Foundations of College Math

Foundations of College Math

Curriculum

2744

Northern Berkshire Vocational RegionalSchool District

CharlesH.McCannTechnicalHigh School

70 Hodges Cross Road

North Adams, MA01247

Teacher: Kara Dougherty

March 2011

Course Philosophy

In order to fulfill our mission of graduating “individuals who are technically skilled and academically prepared to meet the challenges of a global economy” (Charles H. McCann mission statement), it is important that our graduates have achieved mathematical competence in many areas. Foundations of College Mathis an elective. Students will achieve competence in reaching the following goals:

To express mathematical ideas coherently both verbally and in writing
To explore the connections that exist within mathematics and with other disciplines
To develop critical thinking and problem solving skills
To demonstrate understanding of more advanced math concepts

Course Description

Foundations of College Math is a full year, double period course that meets every other week. This course goes beyond the scope and sequence of a traditional High School math courses, requiring the students to perform at a high level of abstraction. Topics include: algebra, geometry, and trigonometry.

Course Syllabus

Instructional Philosophy

Foundations of College Math will allow students to explore and experience mathematics through a variety of activities and real world applications. Emphasis will be placed on students’ understanding of key concepts and the ability of students to demonstrate their learned knowledge through exams, projects, discussions and written work. Students will be encouraged to inquire, discuss, analyze, and question the various topics presented throughout the course in order to promote complete mastery of topics.

Major Course Projects and Activities

Homework
A variety of homework assignments will be given to students throughout the course to help reinforce learning objectives. Homework assignments are worth 20% of a student’s grade each quarter.
Notebook/Portfolio
Students will compile a course notebook/portfolio which will include all class notes, homework assignments, homework corrections, handouts, classroom activities/projects, quizzes, and exams.
Students are encouraged to organize this notebook/portfolio in order to have a master resource for the course.
Attendance/Participation
Daily attendance, preparation, and participation are expected, will be recorded, and are worth 10% of a student’s grade each quarter. This is in accordance with McCann’s Attendance Policy which is outlined in

detail in the Student/Parent Handbook.

When an attendance/participation grade is given, the following items are being considered: being present and prepared for class, whether students display cooperation, successful progress towards completing class work, and participation in daily activities. .

Other
A variety of projects and activities may be incorporated as deemed appropriate by the individual course instructors.

COURSE ASSESSMENT PLAN

For the Foundations of College Mathstudents at Charles H. McCannTechnicalSchool the following assessment plan will be followed. This plan is in alignment with the program assessment plan of the Mathematics Department at CharlesH.McCannTechnicalSchool which is stated as follows:

GRADING SYSTEM:

Student assessment and grade reporting is considered a positive tool to measure growth, progress, and the development of the student. Report cards are issued four times each year. In addition, progress reports are issued at the midpoint of each quarter. (2010-2011 Charles H. McCann Student/ Parent Handbook)

A+100-97B86-84C-73-70

A 96-94B-83-80D+69-67

A- 93-90C+79-77D 66-65

B+ 89-87C76-74F64-0

MATH ACADEMIC GRADING POLICY:

Academic Policy(2010-2011 Charles H. McCann Student/ Parent Handbook)

Tests, quizzes, projects, portfolios, laboratory experiments, research papers, and oral presentations – 70%

Attendance, participation, class assignments, homework, notebook, effort – 30%

Extra Help – Homework Club – Tuesday and Thursday from 3-4 PM and with teacher by appointment.

Timeline:

Foundations of College Math: Grade 12

First Quarter

Basic Concepts – with concepts from vocational

Add/Subtract/Multiply/Divide

Whole number

Decimals

Fractions

Percents
Basic measurement – rulers, etc
Unit conversions

Algebra 1 concepts

PEMDAS – order of operations

Distributive property
FOIL
Area
Powers, roots, exponents
Solving one step to multi step equations
Solving Quadratic Equations – factoring, quadratic formula

Geometry concepts

Area/Perimeter/Circumference of polygons
Using linear equations with these formulas
Lateral Surface Area/Total Surface Area/Volume of figures
Polygons – characteristics – sides, angles
Drawing figures – congruent, similar
Special Right triangles – 45-45-90, 30-60-90
Project on a floor plan – to scale with approximate prices of framing –How much would it cost to tile the bathrooms, carpet the bedrooms, and put hardwoods in the other rooms? How much paint do you need to buy and at what cost?

Second Quarter

Trig concepts

Right triangles
Pyt. Theorem – square root expressions
SOH-CAH-TOA
Law of sines/cosines
7 area formulas for non right triangles
Building project – scale model of a bridge – competition – angles and side lengths
Gingerbread house project

Third Quarter
Statistics
Data analysis
Probability/Odds
Surveys – sampling techniques
Graphical representation for a set of data
Frequency Distribution – Variance and Standard deviation

Hypothesis testing

Fourth Quarter
Financial Skills
Banking
Checkbooks
Loans/Credit Cards – interest rates
The real world
Budgeting – determining how much things cost – car, insurance, groceries, phone, cable, internet.
Paychecks – how much is really taken out with taxes, health insurance, union dues, dental, retirement, etc. Depending on their salaries, how much will they actually make in one week, one month, and in one year.

Standards

Massachusetts Mathematics Curriculum Framework

Learning Standards for Grades 11-12 (November 2000)

10.N.1 / Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number.
10.N.2 / Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(24 - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems.
10.N.3 / Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., .
10.N.4 / Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
12.N.2 / Simplify numerical expressions with powers and roots, including fractional and negative exponents.
10.G.5 / Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem.
10.G.6 / Use the properties of special triangles (e.g., isosceles, equilateral, 30°-60°-90º, 45°-45°-90°) to solve problems.
12.G.1 / Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
10.M.1 / Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
10.M.2 / Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
10.M.4 / Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements.
10.D.1 / Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
10.D.2 / Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
10.D.3 / Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
12.D.1 / Design surveys and apply random sampling techniques to avoid bias in the data collection.
12.D.2 / Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.
12.D.3 / Apply regression results and curve fitting to make predictions from data.

Vocational/Technical Education Curriculum Frameworks

Strands 1, 4, 5, and 6

Strand 4: Employability

4.b Develop employability skills to secure and keep employment in chosen field

4.B.01a / Apply strategies to enhance effectiveness of all types of communications in the workplace
4.B.03a / Locate information from books, journals, magazines, and the Internet
4.B.06a / Explain information presented graphically
4.B.07a / Use writing/publishing/presentation applications
4.B.08a / Apply basic skills for work-related oral communication

4.c Solve problems using critical thinking

4.C.01a / Demonstrate skills used to define and analyze a given problem
4.C.04a / Explain strategies used to formulate ideas, proposals and solutions to problems
4.C.05a / Select potential solutions based on reasoned criteria

Strand 6: Underlying Use of Technology

6.c Demonstrate ability to use technology for research, problem solving, and communication

6.C.03a / Demonstrate the use of appropriate electronic sources to conduct research (e.g., Web sites, online periodical databases, and online catalogs)
6.C.04a / Demonstrate proper style (with correct citations) when integrating electronic research results into a research project
6.C.05a / Collect, organize, analyze, and graphically present data using the most appropriate tools
6.C.06a / Present information, ideas, and results of work using any of a variety of communications technologies (e.g., multimedia presentations, Web pages, videotapes, desktop-published documents)

Vocational/Technical Education Curriculum Frameworks

Strand 3:Embedded Academics

Automotive

3.B.01c / 10.D.1 / Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. / 9/10 / Data Analysis, Probability and Statistics
3.B.08c / 10.P.8 / Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. / 9/10 / Patterns, relations, algebra

Carpentry/Cabinetmaking

3.B.01c / 10.P.8 / Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. / 9/10 / Patterns, relations, algebra
3.B.14 / 10.P.2 / Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope. / 9/10 / Patterns, relations, algebra

Electricity

3.B.10c / 10.P.8 / Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. / 9/10 / Patterns, relations, algebra
3.B.15c / 10.P.2 / Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope. / 9/10 / Patterns, relations, algebra
3.B.17 / 10.N.1 / Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number. / 9/10 / Numbers
3.B.18 / 10.N.2 / Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(24 - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems. / 9/10 / Numbers
3.B.19 / 10.N.3 / Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., √32- 1 ≈ 2.8 / 9/10 / Numbers

Machine Technology

Metal Fabrication

3.B.10c / 10.M.1 / Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles. / 9/10 / Measurement
3.B.11c / 10.P.8 / Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. / 9/10 / Patterns, relations, algebra

Information Technology

3.B.07c / 10.D.1 / Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. / 9/10 / Data Analysis, Statistics
3.B.08c / 10.D.3 / Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data. / 9/10 / Data Analysis, Statistics
3.B.17c / 10.P.8 / Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. / 9/10 / Patterns, relations, algebra

Office Technology

3.B.03c / 10.D.1 / Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. / 9-10 / Data Analysis, Statistics and Probability
3.B.04c / 10.P.8 / Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. / 9-10 / Patterns, relations, algebra

Performance Standards

In the Mathematics Department at CharlesH.McCannTechnicalSchool performance standards focus on inquiry-based learning, which include problem solving, research papers, and following the steps of the order of operations. Tests and quizzes are essential. Rubrics are utilized whenever possible to help students understand the goals of the assignment and to aid in keeping grading consistent. Weekly progress reports are shown to each student to allow them to keep track of any missed assignments or low test grades. Students are expected to actively participate in all classroom activities and daily attendance/performance is an integral part of all students’ grades.

Competency Reporting Systems

Math teachers at McCann will be using the school’s database system, which includes an electronic rankbook, for tracking student progress. Mid-quarter progress reports and end of quarter report cards will be issued to students and parents through utilization of this system. Mathematics teachers may also use the “Easy Grade Pro” program as an electronic grade book and competency reporting system. This program allows teachers to provide all students with a weekly assessment of class progress, which all math teachers will attempt to carry out on a regular basis.

Utilization of the high school web site ( will provide students and parents with the expected course requirements. The web site will be updated daily to inform students of their responsibilities. We encourage parents to frequently visit this site to help students make progress towards their goals.

Instructional Activities

Foundations of College Math uses the following instructional activities:

Competency based learning
Project based learning
Cooperative learning groups
Integration with technical areas
Integration with academic subjects
Direct instruction
Open-ended questions
Interactive questioning
Cooperative learning
Whiteboard projects
Library research
Demonstrations
Recitation/Review
Collins Writing Prompts
Other topics may be included in the class as deemed appropriate by the individual course instructors.
Hands-on explorations
Investigations

Resources

Algebra 1; Holt

Geometry

Algebra 2; Holt

Notes for Trigonometry

Instructional Materials and Supplies

Graphing calculators/Scientific calculators

Algebra Tiles

Material from the internet and will be credited when retrieved.

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