NUMBER LINES AND SEQUENCING OF FRACTIONS
Students will be able to:
- Place a fraction on a number line.
- 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.
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.
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.
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.
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.
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:
- Check the positions of 0 and 1 on the line. Remember that the starting point is always 0.
- Find out how many divisions there are between 0 and 1.
- Check to be sure the divisions are equal (that is, the line has been equally divided).
- Figure out the value of one division and express this as a unit fraction.
- For each segment, figure out how many of the unit fraction are included, and express this as a fraction.
- 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.
(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:
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.