# Ordering Rational Numbers

Subjects:

Computers & Internet, Language Arts, Math

8

Title – Ordering Rational Numbers
By – Dawn Agar
Primary Subject – Math
Secondary Subjects – Language Arts, Computers / Internet
Grade Level – 8

Background:

This lesson plan is part of a larger unit covering number sense and operations. The students have demonstrated proficiency at addition, subtraction, multiplication, and division of integers, decimals, and fractions. The objectives addressed in this lesson lead directly into the following objectives of identifying and ordering rational and irrational numbers.

English Proficiency Level: Intermediate

AZ State Mathematics Standards:

• M8S1C1PO-1. Locate rational numbers on a number line.
• M8S1C2PO-8. Use grade level appropriate mathematical terminology.

National Educational Technology Standards for Students:

• 3A. Students use technology tools to enhance learning, increase productivity, and promote creativity.
• 5B. Students use technology tools to process data and report results.

Preparation:

Content Objectives: Students will

• Learn definitions of rational numbers, terminating decimals, and repeating decimals
• Express fractions as terminating or repeating decimals
• Order rational numbers

Language Objectives: Students will

• Read a teacher-prepared skit in groups of three
• Compare methods of writing mixed numbers as decimals
• Plan and conduct a survey of fellow students and present their results

Vocabulary:

rational numbers, repeating decimals, terminating decimals

Materials:

Rational Numbers Skit, Survey Planning Worksheet, Fraction and Decimals Worksheet I, Fraction and Decimals Worksheet II, Fraction Bingo playing cards, bingo markers, shoe box, nametags, arrange for computer lab time

Motivation:

• Lead a class discussion on the meanings of rational, irrational, repeat, and terminate
• Separate the students into groups of three and have them read the Rational Numbers Skit
• Allow a group to volunteer to perform the Rational Number Skit.
• Make the connection between students knowledge of the vocabulary usage in “real life” and what that vocabulary means in mathematics

Presentation:

• Review the parts of a fraction (numerator and denominator)
• Review how to divide decimals by integers (Examples: 2.5 ÷ 5 and 0.72 ÷ 9)
• Show the students how to write a fraction as a decimal. To write a fraction as a decimal, divide the numerator by the denominator (Examples: 3/4 = 0.75 and 1/6 = 0.166666…)
• Ask the students which one of the previous examples is a repeating decimal (1/6) and which is a terminating decimal (3/4)
• Show the students how to order rational numbers. Write fractions and mixed numbers as decimals. Graph the numbers on a number line. Order the numbers from least to greatest or greatest to least (Examples: 0.51, 3/5, 11/20, 2/3, 0.62 and 4/5, 3/10, 3/8, 0.2, 0.4)

Practice:

• Have students return to their skit groups and complete the Fractions and Decimals Worksheet I together
• Ask the groups of students to discuss how they could write a mixed number as a decimal. Ask them to determine two ways to do this, and to discuss which way they prefer
• Have the student groups complete the Survey Planning Worksheet. Allow each group ample computer time to prepare charts and graphs for their presentations

Review

• Have students play Fraction Bingo with the teacher as the caller. The cards to be pulled from the shoe box should have both the fraction and decimal equivalents written on them to make determination of the winner easier

Assessment:

• Assign a fraction or mixed number name tag to each student. Have each individual convert the number on his name tag to a decimal, and have the students make a human number line which orders the rational numbers
• Have students complete the Fractions and Decimals Worksheet II individually
• Allow the students groups to make their presentations based on their Survey Planning Worksheet results

References:

Center for Applied Linguistics. (2005, February 9). The SIOP model of sheltered instruction.
Retrieved March 12, 2006 from http://www.cal.org/siop/
Comparing Fractions and Decimals. (n.d.).
Retrieved March 12, 2006 from http://www.aaaknow.com/g8_64ax1.htm
International Society for Technology in Education. (2004). National educational technology standards for students.
Retrieved March 19, 2006 from http://cnets.iste.org/students/s_stands.html

Appendices:

Rational Numbers Skit
Survey Planning Worksheet
Fraction and Decimals Worksheet I
Fraction and Decimals Worksheet II
Example of a Fraction Bingo Card

Rational Numbers Skit

 Rational: Hello, Terminating and Repeating. How was school today? Repeating: We got into a fight, we got into a fight…(continues repeating) Terminating: Yeah, we got into a fight with Irrational, and I wanted to terminate him. Rational: Children, what was this fight about? You know that I don’t like for you to be fighting at school. Repeating: He just kept saying stupid things, saying stupid things. The teacher was trying to tell us about math, about math, and Irrational kept saying stuff, saying stuff, like, “I like pie,” and “Oops, I did it again” while the teacher was trying to talk, trying to talk. Terminating: And I told him to be quiet. But he just kept talking and I wanted to terminate him. Rational: What did the teacher do? Terminating: She took us outside and told us that Irrational did not think the same way we did, but I still wanted to terminate him! Repeating: What did she mean, what did she mean? Why doesn’t he think like us, think like us? Rational: Irrational is well, irrational, and he doesn’t always make sense. You two are part of the rational number family, and it’s hard for you to understand when things don’t make sense. Repeating: Yes, it is, yes, it is. Terminating: I want to terminate numbers that don’t think like us. Rational: No, you can’t do that. Irrational is a necessary number. But you can always make sense because you are part of the rational number family. Now, go do your homework so that you can play before dinner. Repeating: Thanks, Mom. Thanks, Mom…(continues repeating) Terminating: Yeah, thanks, Mom. I don’t want to terminate you. THE END

Survey Planning Worksheet

Your group is going to conduct a survey. You will present the results of the survey to the class. There are several steps that must be completed to make this project a success.

1. You must first decide on a survey question. An example survey question is, “What is your favorite breakfast food?” Your survey question must a question that is appropriate for you to ask and present to your classmates. Think of it this way: Is this something I would want my parents to know that I’m asking? If the answer is no, it’s not appropriate.

2. You must decide on a target population and the number of people you will survey. For instance, your target population could be student at our school that are ages 13-15, and you could decide to survey 20 students. Each person that you survey must be contained in your target population. You could not interview a teacher if your target population was students aged 13-15. The number of people that you decide to survey must give you an adequate representation of the target population. For example, if you decide to survey 5 people, you may get 5 different responses, but the more people that you survey, the more representative your survey will be.

3. You must conduct the survey. It is best if each person in your group agrees to interview an equal number of students. You must be careful, however, to not interview the same people. You should record your results.

4. After you have completed your survey, you will count up the number of people who chose each option. You will then enter your results into a Microsoft Excel spreadsheet. Your completed spreadsheet should be similar to the one shown below for breakfast food preferences.

 Breakfast Food Bagels Bacon Eggs Cereal Pancakes Number of Students 10 12 9 21 5

5. Now you will determine the fraction and decimal that correspond for each of the responses to your survey. You divide the number of students for each of the categories by the total number of people that you interviewed. Do this on your own first. You will then check your answers using Microsoft Excel. To calculate the decimal equivalent in Excel, click on the cell directly below your first value. (In the above example, I would click the cell directly under the 10 under Bagels). Then type in =, click in the cell with the number (in my case, 10), type /, and then put the total number of people your surveyed (in my case, 52). The command will look something like this: = B2/52. Once you get a decimal value, click in that cell, and drag across to your last value. (In my case, I would drag until I was under the 5 under Pancakes). The decimal equivalents should now be under each cell. Check them with what you calculated.

6. Finally, you will make a circle graph which shows your results. Highlight your categories and number of students. Then click on the Chart Wizard on the Tool Bar for Excel. Select the Pie graph option, then click Next. You should see a circle graph of your data. Click Next again. Title your graph and then click Finish. An example of a completed circle graph is shown below.

7. Prepare for your presentation. Print your graph in color. We want to know what your survey question was, who you chose to survey, how many people you surveyed and what your results were. Congratulations! You have completed your project.

Fraction and Decimals Worksheet I

Write the fraction or mixed number as a decimal. Tell whether the fraction is a terminating decimal or a repeating decimal.

1. 4/5
2. 2 1/4
3. 1/9
4. 7/12
5. 27/50
6. 14 7/11
7. 8/15
8. 1 7/8
Order the numbers from least to greatest.
9. 9 3/4, 9.74, 9 5/7, 9.72, 9 9/13
10. 3/4, 0.56, 9/11, 1 1/2, 1.3

Fraction and Decimals Worksheet II

Write the fraction or mixed number as a decimal. Tell whether the fraction is a terminating decimal or a repeating decimal.

1. 3/5           2. 2 2/5
3. 1/6           4. 5/12
5. 33/50
6. 14 7/16
7. 2/3
8. 1 4/5
Order the numbers from least to greatest.
9. 1 1/8, 1 3/7, 1.1, 1.43, 1 4/15
10. 1/8, 0.3, 1/3, 4/9, 0.7
Fraction Bingo Example Playing Card

 1.33… 3/4 16/17 0.56 5.84 5/21 4.2121… 0.5 8 5/16 10.2 1.2 0.67 0.66… 5/8 2 6/7 9.98 46.3 9 1/4 8.789 3.21 5/3 22/7 3.15 9/10 5 8/11

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