A. Introduction to the Unit
In previous grades, students studied the concept of fractions from several perspectives: as equal parts of a whole, as quantitative fractions, and as representations of ratios. They also studied decimals to three places using cardinal numbers.
In this unit, students build on earlier skills to learn the characteristics of equivalent fractions; the reduction (renaming) of fractions to simplest form; fractions as expressions of quotients; and the concepts of common denominator and least common denominator. They also learn to use the greatest common divisor in reducing (renaming) fractions to simplest form; use the least common multiple to find least common denominator; compare the sizes of different fractions; and compare the sizes of fractions and decimals.
The textbook for this unit is structured as follows:
Main content
- Equivalent fractions
- Students understand the meaning and characteristics of equivalent fractions through manipulation of actual objects.
- Reduction (Renaming)
- Students understand the meaning of the terms fraction in simplest form and reduction (renaming) and how to reduce (rename) fractions to simplest form.
- Least common denominator
- Students understand the meaning and method for finding common denominators, and express two fractions with different denominators as fractions with the least common denominator.
- Least common denominator for three fractions
- Students express three fractions with different denominators as fractions with the least common denominator.
- Comparing the sizes of fractions
- Students compare fractions with different denominators after changing them to fractions with a common denominator.
- Relationship between a fraction and a decimal
- Students understand and learn the method for changing a fraction to a decimal and a decimal to a fraction.
- Comparing the sizes of a fraction and a decimal
- Students compare a fraction and a decimal after changing them to the same form (both fractions or both decimals).
Practice
Students apply the mastered content to:
- Practice the skills of reducing fractions and finding the least common denominator.
- Compare two fractions with different denominators after changing them to fractions with a common denominator; compare a fraction and a decimal.
- Solve application problems using fractions.
B. Unit Objectives
Students will be able to:
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