Improve Workforce Efficiency

Course #: Block X21
Duration: 30 hours (includes 6 tests)
What Students Learn:

This module of six study units offers the trainee arithmetic and basic mathematics, metric measurement, and calculator fundamentals. The Metric System is an introductory unit which includes metric conversions. Problem exercises and examples in this module are presented in on-thejob scenarios with applications drawn from the industrial context.

• These updated study units replace lessons contained within the current version of Practical Math and Measurements, Block X01. Each study unit contains a progress exam.
• Formulas, study unit 186012 replaces Formulas, study unit 2468.

• 186008 Addition and Subtraction
• 186009 Multiplication and Division
• 186010 Fractions, Percents, Proportions, and Angles
• 186011 Metric System
• 186012 Formulas
• 186013 Introduction to Algebra

Course #: 186008
Course Objectives:

• Define the terms: whole number, numeral, digit, decimal, place value, addend, sum, minuend, subtrahend, and difference.
• Explain the significance of the digit zero in a number.
• Differentiate between concrete and abstract numbers.
• Properly prepare numbers for addition and subtraction.
• Perform addition and subtraction on numbers.
• How to check your answers to both addition and subtraction problems.
• How to use a calculator to add and subtract numbers.

Course #: 186009
Course Objectives:

• Define the terms: factor, multiplicand, multiplier, partial product, dividend, divisor, quotient, and remainder.
• Recognize the various signs used for multiplication and division.
• Properly prepare numbers for multiplication and division.
• Perform multiplication and division on whole numbers and decimals.
• How to check your answers to both multiplication and division problems.
• How to find the average of a group of numbers.
• How to use a calculator to multiply and divide numbers.

Course #: 186010
Course Objectives:

• Define the terms: fraction, proper fraction, improper fraction, lowest common denominator, percent, ratio, and proportion.
• How to add, subtract, multiply, and divide fractions and decimals.
• How to change fractions to decimals and decimals to fractions.
• Solve problems involving percent.
• How to use a protractor to measure angles.
• Lay out templates for checking angles.
• How to use a calculator to solve percent problems and to convert fractions to decimals.

Course #: 186011
Course Objectives:

• Name the base units most commonly used in the metric system.
• Identify metric prefixes and their values.
• Apply conversion factors to increase or decrease metric base units.
• Estimate lengths in metric units.
• Express temperature in degrees Celsius.
• Define the terms: mass, density, force, torque, and pressure. Identify the metric units used to measure each one.
• How to use a calculator to convert one metric unit to another.

Course #: 186012
Course Objectives:

• Explain the use of letters in formulas.
• Prepare and use formulas to solve problems.
• The use of formulas to calculate the perimeter of a triangle and rectangle, distance, area of a triangle, rectangle, and circle, volume of a pyramid, current in a circuit, and volume of a sphere.
• How to use a calculator to find square root and solve formulas.
• Transform and solve an equation.
• Perform basic arithmetic operations with signed terms.
• Substitute given numerical values for letters in a formula and find the unknown quantity.

Course #: 186013
Course Objectives:

• Define the terms: term, constant, coefficient, exponent, monomial, trinomial, and polynomial.
• Identify and combine like terms in an expression.
• Multiply and divide terms containing exponents.
• Remove parentheses from an expression and simplify the expression.
• Perform basic arithmetic operations with signed terms.

Course #: Block X22
Duration: 25 hours (includes 5 tests)
What Students Learn:

The five lessons in this block present the trainee with a broad overview of measurements found in an industrial setting. In addition to the basic measurements of length, temperature, energy, force, and power, the trainee will learn how materials are measured and handled in bulk quantities. Fluid measurements include the measuring of fluid flow, fluid pressure, and fluid level. All lessons include the metric conversions in addition to the English units.

• This Block replaces the X0105 to X0109 lessons contained within Practical Math and Measurements. Each study unit contains a progress exam.

• 186021 Linear and Distance Measurement
• 186022 Bulk Measurement
• 186023 Temperature Measurement
• 186024 Energy, Force, and Power
• 186025 Fluid Measurement

Course #: 186021
Course Objectives:

• Recognize the difference between English and metric units of length.
• Find the perimeter of rectangular, square, or triangular areas or objects, such as rooms or machine bases, after measuring the sides.
• Calculate the circumference of circular objects like pipes of tanks after measuring the diameter.
• Measure lengths with the aid of rigid and flexible rules, thickness gauges and screw pitch gauges.
• Read a typical vernier scale and micrometer to take precise measurements.

Course #: 186022
Course Objectives:

• Measure an angle by degrees.
• Find the areas of rectangles, triangles, and circles.
• Find the volumes of prisms, cylinders, and cones.
• Find the weight of material stored in a container.
• Determine the amount of material that can be stored or handled.
• Discuss the types and uses of conveyors and weighing systems.

Course #: 186023
Course Objectives:

• Change temperature units from one system to another.
• Discuss the use of the various types of thermometers.
• Select the type of thermometer to be used at certain temperatures.

Course #: 186024
Course Objectives:

• Distinguish between the concepts of energy, force, and power.
• Explain what the term “work” means, and how it is measured.
• Know by sight the basic machines, lever, inclined plane, wedge, wheel and axle, and screw.
• Solve simple problems that involve levers, mechanical advantage, and machine efficiency.
• List the forms of energy that have important industrial applications, and the instruments used for measuring energy.

Course #: 186025
Course Objectives:

• Understand the properties of fluids.
• Determine the density, specific gravity, and viscosity of fluids.
• Express pressure in three different units.
• Measure the pressure of fluids using manometers and Bourdon tubs pressure gauges.
• Measure the flow rate of fluids using different types of flowmeters.

Course #: 186073
Duration: 10 hours (includes 1 test)
What Students Learn:

Basics of problem solving, troubleshooting, and critical thinking

Applying a logical procedure to solving problems and troubleshooting systems

Selecting and using the right troubleshooting tools

Focusing on and collecting information related to the problem at hand

“Using what you know” to understand complex systems

Course #: 186085
Duration: 5 hours (includes 1 test)
Course Objectives:

• Recognize characteristics of angles and closed plane figures
• Distinguish between common geometric solids
• Apply basic geometric construction techniques
• Calculate perimeters and areas of a polygon, circle, and ellipse
• Apply the formula for area and volume of geometric solids

• This course replaces course X0211.

Course #: 186086
Duration: 5 hours (includes 1 test)
Course Objectives:

• Define trigonometric functions and use a calculator to perform them
• Use trigonometric tables and apply interpolation
• Solve right triangles for angular and side dimensions
• Apply the laws of sines and cosines in solving oblique triangles

• This course replaces course X0212.

Course #: X0201
Course Objectives:

• Remove grouping symbols from algebraic expressions, dividing by a monomial when indicated.
• Multiply binomials by monomials, trinomials, and other inomials.
• Calculate the square root and the third power of given monomials.
• Find special products involving binomials.
• Divide one polynomial by another polynomial of lower degree.

Course #: X0202
Course Objectives:

• Find the prime factors of certain binomials and trinomials.
• Factor a given trinomial.
• Use the Factor Theorem to factor a given polynomial.
• Use factoring to find the roots of an equation.
• Divide one polynomial by another polynomial of lower degree.
• Find the lowest common multiple of several polynomials.

Course #: X0203
Course Objectives:

• Recognize equivalent algebraic fractions.
• Perform additions and subtractions involving algebraic fractions.
• Reduce an algebraic fraction to its lowest terms.
• Find the least common denominator for a group of algebraic fractions.

Course #: X0204
Course Objectives:

• Perform multiplications and divisions involving algebraic fractions.
• Reduce an algebraic fraction to its lowest terms.
• Find the least common denominator for a group of algebraic fractions.
• Solve equations involving fractions or decimals.
• Simplify complex fractions.

Course #: X0205
Course Objectives:

• Recognize equations expressing mixture problems and other word problems.
• Solve number problems, digit problems, and age problems.
• Recognize the graph of a linear equation, given the graph or a set of points.

Course #: X0206
Course Objectives:

• Recognize essential steps in the solving of simultaneous linear equations by addition, subtraction, comparison, graphing, and clearing of fractions.
• Identify the classification of a system of equations.
• Solve a system of linear equations.
• Solve interest problems, lever problems, and work-sharing problems.

Course #: X0207
Course Objectives:

• Evaluate a second-order determinant and expand a third-order determinant.
• Recognize the standard form to be used in solving simultaneous equations by determinants.
• Recognize determinants that represent the solutions of simultaneous equations in two or three unknowns.

Course #: X0208
Course Objectives:

• Recognize the graphical solution of two equations.
• Solve and recognize steps in the solution of systems of quadratic equations and systems of a quadratic and linear equation.
• Solve a fourth-degree polynomial equation in quadratic form.
• Use the quadratic formula to solve a quadratic equation, calculate the discriminant of a quadratic equation, and point out what can be known from a given discriminant.
• Write a quadratic equation which has given roots.
• Solve word problems involving quadratic equations.

Course #: X0209
Course Objectives:

• Demonstrate an understanding of the meaning of a fractional exponent.
• Apply the rules for positive and negative exponents in multiplication, division, and raising to powers.
• Use radicals to convert fractional exponents and use fractional exponents to convert radicals.
• Write a given number in standard form.

Course #: X0210
Course Objectives:

• Simplify several radicals and then add like terms.
• Rationalize the denominator of a fraction and eliminate an imaginary number from the denominator of a fraction.
• Solve an equation containing several square roots.
• Multiply, divide, and raise to powers terms containing radicals.

Course #: X0221
Testing/Completion:

• Examination

Course #: X0222
Testing/Completion:

• Examination

Course #: X0223
Testing/Completion:

• Examination

Course #: X0220
Testing/Completion:

• Examination

Course #: X0250
Testing/Completion:

• Examination

Course #: Block X02
Duration: 72 hours (includes 4 tests)
Prerequisites:

• Basic Industrial Math (Block X21)
• Practical Measurements (Block X22)

This twelve lesson block is for those trainees requiring more advanced math subjects. The subject of algebra is covered in detail and the subjects of geometry and trigonometry are introduced in a practical manner. Because math skills vary widely, a placement test is available to determine the trainee’s specific knowledge of the various areas. Test X0250: Introduction to Algebra, Geometry, and Trigonometry is divided into four sections: lessons X0201 through X0204; lessons X0205 through X0208; lessons X0209 through X0210; and lessons 186085 and X0212.

• X0250 Placement Test: Introduction to Algebra, Geometry, and Trigonometry
• X0201 Algebra: Monomials and Polynomials
• X0202 Algebra: Factoring
• X0203 Algebra: Addition and Subtraction of Fractions
• X0204 Algebra: Multiplication and Division of Fractions
• X0221 Progress Examination
• X0205 Algebra: Linear Equations
• X0206 Algebra: Simultaneous Linear Equations
• X0207 Algebra: Determinants
• X0208 Algebra: Quadratic Equations
• X0222 Progress Examination
• X0209 Algebra: Exponents
• X0210 Algebra: Radicals and Imaginary Numbers
• X0223 Progress Examination
• 186085 Applied Geometry
• 186086 Practical Trigonometry
• X0220 Progress Examination Booklet