Introduction to Fractions

Learning Topics: 

Introduction, classifying, equivalent fractions, simplifying, comparing, ordering. Converting fractions to mixed numbers and mixed numbers to fractions.

This page lists the Learning Objectives for all lessons in Unit 14.


Introduction to Fractions

The student will be able to:

  • Define fraction, numerator, denominator, fraction bar, unit fraction, and multiple.
  • Identify the number of shaded parts and the number of equals parts in a shape (circle, rectangle).
  • Identify a fraction by comparing the number of shaded parts to the number of equal parts.
  • Write a fraction using mathematical notation and using words.
  • Recognize, the value of a fraction is not changed by which sections of a shape are shaded.
  • Recognize, the positioning of a shape does not change the value of the fraction it represents.
  • Explain what a fraction is.
  • Apply fraction concepts to complete five interactive exercises.

Classifying Fractions

The student will be able to:

  • Define proper fraction, improper fraction, mixed number.
  • Classify a fraction as proper or improper.
  • Write an improper proper fraction using words.
  • Recognize that one whole can be represented by many different fractions.
  • Recognize the difference between an improper fraction equal to one and an improper fraction greater than one.
  • Identify the whole-number part and the fractional part of a mixed number.
  • Classify a number as a proper fraction, an improper fraction, or as a mixed number.
  • Explain the difference between a proper fraction and an improper fraction.
  • Apply proper and improper fraction concepts to complete five interactive exercises.

Equivalent Fractions

The student will be able to:

  • Define equivalent fractions, whole number.
  • Determine if two fractions are equivalent using shapes.
  • Determine if two fractions are equivalent using arithmetic.
  • Explain why two given fractions are or are not equivalent
  • Recognize that multiplying a fraction by one does not change its value.
  • Recognize that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.
  • Recognize that equivalent fractions are equal in value.
  • Describe the procedure for finding equivalent fractions.
  • Give examples of 3 equivalent fractions for a given fraction.
  • Convert a fraction to an equivalent fraction with a specified numerator.
  • Convert a fraction to an equivalent fraction with a specified denominator.
  • Restate the definition of equivalent fractions.
  • Apply equivalent fraction concepts and procedures to complete five interactive exercises.

Simplifying Fractions

The student will be able to:

  • Define simplifying a fraction, lowest terms, greatest common factor.
  • Determine the common factors of the numerator and denominator of a given fraction.
  • Simplify a fraction by dividing its numerator and its denominator by a common factor.
  • Determine the greatest common factor of the numerator and denominator of a given fraction.
  • Simplify a fraction by dividing its numerator and its denominator by their greatest common factor. 
  • Recognize that a fraction is in lowest terms when the greatest common factor of its numerator and denominator is one.
  • Describe the procedure for simplifying fractions.
  • Apply procedures for simplifying fractions to complete five interactive exercises.

Comparing Fractions

The student will be able to:

  • Define common denominator, least common multiple, least common denominator (LCD), unit fraction.
  • Describe the procedure for comparing fractions with like denominators.
  • Apply LCD to write equivalent fractions with a common denominator.
  • Describe the procedure for comparing fractions with unlike denominators.
  • Describe the procedure for comparing fractions with like numerators.
  • Apply all procedures for comparing fractions to complete five interactive exercises.

Ordering Fractions

The student will be able to:

  • Describe the procedure for ordering three or more fractions with like denominators.
  • Describe the procedure for ordering three or more fractions with unlike denominators.
  • Describe the procedure for ordering three or more fractions with like numerators. 
  • Recognize the need to compare fractions two at a time when ordering three or more fractions.
  • Recognize the need to write a number in a circle next to each fraction to compare them more easily.
  • Apply all procedures for ordering fractions to complete five interactive exercises..

Converting Fractions to Mixed Numbers

The student will be able to:

  • Convert an improper fraction to a mixed number using shapes.
  • Convert an improper fraction to a mixed number using long division.
  • Recognize that only an improper fraction greater than one can be converted to a mixed number.
  • Describe the arithmetic procedure for converting an improper fraction to a mixed number.
  • Apply the conversion procedure to complete five interactive exercises.

Converting Mixed Numbers to Fractions

The student will be able to:

  • Convert a mixed number to an improper fraction using shapes.
  • Convert a mixed number to an improper fraction by converting the whole-number part to an improper fraction, and then adding the fractional part.
  • Convert a mixed number to an improper fraction by multiplying the denominator by the whole-number part, then adding the numerator.
  • Describe the procedures for converting a mixed number to an improper fraction.
  • Apply conversion procedures to complete five interactive exercises.

Practice Exercises

The student will be able to:

  • Examine ten interactive exercises for all topics in this unit.
  • Identify the procedures needed to complete each practice exercise.
  • Compute answers and solve problems by applying appropriate procedures.
  • Self-assess knowledge and skills acquired from this unit.

Challenge Exercises

The student will be able to:

  • Evaluate ten interactive exercises with word problems for all topics in this unit.
  • Analyze each word problem to identify the given information.
  • Formulate a strategy for solving each problem.
  • Apply strategies to solve problems and write answers.
  • Synthesize all information presented in this unit.
  • Develop strong 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 and procedures need to be reviewed from this unit.