Kid Fractions

Est. Class Sessions: 1

Developing the Lesson

Discrete Models and Area Models. Students need many opportunities to work with different concrete representations of fractions. Two types of models are discrete models and area models. A fraction can describe a part of a group. At times, we want to find out how many objects the fraction represents. In this lesson, Kid Fractions, students will identify the fractional part of a set of objects represented by students. When you find a fractional part of a set of individual objects, we call this a discrete model. In later lessons, students will use circle pieces, fraction strips, and drawings to represent fractions. When students use these shapes, they are using area models.

Play Kid Fractions Game. To begin, ask a group of 4 students to come to the front of the class. Figure 2 is an example of such a group. Two of the four children in the figure are girls. Three-fourths are wearing pants. Three-fourths are wearing glasses. One of the four is wearing a skirt.

Tell students that you are going to write an incomplete sentence on the board about part of the group that is in front of the class. The challenge is to complete the sentence. Write prompts similar to those below. Discuss each one and then fill in a row of the chart.

Display an incomplete sentence about part of the group that is in front of your class. The following sentences are examples that refer to the sample group of four students shown in Figure 2.

3 out of 4 students are _________________.
1 out of 4 students is _________________.
2 out of 4 students are _________________.
All of the students are _________________.

Point out that fractions can be presented either with the numerator and denominator separated by a diagonal line, such as 2/3, or stacked, such as 2/3 .

Challenge students to complete the sentence. For example, in the sample group, 3 out of 4 students are wearing pants.

Demonstrate filling in the Kid Fractions Table you prepared and displayed prior to the lesson. See Materials Preparation. Row A of the sample table in Figure 3 and the following prompts show how to record that 3/4 of the students in the sample group are wearing pants. Use similar prompts to describe the fraction shown by your group of students as you fill in the table.

Ask:

For Column 1: How many students are in the whole group? (4 students)
For Column 2: How many students are wearing pants? That is the part of the group that we are talking about. (3 students)
For Column 3: We can use the words “3 out of 4” or “three-fourths” to describe the fraction of students in front of the room who are wearing pants.
For Column 4: We can write the fraction as a number by writing 3/4 .

Give students several more sentences to complete about the set of students in front of the class. Ask a student to fill in a row of the table each time.

Encourage students to use the Writing Numbers in Words page in the Student Guide Reference section as needed.

Keep the Kid Fractions Table posted in the classroom where students can refer to it throughout the unit.

Change the Unit Whole. Ask another set of students to come to the front of the class. Choose a different number of students for the unit whole. This time fill in either the second or third column in a row of the table to start the discussion. For example, using a group of six students, fill in the fourth column with the fraction 2/6 as shown in Row E of the table in Figure 3. Students must then find a characteristic that matches that fraction and complete the row of the table. The unit whole is now a set of 6 students and the fraction can be written in words as 2 out of 6 or two-sixths.

Ask:

Tell me something about 2/6 of the students in this group.
What does the 2 tell us? (Responses will vary. Possible response: 2 students have ponytails.)
What does the 6 tell us? (There are 6 students in the whole group.)

Ask a student to fill in the empty columns of the Kid Fractions Table.

When creating fractions that describe a part of a group, some characteristics to consider are the fraction of students in the group with:

Long or short hair
Brown eyes or blue eyes
Short-sleeved shirts or long-sleeved shirts
Dark-colored hair or light-colored hair
Earrings
Headbands
Blue jeans or other pants
Ponytails

Introduce the terms numerator and denominator. In a fraction such as 2/6 , the 6 is the denominator. It tells the number of equal parts in the whole. The 2 is the numerator. It tells the number of parts being considered.

Continue the activity with different groupings of students so that students experience fractions with different unit wholes and denominators. Emphasize that the denominator gives the number of parts into which the unit whole is divided while the numerator tells how many of those parts you are interested in.

Ask:

What fraction of this group is girls?
Which number is the denominator and what does it tell us about this group? (Answers will vary. The denominator tells the number of students in this group.)
Which number is the numerator and what does it tell us about this group? (Answers will vary. The numerator tells the number of girls in this group.)

Introduce Equivalence to 1/2 . Introduce fractions equivalent to one-half. Equivalent fractions will likely be a new idea for children, so keep the examples simple to start students' thinking about equivalence.

Ask:

What do you think of when you hear one-half? (Possible responses: 1/2 of a sandwich; sharing 6 cookies equally between 2 people so each gets 3; two 1/2 hours in one hour)
What do you know about “one-half”? (Possible response: If I cut something into 2 parts that are the same size, each one of the parts is one-half.)
If you cut a sandwich into 2 equal parts, is each part one half? (Yes.)
If you share 6 cookies equally between 2 people, yourself and a friend, how many cookies are half? (3 cookies)
Each person gets what fraction of the cookies? ( 3/6 or 1/2 )
How can there be 3 of something in 1/2 ? (Possible response: If you take the 6 cookies and make two equal piles so that it is fair, each person will have 3 cookies.)

Some students may be ready to agree that 3/6 can be 1/2 and some may not. Use the following scenario to provide another example.

Suppose, for example, there are six students, three of whom wear eyeglasses. See Figure 4. Either of the fractions 3/6 or 1/2 fits the part of the group wearing glasses. The fraction 3/6 can be interpreted to mean that three out of six students are wearing glasses. The fraction 1/2 can be interpreted to mean that out of two equal groups of students, one group has glasses.

To illustrate this idea, choose 3 students wearing shoes with laces and 3 students wearing shoes that do not have laces (or 3 wearing glasses and 3 without glasses, etc.) Ask them to stand in front of the class.

Ask:

How many students are in the whole group? (6)
How many students are wearing shoes with laces? (3)
What is the fraction of students wearing shoes with laces? ( 3/6 )

Write the fraction 3/6 . Now ask the class to divide the students and cluster them into two distinct groups—one of students wearing shoes with laces and one wearing shoes without laces. Point out that each group has the same number of students.

Ask the class to think about these groups:

How many different groups are there? (2)
Have we divided the students fairly into 2 groups? (Possible response: Yes, because there is the same number of students in each group.)
How many groups have students wearing shoes with laces? (1)
What is the fraction of groups of students wearing shoes with laces? ( 1/2 )

Write “ 3/6 = 1/2 ” to emphasize that either fraction can be used to describe the part of the group wearing shoes with laces. Decide whether to illustrate another fraction equivalent to 1/2 with a student group such as 2/4 , 4/8 , or 5/10 .

Compare Kid Fractions. At this point, introduce the issue of the relative size of different fractions. Ask a group of 6 boys and 2 girls to stand in front of the class.

Ask the class to think about these groups:

What is the unit whole? (8 students)
What fraction of this group is boys? ( 6/8 )
What fraction of this group is girls? ( 2/8 )

Write 6/8 > 2/8 to show that there are more boys than girls in this group.

Write “greater than” above the symbol (>) and explain that this number sentence is read: 6/8 is greater than 2/8 . Explain that when you write number sentences that compare two numbers just as you use the symbol (=) to mean equal to, you can also use the symbol (>) to mean greater than and the symbol (<) to mean less than.

Use the same group of students to pose different questions that generate fractions that students can compare. Use the comparisons to write number sentences that use the less than (<), greater than (>), and equal to (=) symbols. Use the Sample Dialog Box to help guide this discussion.

Use this Sample Dialog to guide students in writing number sentences and symbols to show the comparison of fractions.

Teacher: There are 3 out of 8 students wearing glasses. What fraction of the group is wearing glasses?

Peter: 3/8 of the students are wearing glasses.

Teacher: Good, 5 out of 8 of the students are not wearing glasses. What fraction of this group of students is not wearing glasses?

Carla: 5/8 of the students do not have glasses.

Teacher: Is 3/8 greater than, less than, or equal to 5/8 ?

Peter: 3/8 is less than 5/8 .

Teacher: That is correct. You can write this number sentence to show that 3/8 is less than 5/8 . (Teacher writes 3/8 < 5/8 on a display.) Who can read this number sentence?

Carla: 3/8 is less than 5/8 .

Teacher: That is right. Let's compare some other fractions about our students in this group.

When students are comparing fractions and showing those comparisons with symbols, have students circle the largest fraction in the number sentence before deciding the correct symbol.

Student Guide: Reference

Answers