A. Introduction to the Unit

Fractions were introduced in the second grade. Students equally divided a continuous quantity and studied the meaning of a fraction based on that.

In this unit, students study the concept of a fraction through equal division of objects in both continuous and discrete measure, based on the material studied in the second grade. They also examine the relationship between a unit fraction and a proper fraction to gain deeper understanding of proper fractions, and use concrete objects to compare fractions with the same denominator and to compare unit fractions. Finally, they solve various basic problems related to the characteristics of a fraction, and applied problems such as sequencing fractions using a number line, and adding and subtracting fractions with the same denominator.

In fourth grade, students will study fractions related to a ratio, improper fractions, mixed numbers, and creating equivalent fractions.

The textbook for this unit is structured as follows:

Main content

• Equal division of concrete objects
  • Students equally divide a number of concrete objects into groups, and express one of several equal parts as a fraction (1 over the total number of parts).
• Relationship between a unit fraction and a proper fraction
  • By playing with concrete objects, students discover how many unit fractions are included in a given proper fraction.
• Comparing fractions
  • Students use concrete objects to compare proper fractions with the same denominator, and to compare unit fractions.
• Sequencing of fractions
  • Students match a fraction to a number line using the concept of an equal division, and study the sequence of a set of fractions with the same denominator.
• Adding and subtracting fractions with the same denominator
  • By playing with concrete objects, students understand the principal and do simple calculation of addition and subtraction of fractions with the same denominator.
• Word Problems
  • Students solve, using comparison, addition, and subtraction of fractions.

Practice

Students apply what they have learned, using supplementary and extended materials to:

• Equally divide a concrete object or group of objects and express the division as a fraction.
• Demonstrate the relationship between a unit fraction and a proper fraction.
• Compare proper fractions with the same denominator.
• Compare unit fractions.
• Add and subtract fractions with the same denominator.
• Solve word problems.

B. Unit Objectives

Students will be able to: