## Fraction Feud: Comparing and Ordering Fractions

- Lesson

In this lesson, students use fraction bars to explore
how to compare sizes of fractions. They conclude with an online Calculation
Nation** ^{®}** game
called Fraction Feud.

The
game Fraction Feud on Calculation Nation^{®} allows students to create
fractions by inserting a numerator and denominator. They earn points by
creating a fraction that is greater or less than the fraction created by
their opponent (if one can not be made, then credit will be given for equivalent fractions). The game allows them to practice the skill of comparing
fractions, and a fraction chart is included that allows them to make a visual
comparison.

In this lesson, students learn tactics for comparing fractions and fraction models. At the end of the lesson, they can use what they’ve learned to play Fraction Feud.

To prepare for the lesson, make sure that each student has a copy of the Fraction Feud Activity Sheet.

To begin the lesson, ask students:

Which is larger, 1/3 or 1/4? How can you tell?

Students will likely respond that one-third is larger because the whole is cut up into three equal pieces instead of four. They may also use a visual model that shows which is bigger:

As a hanging question, ask, “How can you tell which is larger when the numerator is not one?” Students will spend the rest of the lesson learning how to compare fractions when the numerator is not one.

For the main activity, distribute a set of fraction bars to each student. (If you do not already have a class set of these manipulatives, you can print out Fraction Bars.

You can pre-cut these, or have students cut them at the beginning of the lesson. Copying these sheets onto heavy cardstock will allow students to have a durable set that can be used repeatedly.) Ask students to model these fractions with numerators greater than one: three-fourths, five-sixths, and six-twelfths. Have students place these examples in rows, aligned on the left. Can they name the fractions from least to greatest? [6/12, 3/4, 5/6.] Which fraction is largest? [5/6.] Can they make a fraction larger than five-sixths? [Yes; an example is 11/12.] Which fraction is smallest? [6/12.] Is there another fraction that is equivalent to 6/12? [Yes. 1/2 is an example.] What is the smallest fraction you can make using the fraction bars? [1/12.] Give students another set of three fractions to model. Ask students to order these fractions from least to greatest on a piece of paper. Circulate the room while students complete this task and ask the questions above to assess their comprehension. Keep referring struggling students back to the fraction bars for support.

After students successfully order the three fractions given, write the following on a white board or interactive board:

2/4 ☐ 3/6

Ask students to model the two fractions with their fraction bars. What do they notice? [The two fractions are equivalent.] Ask students what symbol should be placed inside the box. [=.]

Next, tell students that if two fractions are not equal to each other, then the symbol they must use to compare the fractions is called an *inequality*. There are four (4) inequalities: less than (<), less than or equal to (≤), greater than (>), and greater than or equal to (≥). Tell students that technically, 2/4≤3/6 and 2/4≥3/6, but it is more accurate to use the equal sign. (Stress the"or" in less than or equal to and greater than or equal to).

Next, write 2/3 ☐ 7/12 on the board.

Ask students which fraction is greater. [2/3]. Have students use the fraction bars to find the answer. After students have found the answer of 2/3, remind them that since 2/3 is greater than 7/12 they would place the > symbol in the box.

Lastly, write 5/11 ☐ 5/9 or another pair of fractions that can't be made with fraction bars.

Ask students which fraction is greater. [5/9]. How did they know? [Elevenths is smaller than ninths, so 5/11 will be less than 5/9.] Which inequality should be placed in the box? [<.] Keep this on the board, as it will be referred to later in the class.

Distribute the Fraction Feud Activity Sheet to each student. Help students as needed to complete the sheet. This can be collected and used as a form of assessment. Before collecting the worksheet, point out #1 and also the class example: 5/11 < 5/9. Ask students what is similar about these two problems. [The numerators are the same.] Ask students if there is a hypothesis they can make about comparing two fractions with common numerators. [The fraction with the smaller denominator is larger.] After collecting the worksheets, tell students that they will continue practicing comparing fractions using a computer game.

Calculation Nation: Fraction Feud

Demonstrate how to play the “Fraction Feud” game on the
Calculation Nation^{®} web site. Remind students that they can use their fraction
bars to compare fraction, if needed. The game also provides a fraction
comparison guide for students who do not need a concrete model. The "Show me why I won," "Show me why I tied," and "Show me why I lost" can provide students with additional support if necessary. If your
students are registered on the site and sign in, they can challenge each other
on the game.

- Fraction bars, one set per student or pair of students (alternative: Fraction Bars printout)
- Fraction Feud Activity Sheet
- Fraction Feud Answer Key
- Computers with online access, preferably 1 per student

**Assessment Options **

- Use students’ answers on the Fraction Feud activity sheet to make sure that they can compare fractions.
- Check if students are forming the fractions correctly with the fraction bars and able to line them up appropriately. Are they able to make accurate comparisons visually?
- Watch to see which students need to use the fraction bars or other assistance when playing the Fraction Feud game.

**Extensions **

- Allow students to place fractions on a number line as close as possible to its exact location. The Calculation Nation game, Dig It, can be used as a motivator. In this game, the closer you place a chosen fraction on the number line, the more jewels are collected.
- Give students fractions to compare that cannot be formed with the fraction bars in the form given, such as 3/7 and 4/11. Ask students to find ways that the fraction bars could still be used.
- Give students fractions than cannot be formed with the fraction bars, and demonstrate how they can find a common denominator to find the larger fraction. Which is larger, 3/7 or 4/9? Tell students they can multiply the two denominators together to find a common multiple of both 7 and 9. [7×9=63.] Then, show students that they must use cross multiplication to find equivalent fractions of both 3/7 and 4/9. 3×9=27 and 4×7=28, so the two fractions become 27/63 and 28/63, respectively. Since 27/63 < 28/63, 3/7 < 4/9. It might be advisable to allow students to use calculators for this activity since the focus needs to be on the fractions and not the calculations.

**Questions for Students**

1. What are some ways that we can find which fraction is smallest in any pair?

[Use fraction bars. Some students may also know how to find common denominators and/or use cross multiplication]

2. What could you do to create a model if you didn’t have any pieces to use?

[Draw whole pieces and divide them into equal sections.]

3. Are there ways we can look at the fractions and know which one is largest, without using models or illustrations?

[Compare fractions to benchmarks. For example, if comparing ¾ to 4/8, we know that 4/8 is equal to ½, but ¾ is greater than ½, therefore it is the larger fraction.]

**Teacher Reflection**

- Were the students able to shift their understanding from the manipulatives to other methods?
- How did your lesson address the varying styles of learning, such as visual, tactile, and auditory?
- What were some of the ways that the students illustrated that they were actively engaged in the learning process?
- Did you set clear expectations so that students knew what behaviors were expected of them with the manipulatives and computers? If not, how can you make them clearer?

### Learning Objectives

Students will:

- Model fractions with single digit denominators.
- Compare and order fractions with single digit denominators.

### NCTM Standards and Expectations

- Use models, benchmarks, and equivalent forms to judge the size of fractions.

### 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.

Grade 3, Geometry

- 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 4, Num & Ops Fractions

- CCSS.Math.Content.4.NF.A.2

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP4

Model with mathematics.