## Making and Investigating Fraction Strips

• Lesson
3-5
1

Students make and use a set of fraction strips to represent the length model, discover fraction relationships, and work with equivalent fractions.

To assess prior knowledge, ask students to create a list of ways they use fractions in their daily lives. Engage them in a discussion of nonstandard ways they use fractions daily. Some simple examples include dividing a treat in half (1/2) to share it with a friend, or noticing that your brother ate 3/8 of a pizza last night at dinner.

Some students may suggest that they fold or use a ruler to measure lengths to determine fractional parts. If students suggest such strategies, you might use this as an introduction to the lesson using fraction strips.

To begin the lesson, give students six strips of paper in six different colors. Specify one color and have students hold up the strip of this color. Tell students that this strip will represent the whole. Have students write "one whole" on the fraction strip. The term whole is included in the labeling instead of 1 because it eliminates confusion between the numeral 1 in fractions such as 1/2.

Next, ask students to pick a second strip, fold it, and cut it into two equal pieces. (Note that students may prefer to highlight the fold marks, rather than physically cutting the individual fraction pieces.) Ask them what they think each of these strips should be called ["one‑half" or 1/2]. Have students label their strips accordingly using both the word and the fractional representation.

Have students take out another strip, fold it twice, and divide it into four congruent pieces. Ask them what they think each of these strips should be called ["one‑fourth" or 1/4]. Have students label their strips using both the word and the fractional representation. Repeat this process of folding, cutting, and naming strips for eighths, thirds, and sixths.

Have students take out their "whole" and ask, "Which strip is 1/2 of the whole?" Then ask, "Which strip is 1/4 of the whole?" Ask similar questions about 1/8, 1/3, and 1/6. Students should experiment with the strips until they are consistently arriving at the correct answer.

Have students work in pairs to line up their fraction strips and find as many relationships as they can. For instance, they might notice that three of the 1/6 pieces are equal to four of the 1/2 pieces, or that two of the 1/3 pieces are equal to four of the 1/6 pieces. Have students record these relationships on paper. When they have finished, have them share the relationships they discovered. Record relationships on chart paper and discuss.

Students will notice that one whole is the same as 2/2, 4/4, 8/8, 3/3, or 6/6. Another example includes the relationship between 1/2, 2/4, 4/8, and 3/6. Tell students that when fraction strips are the same length, they represent equivalent fractions. Students may also notice that for each of these fractions, the numerator is 1/2 of the denominator. Record this relationship.

Have students create a virtual set of fraction strips using the Fraction Bars Applet. Instructions for using the virtual fraction strips should be reviewed ahead of time. Students will have to be guided in clicking on the "Add Bar" and then breaking the bar into various pieces or fractions.

Have students explore fraction relationships using the virtual fraction strips. Relationships should be noted in written reflections. When all students have completed recording fraction relationships using the applet, discuss relationships as a class. Record any additional relationships on chart paper for future reference.

• 18 × 24 sheets of construction paper in six different colors (cut into three 6 × 24 strips; each child will need six strips, one of each color)
• Scissors
• Chart paper
• Fraction Bars Applet

Assessments

1. At this stage of the unit, students should be able to do the following:
• demonstrate understanding that a fraction can be represented as part of a linear region
• describe part of a linear region using fractions
• demonstrate understanding of fraction relationships by representing fractions in a variety of ways.
2. Examining students’ recordings and written reflections can be helpful in making instructional decisions about their understanding of fraction relationships.

Questions for Students

1. When you folded your strip into two parts, what fraction of the whole strip did one strip represent?
[1/2]
2. When you folded your strip into four parts, what fraction of the whole strip did one strip represent?
[1/4]
3. What other fractions have the same value as 1/2?
[2/4, 3/6, 4/8]
4. What other fraction has the same value as 2/3?
[4/6]
5. What do you notice about the fractions that are the same as 1/2?
[Prompt students to examine the relationship between the numerator and the denominator. Students should notice that the denominators are always double the numerators.]
6. Can you identify other fractions for which there are no fraction strips that are the same as 1/2 based on this pattern?
[Accept any equivalent fraction such as 6/12, 7/14, 8/16, 9/18, 10/20.]
7. For each of the strips (halves, fourths, sixths, eighths), we can show a fraction equivalent to 1/2. Why do we not include 1/2 of our thirds strip?
[These pieces cannot be divided evenly into halves. Prompt students to also notice that the denominators are even for those fractions that can be divided into 1/2s.]
Teacher Reflection

• Which students understand that a fraction can be represented as part of a linear region? What activities are appropriate for students who have not yet developed this understanding?
• Which students can describe part of a linear region using fractions? What activities are appropriate for students who have not yet developed this understanding?
• Which students can articulate the relationships between fractions? What activities are appropriate for students who have not yet developed this understanding?

### Learning Objectives

Students will:

• Demonstrate understanding that a fraction can be represented as part of a linear region
• Describe part of a linear region using fractions
• Demonstrate understanding of fraction relationships by representing fractions in a variety of ways

### Common Core State Standards – Mathematics

Grade 3, Num & Ops Fractions

• CCSS.Math.Content.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• CCSS.Math.Content.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Grade 4, Num & Ops Fractions

• CCSS.Math.Content.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Grade 5, Num & Ops Fractions

• CCSS.Math.Content.5.NF.B.3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.