# 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.