Introduction to Fractions

Fractions Learning Objectives for all Introduction to Fractions 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.