# Integers Introduction

## Learning Objectives for all Integers Lessons in Unit 5.

**Introduction to Integers**

The student will be able to:

- Define the set of integers, positive numbers, negative numbers, opposites and signs.
- List real-life situations involving opposites.
- Identify an integer to represent a given real-life situation.
- Identify the opposite of an integer.
- Indicate an integer from a number line.
- Differentiate between a positive integer and a negative integer.
- List real-life situations involving integer opposites.
- Recognize that a positive integer can be written with or without a sign.
- Apply integer concepts to complete five interactive exercises.

**Absolute Value**

The student will be able to:

- Define absolute value.
- Describe the relationship between distance and absolute value.
- Identify the absolute value of an integer using the number line.
- Identify the absolute value of each integer in a given set of numbers.
- Express the absolute value of an integer using the proper notation.
- Determine all integers that satisfy a given condition for absolute value.
- Apply absolute value concepts to complete five interactive exercises.

**Comparing and Ordering Integers**

The student will be able to:

- Differentiate between the inequality symbols < and >.
- Compare two integers, using the proper inequality symbol.
- Order a set of integers from least to greatest.
- Order a set of integers from greatest to least.
- Recognize that Integers get smaller in value as you move to the left, and larger as you move to the right on the number line.
- Apply procedures for comparing and ordering integers to complete five interactive exercises.

**Adding Integers**

The student will be able to:

- Review the definition of absolute value.
- Describe the relationship between a negative integer and owing money.
- Recognize that the sum of two negative integers is a negative integer.
- Perform addition of two negative integers.
- Recognize that the sum of two positive integers is a positive integer.
- Perform addition of two positive integers.
- Describe the procedure for adding integers with unlike signs.
- Describe how absolute value concepts are used in this procedure.
- Perform addition of integers with unlike signs by applying the procedure.
- Differentiate between the sign of an integer and the operation being performed.
- Recognize that the sum of any integer and its opposite is equal to zero.
- Apply the procedures for adding integers to complete five interactive exercises.

**Subtracting Integers**

The student will be able to:

- Perform subtraction of integers using the number line.
- Recognize the need for an arithmetic procedure for subtracting large integers.
- Describe the arithmetic procedure for subtracting integers.
- Perform subtraction of integers using the arithmetic procedure.
- Describe how to convert an integer subtraction problem into an addition problem.
- Apply the procedure for subtracting integers to complete five interactive exercises.

**Multiplying Integers**

The student will be able to:

- Restate that the product of two integers with unlike signs is a negative integer.
- Restate that the product of two integers with like signs is a positive integer.
- Define the Associative Law of Multiplication.
- Perform multiplication of two integers with like signs.
- Perform multiplication of two integers with unlike signs.
- Recognize that the Associative Law of Multiplication applies to integer multiplication.
- Perform multiplication of three integers, two at a time, applying the rules for multiplying integers.
- Recognize that when multiplying three integers, one can multiply the product of any two by the third.
- Apply the procedures for integer multiplication to complete five interactive exercises.

**Dividing Integers**

The student will be able to:

- Restate that the quotient of two integers with unlike signs is a negative integer.
- Restate that the quotient of two integers with like signs is a positive integer.
- Perform division of two integers with like signs.
- Perform division of two integers with unlike signs.
- Describe the procedure for dividing integers with like signs.
- Describe the procedure for dividing integers with unlike signs.
- Apply the procedures for integer division to complete five interactive exercises.

**Operations With Integers**

The student will be able to:

- Review the rules and procedures for adding, subtracting, multiplying and dividing integers.
- Evaluate ten interactive exercises that provide mixed review of integer operations.
- Identify which procedure is needed for each exercise.
- Apply the procedures for integer operations to complete each exercise.
- Differentiate between the rules and procedures for all integer operations.

**Practice Exercises**

The student will be able to:

- Examine ten interactive exercises for all topics in this unit.
- Determine which concepts and procedures are needed to complete each practice exercise.
- Compute answers by applying appropriate formulas and procedures.
- Self-assess knowledge and skills acquired from this unit.

**Challenge Exercises**

The student will be able to:

- Evaluate ten interactive exercises with real-world word problems for all topics in this unit.
- Analyze each problem to identify the given information.
- Formulate a strategy for solving each problem.
- Apply strategies to solve routine and non-routine problems.
- Synthesize all information presented in this unit.
- Connect integers to the real world.
- Develop problem-solving skills.

**Solutions**

The student will be able to:

- Examine the solution for each exercise presented in this unit.
- Identify which solutions need to be reviewed.
- Compare solutions to completed exercises.
- Identify and evaluate incorrect answers.
- Amend and label original answers.
- Identify areas of strength and weakness.
- Decide which concepts, formulas and procedures need to be reviewed from this unit.