# Applied Mathematics

## Basic Skills

### Course 1 – Whole Number Operations

**Prerequisites**: This lesson is designed so that no prior knowledge is required.

**Description**: This lesson reviews the basic concepts of comparing, rounding, adding, subtracting, multiplying, and dividing whole numbers. It also reviews the steps for solving addition, subtraction, multiplication, and division problems. Participants learn about using estimating techniques and the calculator to solve mathematical problems. Participants also learn about a basic problem-solving strategy that can be applied to solve many mathematical problems.

**Objectives**:

- Recognize place values
- Compare values
- Round whole numbers
- Add whole numbers (no carrying)
- Add whole numbers with paper and pencil (with carrying)
- Add numbers with a calculator
- Estimate whole numbers
- Identify the steps of a problem-solving strategy
- Subtract whole numbers with paper and pencil (no borrowing)
- Subtract whole numbers with paper and pencil (with borrowing)
- Subtract whole numbers with multiple zeros
- Subtract whole numbers using a calculator
- Estimate differences
- Understand the concept of multiplication of whole numbers
- Multiply whole numbers using paper and pencil (no carrying)
- Multiply whole numbers using paper and pencil (with carrying)
- Multiply whole numbers with carrying and zeros
- Multiply using a calculator
- Estimate product
- Apply a problem-solving strategy to a multiplication problem
- Recognize the concept of dividing whole numbers
- Divide whole numbers using paper and pencil (with zero)
- Divide whole numbers using a calculator
- Estimate quotient

### Course 2 – Decimals

**Prerequisites**: This lesson is designed to build on the skills presented in the first lesson of this program, Whole Number Operations.

**Description**: This lesson provides instruction in mathematical operations that require the use of decimals. Participants learn how to read decimal numbers as well as compare their values and round them. Participants also learn how to add, subtract, multiply and divide decimals, both with pencil and paper and with a calculator. The lesson provides many examples of applications at home and at work where knowledge of decimals is essential.

**Objectives**:

- Use decimals to describe parts of a whole
- Read decimal numbers and properly interpret their value
- Compare and rank decimal numbers
- Round decimals to a specified place value
- Properly interpret a target value
- Find the upper and lower limits and identify values that fall within the acceptable range
- Add decimals using paper and pencil
- Use a calculator to add decimals
- Use rounding to estimate decimal sums
- Use the calculator memory to store subtotals when performing a multi-step addition problem
- Subtract decimals using paper and pencil
- Use a calculator to subtract decimals
- Use addition to check subtraction, and subtraction to check addition
- Properly interpret specifications that have indicated tolerances
- Find the upper and lower limits of the specification and identify values that fall within the specified range
- Multiply decimals using paper and pencil
- Use a calculator to multiply decimals
- Properly use zeros as place holders in decimal multiplication
- Calculate the area of a rectangular space
- Divide decimals using paper and pencil
- Use a calculator to divide decimals
- Calculate a mean (or average) using sample values that contain decimals
- Calculate the range for a sample that contains decimal values

### Course 3 – Fractions

**Prerequisites**: This lesson is designed to build on the skills presented in the second lesson of this program, Decimals.

**Description**: This lesson teaches participants how to add, subtract, multiply, and divide fractions.

**Objectives**:

- Identify a simple fraction and its components
- Find equivalent fractions
- Reduce fractions to lowest terms
- Change improper fractions to mixed numbers
- Change fractions to decimal equivalents
- Estimate answers
- Add fractions with common denominators
- Add fractions with different denominators
- Add fractions using pencil and paper
- Add fractions using a calculator
- Subtract fractions with common denominators
- Subtract fractions by regrouping whole numbers
- Subtract fractions by regrouping mixed numbers
- Subtract fractions using a pencil and paper
- Subtract fractions using a calculator
- Multiply simple fractions
- Multiply fractions and whole numbers
- Multiply fractions and mixed numbers
- Multiply fractions using a pencil and paper
- Multiply fractions using a calculator
- Divide simple fractions
- Divide fractions and whole numbers
- Divide fractions and mixed numbers
- Divide fractions using pencil and paper
- Divide fractions using a calculator

### Course 4 – Percent, Ratio and Proportion

**Prerequisites**: This lesson is designed to build on the skills presented in the third lesson of this program, Fractions.

**Description**: In this lesson, participants learn how to draw comparisons between one amount and another. The concepts of percent, percentage, and base are taught and the relationship of these concepts to each other. Participants also learn how to find percent, percentage, and base by using paper and pencil as well as with a calculator. In addition, the lesson explains the concepts of ratio and proportion. This lesson teaches how to identify and construct both a ratio and proportion. Participants also learn how to use proportions to convert measurements from English to metric units.

**Objectives**:

- Understand how words are translated into numerical values
- Describe the concepts of base, percent, and percentage
- Compare fractions and decimals to percents
- Understand the concept of percentage and recognize examples
- Calculate percentage with paper and pencil
- Use the calculator to find percentage
- Understand the concept of percent and recognize examples
- Calculate percent with paper and pencil
- Use the calculator to find percent
- Understand the concept of base and recognize examples
- Calculate base with paper and pencil
- Use the calculator to find base
- Describe the concept of a ratio
- Relate ratios to fractions
- Given comparative data, construct ratios
- Describe the concept of proportion
- Find an unknown value in a proportion
- Use proportions to convert measurements from one unit to another

### Course 5 – Positive and Negative Numbers, Powers, and Roots

**Prerequisites**: This lesson is designed to build on the skills presented in the fourth lesson of this program, Percent, Ratio, and Proportion.

**Description**: This lesson introduces the concepts of positive and negative numbers, powers and roots. Participants learn how to use positive and negative numbers in addition, subtraction, multiplication and division. Participants learn common squares and their roots and how to use these to solve problems. In addition, the lesson explains formulas and how to use them. The concepts presented in this lesson are designed to prepare participants for algebra.

**Objectives**:

- Describe the concept of positive and negative numbers
- Recognize positive and negative values and their opposites
- Add, subtract, multiply and divide positive and negative numbers using pencil and paper
- Use the +/, (plus/minus) key to enter negative values on the calculator
- Add, subtract, multiply and divide positive and negative values using a calculator
- Use positive and negative numbers to describe deviation from a target value
- Recognize a power
- Describe the concept of a squared number
- Square numbers by multiplication using pencil and paper
- Square numbers by multiplication and by using the square key on a calculator
- Describe the concept of a square root
- Recognize perfect squares and their square roots
- Use the square root key on a calculator to find square roots
- Estimate answers to problems that involve positive and negative numbers, squares and square roots
- Use formulas that involve squares and square roots
- Solve problems involving positive and negative numbers, powers and roots

### Course 6 – Introduction to Algebra

**Prerequisites**: This lesson is designed to build on the skills presented in the fifth lesson of this program Positive and Negative Numbers, Powers, and Roots.

**Description**: This lesson introduces algebra by presenting typical symbols that are used in mathematical expressions. In this lesson, participants learn how to write and solve equations.

**Objectives**:

- Define the term variable
- Substitute symbols for words in mathematical expressions
- Combine like terms in a mathematical expression
- Use unit analysis to estimate answers to mathematical equations
- State the rules for adding and subtracting like and unlike terms
- State the rules for multiplying and dividing like and unlike terms
- Define the term equation
- Given a word problem, write the corresponding equation
- Recognize common equations (formulas)
- Use common equations to solve problems
- Estimate the answers to problems involving variables
- Manipulate equations to solve for an unknown variable
- Identify the proper order of operations
- Use positive and negative signs in equations
- Use powers and roots in equations; solve equations
- Identify key words in the problem
- Solve a multiple-equation problem

### Course 7 – Measurement

**Prerequisites**: This lesson is designed to build on the skills presented in the sixth lesson of this program, Introduction to Algebra.

**Description**: This lesson reviews the concepts and basic procedures of recognizing, converting, and solving problems using the English and the metric measurement systems. It introduces strategies that participants can apply to estimate metric and English equivalents as well as solving measurement problems with or without a calculator. In addition, participants learn the process of setting up and solving measurement problems with multiple conversions using unit analysis.

**Objectives**:

- Recognize and use common English measurement units for length, area, and volume
- Recognize and use common English measurement units for weight, temperature, and time
- Convert from one unit to another in the English measurement system
- Convert from one unit to another in the English system using ratio
- Convert units using a calculator
- Explain the organization of the metric system
- Recognize and use common metric units for length, area, volume, weight, and temperature
- Convert from one unit to another in the metric system
- Estimate metric/English equivalents
- Convert length, weight, and capacity
- Convert temperature between Fahrenheit and Centigrade
- Multiply, divide, add, and subtract measurement units
- Properly set up and solve measurement problems with multiple conversions using unit analysis
- Solve measurement problems with or without a calculator

### Course 8 – Introduction to Geometry

**Prerequisites**: This lesson is designed to build on the skills presented in the seventh lesson of this program, Introduction to Geometry.

**Description**: This lesson teaches participants the basics of plane and solid geometry. It also specifically prepares participants to use geometric formulas in solving everyday problems. Topics presented in this lesson include the concepts of perimeter, area, and volume. Each topic introduces the appropriate formulas for determining these measurements of the most common geometric shapes, including squares, rectangles, triangles, cylinders, and spheres.

**Objectives**:

- Recognize and define common geometric shapes
- Define the term perimeter
- Use geometric formulas to find the perimeter of rectangles, squares, and triangles
- Define the terms circumference, diameter, radius, and pi
- Use geometric formulas to find the circumference, diameter, and radius of circles
- Estimate the perimeter of rectangles, squares, triangles, and circles
- Find the missing dimension if the perimeter is known of a square, rectangle, triangle, or (circumference of a) circle
- Define the term area; use geometric formulas to find the area of rectangles, squares, triangles, and circles
- Divide complex shapes into common geometric shapes to find areas
- Find the missing dimension if the area is known of a square, rectangle, triangle, or circle
- Estimate the area of rectangles, squares, triangles, and circles
- Use geometric formulas to find the surface area of three-dimensional shapes
- Define the term volume
- Use geometric formulas to find the volume of rectangular solids, spheres, and cylinders
- Estimate the volume of rectangular solids, cylinders, and spheres
- Define a right triangle
- Define and use the Pythagorean Theorem
- Be able to square numbers and find the square root of numbers
- Apply the Pythagorean Theorem
- Use the geometric formulas to solve problems

### Course 9 – Introduction to Statistics

**Prerequisites**: This lesson is designed to build on the skills presented in the eighth lesson of this program, Introduction to Geometry.

**Description**: This lesson provides an introduction to some basic principles of statistics. Emphasis is on statistical functions that are most commonly encountered in the workplace and everyday life. The topics covered include construction and interpretation of charts and graphs. The lesson also explains averages such as mean, median and mode and the appropriate use of each. Finally, the lesson discusses measuring and interpreting variation using the range and standard deviation.

**Objectives**:

- Recognize and interpret tally charts
- Recognize and interpret bar graphs
- Recognize and interpret pie charts
- Recognize and interpret line graphs
- Construct graphs and charts to display data
- Explain the concept of central tendency
- Calculate the mean for a sample
- Find the mode of a sample
- Explain the concept of variation
- Calculate the range of a sample
- Explain the concept of a normal curve
- Using a normal curve, explain the concept of standard deviation