Integers

Learning Topics: 

Introduction, absolute value, comparing and ordering, adding, subtracting, multiplying, dividing, and all four operations.

This page lists the Learning Objectives for all 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.