Integers

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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.

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