Course Content and Outcomes Guides (CCOG)

CCOG for APR 162 Winter 2025


Course Number:
APR 162
Course Title:
Calculations for the Trades
Credit Hours:
4
Lecture Hours:
40
Lecture/Lab Hours:
0
Lab Hours:
0

Course Description

Covers measurements and calculations used in industrial and commercial facilities settings. Includes linear and volume measurement methods using analog and digital tools and instruments including rulers, calipers, micrometers, and dial indicators. Focuses on the use of fractions, decimals, powers, roots, algebraic equations, geometry, and right angle trigonometry to perform calculations for equipment repair, maintenance, installation, and operation. Prerequisites: MTH 20 or completion of any course for which it is a prerequisite. Audit available.

Addendum to Course Description

Required course for Apprentices registered in the Millwright/Industrial Maintenance Technician Apprenticeship Program. It is open to any other student but requires Department Permission to take this course.

Intended Outcomes for the course

Upon completion of the course students should be able to:

  • Obtain and record measurements in facilities and industrial settings using a variety of measuring instruments in order to repair, maintain, install and operate mechanical equipment.
  • Calculate areas, volumes, lengths, angles, speeds, velocities, pressures, temperatures, volts, amps, ohms, and watts in facilities and industrial settings in order to repair, maintain, install, and operate mechanical equipment.
  • *Calculate elementary algebraic equations and formulas (*required statewide outcome).
  • *Apply appropriate formulas to mathematical situations (*required statewide outcome).

Course Activities and Design

The course design is primarily lecture with emphasis on measurements and calculations that apply to real-world scenarios in Facilities and Industrial settings which are relevant to repair, maintenance, installation and operation of equipment.

Course activities include:

  • Calculating areas and volumes
  • Calculating speed and velocity
  • Calculating pressures and temperatures and their relationship
  • Ohm's Law calculations
  • Application of a variety of measuring instruments to calculations
  • Using a hand held calculator
  • Reliance on specific long hand calculations
  • Use of the Vernier micrometer
  • Use of the Caliper
  • Care of measuring instruments

Outcome Assessment Strategies

Assessment will be accomplished using skills' checklists filled out by an adequate sampling of Millwright/Industrial Maintenance Technician Training Agents and/or an Apprentice's Journey Person.

Course Content (Themes, Concepts, Issues and Skills)

THEMES:
  • Algebraic manipulation
  • Graphical understanding
  • Problem solving
  • Effective communication
  • Critical thinking
  • Applications formulas and modeling
SKILLS: 1. Basic Concepts
  1. Review of Basic  Operations                                       
  2. Order of Operations  
  3. Area and  Volume    
  4. Formulas   
  5. Prime Factorization
  6. Introduction to Fractions
  7. Addition and Subtraction of Fractions    
  8. Multiplication and Division of Fractions   
  9. The U.S. System of Weights and Measures
  10.  Addition and Subtraction of Decimal Fractions    
  11. Rounding Numbers
  12. Multiplication and Division of Decimal Fractions   
  13. Percent   
  14. Rate, Base, and Part   
  15. Powers and Roots
  16.  Applications Involving Percent: Business and Personal Finance
2. Signed Numbers and Powers of 10
  1. Addition of Signed Numbers
  2. Subtraction of Signed Numbers                                                                   
  3. Multiplication and Division of Signed Numbers
  4. Signed Fractions                       
  5. Powers of 10                            
  6. Scientific Notation                   
  7. Engineering Notation
3. THE METRIC SYSTEM
  1. Introduction to the Metric System   
  2. length 
  3. Mass and Weight        
  4. Volume and Area       
  5. Time, Current, and Other Units          
  6. Temperature  
  7. Metric and U.S. Conversion
4.  MEASUREMENT
  1. Precision and Greatest Possible Error
  2. The Vernier Caliper    
  3. Approximate Numbers and Accuracy
  4. The Micrometer Caliper        
  5. Addition and Subtraction of Measurements 
  6. Multiplication and Division of Measurements         
  7. Relative Error and Percent of Error    
  8. Color Code of Electrical Resistors       
  9. Reading Scales
5.  POLYNOMIALS: AN INTRODUCTION TO ALGEBRA
  1. Operations            
  2. Simplifying Algebraic Expressions
  3. Addition and Subtraction of Polynomials     
  4. Fundamental Multiplication of Monomials  
  5. Multiplication of Polynomials   
  6. Division by a Monomial          
  7. Division by a Polynomial
6.  EQUATIONS AND FORMULAS
  1. Equations       
  2. Equations with Variables in Both Members  
  3. Equations with Parentheses  
  4. Equations with Fractions       
  5. Translating Words into Algebraic Symbols    
  6. Applications Involving Equations       
  7. Formulas          
  8. Substituting Data into Formulas       
  9. Reciprocal Formulas Using a Calculator
7.  RATIO AND PROPORTION
  1. Ratio   
  2. Proportion      
  3. Direct Variation          
  4. Inverse Variation
8.  GRAPHING LINEAR EQUATIONS
  1. Linear Equations with Two Variables                                      
  2. Graphing Linear Equations 
  3. The Slope of a Line             
  4. The Equation of a Line
9.  SYSTEM OF LINEAR EQUATIONS
  1. Pairs of Linear Equations by Graphing          
  2. Solving Solving Pairs of Linear Equations by Addition           
  3. Solving Pairs of Linear Equations by Substitution      
  4. Applications Involving Pairs of Linear Equations
10.  FACTORING ALGEBRAIC EXPRESSIONS
  1. Monomial Factors
  2. Finding the  Product of Two Binomials Mentally
  3. Finding Binomial Factors
  4. Special Products        
  5. Finding Factors of Special Products
  6. Factoring General Trinomials
11.  QUADRATIC EQUATIONS
  1. Quadratic Equations by Factoring    
  2. Solving The Quadratic Formula         
  3. Applications Involving Quadratic Equations 
  4. Graphs of Quadratic Equations         
  5. Imaginary Numbers
12.  GEOMETRY
  1. Angles and Polygons                      
  2. Quadrilaterals                               
  3. Triangles                                        
  4. Similar Polygons                            
  5. Circles
  6. Radian Measure                            
  7. Prisms                                            
  8. Cylinders                                       
  9. Pyramids and Cones                      
  10. Spheres
13.  RIGHT TRIANGLE TRIGONOMETRY
  1. Trigonometric Ratios                   
  2. Using Trigonometric Ratios to Find Angles                                                 
  3. Using Trigonometric Ratios to Find Sides                                                 
  4. Solving Right Triangles                 
  5. Applications Involving Trigonometric Ratios
14.  TRIGONOMETRY WITH ANY ANGLE
  1. Sine and Cosine Graphs                 
  2. Period and Phase Shift                  
  3. Solving Oblique Triangles: Law of Sines                                                  
  4. Law of Sines: The Ambiguous Case                                                   
  5. Solving Oblique Triangles: Law of Cosines
15.  BASIC STATISTICS
  1. Bar Graphs
  2. Circle Graphs
  3. Line Graphs
  4. Other Graphs
  5. Mean Measurement  
16.  BINARY NUMBERS
  1. Introduction to Binary Numbers
  2. Addition of Binary Numbers 
  3. Subtraction of Binary Numbers        
  4. Multiplication of Binary Numbers
  5. Conversion from Decimal to Binary System 
  6. Conversion from Binary to Decimal System  
OTHER SKILLS
  • Measure and calculate volts, amps, ohms, and watts in Facilities and Industrial settings
  • Measure and calculate volume in Facilities and Industrial settings
  • Measure and calculate length in Facilities and Industrial settings
  • Measure and calculate angles using a variety in instruments in Facilities and Industrial settings
  • Measure and calculate speed in Facilities and  Industrial settings
  • Measure and calculate velocity in Facilities and Industrial settings
  • Measure and calculate pressure in Facilities and Industrial settings
  • Measure and calculate temperature in Facilities and Industrial settings