 7.9 Statistics and Probability Concepts Mathematical Problem Solving and Reasoning

1.0 Credit – Year

247 PRE CALCULUS (A)

SUMMARY:

This course is offered as a prerequisite for those students interested in taking Advanced Placement Calculus at MHS. It can also be taken by a student who plans to take Calculus in college. The course will include a thorough study of analytical geometry, including trig, polynomial, exponential, and logarithmic functions. Graphing calculators will be used extensively and are required for tests, class work and homework. The course, Functions, Statistics and Trigonometry may not be taken after the student has completed Pre Calculus.

Prerequisites: Minimum "B" in Algebra II, Advanced Algebra II, or Functions, Statistics, and Trigonometry

Graphing Calculator required (TI-83 recommended)

EXPECTATIONS FOR STUDENTS:

Homework: Homework will be assigned daily and will need to be completed on time. Homework must be maintained in a notebook. Quizzes: Frequent unannounced quizzes covering recent work will be given. Questions may be asked which require problem solving skills and written answers which demonstrate understanding of homework. Tests: Tests will cover individual chapters and the Tool Kit Journal. Cumulative information will be included on tests. Problem Solving/Projects: There will be at least two problem solving activities per quarter. A long-term project is the “Tool Kit of Functions” Journal. Midterm and Final Exams: There will be a midterm in January and a final in June. Each exam will be 1 ½ hours long and will be cumulative. The final will focus on the second half of the year .

ASSESSMENT:

A variety of assessments are used: individual student class work, homework, quizzes, tests, group work, oral presentations, written problem solving, and projects. Self evaluation will occur quarterly.

KEY STANDARDS:

· Vital Results: 1.20,1.21 Information Technology, 2.2, 2.3 Problem Solving, 2.5 Mathematics Dimensions

· Fields of Knowledge: 7.6 Mathematical Understanding - Arithmetic, Number and Operation Concepts, 7.8 Function and Algebra Concepts 7. 10 Mathematical Problem Solving and Reasoning - Applications

1.0 Credit - Year

254 ADVANCED PLACEMENT CALCULUS (A)

SUMMARY:

This course is designed for students who have completed a Pre-Calculus course. The curriculum reflects the topics that are included on the Calculus (AB) Advanced Placement Exam that is given in May of each year. These topics include limits, derivatives of polynomial, exponential, logarithmic, trigonometric and other functions, integrals, and applications of the derivative and integral. Graphing Calculators are required for the AP Exam and for the course.

Prerequisite: Minimum "B" average in Pre-Calculus

Graphing Calculator required (TI-83 are recommended)

EXPECTATIONS FOR STUDENTS:

Students are expected to do nightly homework assignments, They are expected to be active participants in class discussions. They are expected to keep up with the current material and seek help from the teacher outside of class if necessary. Students are expected to be able to communicate their knowledge of calculus in four ways: graphically, numerically, algebraically and verbally.

ASSESSMENT:

A variety of assessments are used: individual student class work, homework, quizzes, tests, written responses to open-ended questions, group work, oral presentations.

KEY STANDARDS:

· Vital Results: 1.20 & 1.21 Information Technology, 2.2 & 2.3 Problem Solving, 2.5 Mathematics Dimensions

· Fields of Knowledge: 7.6 Mathematical Understanding - Arithmetic, Number and Operation Concepts 7.8 Function and Algebra Concepts, 7.10 Mathematical Problem Solving and

Reasoning - Applications

1.0 Credit - Year