Expressing equally divided quantities as fractions: Lesson 1
Relationship between unit and proper fraction: Lesson 2
Comparing fractions: Lesson 3-4
Adding and subtracting fractions with the same denominator: Lesson 6-7
Practice: Lesson 8
 

Lesson 5

NUMBER LINES AND SEQUENCING OF FRACTIONS

A. Objectives

Students will be able to:

  1. Place a fraction on a number line.
  2. Make a sequence of fractions with the same denominator.

B. Instructional Content and Activities

Expressing a fraction on a number line

Using the number line below, review with students what they have already learned about placing natural numbers on number lines.

Example 1

Ask students whether they think a fraction can be placed on a number line, too.

Provide the following line segment. Point out that it starts with 0 and ends with 1 and has been divided into two equal parts.

Example 2

Review with the students how to represent 1 of 2 equal parts as a fraction (1/2). Then help them recognize that, since 1 of 2 equally divided parts is 1/2, the division on the line corresponds to 1/2.

Now, divide the following segment into 3 parts.

Example 3

Again, review with students how to represent 1 or 2 of 3 equal parts as fractions (1/3, 2/3). Then get them to realize that, in the figure, the first of the 3 equal divisions between 0 and 1 is 1/3, and the second is 2/3. Discuss this and express it.

Provide the following 1-meter bar divided into 5 equal sections. Have students find the corresponding fractions for each section.

Example 4

Since 1 section from a 1-meter bar equally divided into 5 sections is 1/5 m, then

  • 2 sections is two 1/5's or 2/5 m
  • 3 sections is three 1/5's or 3/5 m
  • 4 sections is four 1/5's or 4/5 m

Given a line segment divided into 5 equal sections between 0 and 1, as shown below, have students write the fractions corresponding to each division.

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Example 5

Relationship between a unit fraction and a proper fraction on a number line

In this section, students learn to sequence proper fractions with the same denominator by placing the fractions on a number line, and use a number line to extend their understanding of the relationship between a unit fraction and a proper fraction.

Have students practice by filling in the fractions on the number lines in their books. Remind them to use the following steps:

  1. Check the positions of 0 and 1 on the line. Remember that the starting point is always 0.
  2. Find out how many divisions there are between 0 and 1.
  3. Check to be sure the divisions are equal (that is, the line has been equally divided).
  4. Figure out the value of one division and express this as a unit fraction.
  5. For each segment, figure out how many of the unit fraction are included, and express this as a fraction.
  6. Match each fraction to its corresponding division on the number line.

Provide the following number line and have students place the given fractions on it.

Example 6

(1/4, 2/4, 3/4, 4/4)

Discuss how many of the equal divisions between 0 and 1 are needed to express each of the fractions (1 for 1/4, 2 for 2/4, 3 for 3/4, and 4 for 4/4).

C. Teaching Tip

  • Watch for the following error in placing fractions on a number line:

    Example 7

    Correct the error as shown below. Point out that the starting point is 0, and be sure students know how to mark the fractions in relation to the divisions.

    Example 8
Copyright © 2007 by Janice Grow-Maienza