APPLIED MATHEMATICS

Applied mathematics is a course designed around a laboratory work place approach to teaching mathematics. It provides for a hands-on, applicable, useful, and experiential way of learning and using mathematics. The course should be offered to those students who require a more concrete, rather than abstract, approach to learning mathematics.

The overall course shall include material that focuses on arithmetic operations, problem solving, estimation, measurement, geometry, probability and statistics, algebraic principles, and the applications of mathematics. This is a course that must take advantage of the use of technology and in general will have content consistent with courses traditionally taught in arithmetic, algebra, and geometry at the high school level. But, the emphasis should remain on the ability to understand and apply functional mathematics to solve problems in the world of work.

The course does not necessarily offer the content in the same way that is in traditional college preparatory mathematics courses, but Applied Mathematics should enhance the opportunity for students to bridge the gap between their not taking algebra I and taking algebra I. The course should provide a background in mathematics conducive to success at the college level.

Critical Components:

In order to satisfy the state graduation requirement, the content of Applied Mathematics should significantly include:

1. Problem solving techniques

2. Measuring; estimating; precision, accuracy and tolerance

3. Dealing with data; graphing data; using graphs, charts and tables

4. Shapes in two dimensions; working with lines and angles; shapes in three dimensions; scale drawings

5. Ratios and proportions

6. Signed numbers, vectors; solving with formulas

7. Scientific notation; powers and roots

8. Linear equations; nonlinear equations

9. Probability and statistics

10. Right-triangle relations; trigonometric functions

The critical components should be addressed through instruction in:

• Problem Solving
• Number systems and operations
• Measurement and estimation
• Geometry and trigonometry
• Rates, ratios, proportions, and functions relations
• Graphing and equations
• Probability and statistics
• Using technology to solve problems wherever appropriate

I.    Problem Solving

A.    Goal:

Students will be made aware of problem solving strategies and be able to apply such strategies to problems.

Objective:
Students will

1. Use problem solving strategies to include guess arid check, look for a pattern, make a chart or drawing, work backwards, analyze information, and make a plan for solving problems.

B. Goal:

Students will demonstrate proficiency in problem solving with the calculator and computer wherever appropriate.

Objectives:
Students will

1. Use the calculator to solve problems involving long or tedious computations.

2. Use a calculator or a computer as a tool in applying mathematical knowledge.

C.    Goal:

Students will learn and apply the relationships that exist in sequential processes.

Objective:
Students will

1. Apply skills to step-by-step processes in

a. Using a flow chart or sequence of directions
b. Completing forms such as applications, order forms, etc.
c. Completing forms using tables.

II. Numbers and Operations

A. Goals

Students will be able to apply appropriate computational skills to specific applications.

Objectives:
Students will

1. Know and use computational skills of addition, subtraction, multiplication and division of whole numbers, decimals, percents, and fractions, and know when to use each in a problem setting.

2. Estimate solutions to calculations and determine the reasonableness of the results by computation.

B. Goal:

Students will learn appropriate computational skills.

Objectives:
Students will

1. Demonstrate proficiency in computations of addition, subtraction, multiplication and division with integers, fractions and decimals.

2. Demonstrate proficiency in computations with percent, ratios, and proportions, and their applications.

3. Be able to apply appropriate computational skills to specific applications.

C. Goal:

Students will be aware of the uses of technology in the application of the fundamental operations.

Objectives:
Students will

1. Use a calculator as a tool in applying mathematical knowledge.

2. Use computational skills involving whole numbers and decimals through personal accounting, budgeting and check balancing.

3. Use the computer as a problem solving tool wherever appropriate and available.

III. Measurement and Estimation

A. Goal:

Students will become familiar with both customary and metric systems and the seven different kinds of measurement.

Objectives:
Students will

1. Independently perform and interpret standard measurements in both metric and customary systems, and make approximate comparison between metric and customary measures.

2. List the seven kinds of measurement (time, angles, length, area, volume, weight, and temperature) and compare the different ways to measure and apply the problems involving:

a. Time and temperature measurement.
b. Application of perimeter, area, volume, and surface area calculations such as buying fencing, carpeting or painting a house.
c. Metric units and conversion between metric units.
d. Approximation of metric units to customary units for comparison.

3. Develop estimation skills and reasonableness of answers.

IV. Geometry and Trigonometry

Goal:

Students will identify and use common geometric ideas such as lengths, area, volume, and the Pythagorean and the trigonometric relationships.

Objectives:
Students will

1. Identify and define common geometric shapes.

2. Distinguish between area, perimeter, volume and apply the formulas to find these measures for common geometric shapes.

3. Describe the use of geometric shapes in building designs and structures.

4. Apply the Pythagorean theorem to appropriate problems.

B. Goal:

Students will identify and use the number system with geometric applications.

Objectives:
Students will

1. Use number line models and form a coordinate system.

2. Read and apply coordinate systems to problem solving.

3. learn and use the three basic trigonometric ratios in solving problems.

V. Rates, Ratios, Proportions, Functions and Relations

A. Goal:

Students will understand the use of rates, ratios and proportions for applications.

Objective:
Students will

1. Apply ratio concepts and skills to:

a. Scale drawing and maps.
b. Comparison buying through unit pricing.
c. Distance and time relationships.
d. Cost ratios.

B. Goal:

Students will understand that terminating decimals and percents can be expressed as ratios and will be able to apply them in problem solving.

Objectives:
Students will

1. Convert ratios and fractions into decimals and vice versa.

2. Apply decimals and percents to problems in taxes, interest, and real life situations.

C. Goal:

Identify functions and relations

VI. Graphing and Equations

A. Goal:

Students will use information from line, bar and circle graphs, charts and tables.

Objective:
Students will

1. Apply the following methods of data analysis and prediction:

a. Use information from charts and graphs, to predict or explain.
b. Organize data into charts and graphs.
c. Analyze raw data into percentages.
d. Determine mean, median, and mode from a set of data, graph, or chart.
e. Graph equations.

VII. Probability and Statistics

A. Goal:

Students will understand, collect and organize data for analysis.

Objectives:
Students will

1. Collect data from projects.

a. To find range, mean, mode and median.
b. To develop tables, charts, graphs, and histograms.

2. Use fractions or decimals to express probabilities.

3. Read and interpret probabilities as chance.

4. Calculate probabilities of simple experiments, spinners, dice, etc.

5. Examine the use of probabilities in making predictions.

6. Use statistical data to make predictions.

VIII. Technology

A. Goal:

Students will use computers, hand-held calculators and other appropriate tools to solve problems and investigate mathematical concepts.

Objectives:
Students will

1. Use technology tools to enhance problem solving and relieve them of unnecessary computation.

2. Know when the use of technology