Chapter 4: Rational Numbers Numbers... · Chapter 4: Rational Numbers Lesson 2: Compare and Order Rational Numbers ... rational numbers in any form (whole numbers, fractions, and

$Page 1: Chapter 4: Rational Numbers Numbers... · Chapter 4: Rational Numbers Lesson 2: Compare and Order Rational Numbers ... rational numbers in any form (whole numbers, fractions, and$
National Glencoe Math, Course 2, © 2015Chapter 4: Rational Numbers

Lesson 2: Compare and Order Rational Numbers

Printed by: Nicole Sladich Page of 1 14 Printed on 11/04/2014 10:13 PM

Common Core State Standards

Common Core State Standards

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions tomultiply and divide rational numbers.

7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and everyquotient of integers (with non-zero divisor) is a rational number. If and are integers, thenp q –( / ) = (– )/ = /(– ). Interpret quotients of rational numbers by describing real-worldp q p q p qcontexts.

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negativerational numbers in any form (whole numbers, fractions, and decimals), using toolsstrategically. Apply properties of operations to calculate with numbers in any form; convertbetween forms as appropriate; and assess the reasonableness of answers using mentalcomputation and estimation strategies. For example: If a woman making $25 an hour gets a10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salaryof $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 271/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimatecan be used as a check on the exact computation.

Mathematical Practices 1, 3, and 4 are aspects of mathematical thinking that are emphasized in everylesson. Students are given opportunities to be persistent in their problem solving, to express theirreasoning, and apply mathematics to realworld situations.

focus on Mathematical Practice 4 Exercises 11 and 15 Model with mathematics.focus on Mathematical Practice 3 Exercises 12 and 14 Construct viable arguments and critique the

reasoning of others.focuses on Mathematical Practice 1 Exercise 13 Make sense of problems and persevere in solving

them.




1 Launch the Lesson

Focus narrowing the scopeObjective Compare and order rational numbers. 7.NS.2, 7.NS.2b, 7.EE.3

connecting within and across gradesCoherence

PreviousStudents wrote rational numbersas decimals and fractions.

NowStudents compare and orderrational numbers by writing themin the same form.

NextStudents will add and subtractfractions with like denominators.

Rigor pursuing concepts, fluency, and applicationsSee the Levels of Complexity chart in the Practice and Apply section.

Lesson Vocabularyrational numbercommon denominatorleast common denominator

As students enter the classroom, have them complete the to review andCommon Core Quick Checkassess the skills presented in the previous lesson.

Engage Explore Explain Elaborate EvaluateIdeas for UseYou may wish to launch the lesson using a whole group, small group, think-pair-share activity, orindependent activity.

Give students one minute to think through their responses to theThink-Pair-ShareLaunch the Lesson: Vocabulary activity. Have them share their responses with a partner. Then haveeach partner share their response with the whole group. 1, 6, 7Alternate Strategy

Have students generate their own rational numbers that can be placed into each categoryof the Venn diagram. For each number they generate, have them explain why that number can beplaced into that category. 1, 3, 7

ResourcesCommon Core Quick Check: Compare and Order Rational Numbers




2 Teach the Concept

Focus: Mathematical Background can be written as the ratio of two integers (the second integer cannot be 0).Rational numbers

Decimals that neither terminate nor repeat are not rational.When students are memorizing common fraction-decimal equivalents,Fraction-Decimal Equivalents

it is useful to use coin equivalents.

Quarter: = 0.25, = 0.50, = 0.75

Dime: = 0.10, = 0.30, = 0.90

One dollar can be divided equally into fifths, so = 0.20, = 0.40, and = 0.60.

The McGraw-Hill Professional Development Video Library provides short videos that support . The featured videos for mathematical content in this lesson are:Glencoe Math

Compare and Order Whole Numbers, Fractions, and PercentsRational and Irrational NumbersSimplifying Fractions and Expressions

For classroom presentation, use the to demonstrate the examples from theStep-by-Step ExamplesStudent Edition.

Engage Explore Explain Elaborate EvaluateAsk the scaffolded questions for each example to differentiate instruction.

1. Compare rational numbers.

What is the difference between the two mixed numbers? The numerators of each fraction are different. Between which integers does each mixed number lie? -1 and -2

Explain how even though 5 > 1, the mixed number < . Sample answer: The mixed

numbers are negative, and as you move to the left on the number line, values decrease.

Explain how you could compare the numbers without locating them on a number line. Sample answer:

Both mixed numbers have the same whole number part. By comparing the numerators, is

farther left than .

Need Another Example?




Fill in the with <, >, or = to make a true sentence. >


Can we simply compare the numerators 7 and 8 to determine which fraction is greater? Explain. no;The denominators are different.

What is the LCD of 12 and 18? 36

Explain how to rewrite each fraction using the LCD. Multiply by ; multiply by .

How do you know that is equivalent to ? We multiplied by , which is the same as

multiplying by 1.

Would your result be different if you simplified prior to comparing the numbers? Explain. no;

Sample answer: The result is the same because of equivalent fractions.Need Another Example?

Fill in the with <, >, or = to make a true sentence. <


What are you trying to determine? the class that owns more roller shoes What are the two numbers we need to compare? 20% and 5 out of 29

What will you have to do to compare these values? Sample answer: Express each number as adecimal.

How do you determine that 5/29 0.1724? Divide the numerator by the denominator.

How could you use estimation to compare? = and >

Need Another Example?In a football game, the quarterback completed 11 out of 19 passes. The next week, he completed60% of his passes. During which game did he complete the greater fraction of his passes? thesecond game

4. Order a set of rational numbers.

In what form could we compare these numbers? Sample answer: decimal form




1. 2.

3.

Will annexing zeros change the value of a decimal? No, you can annex as many zeros as needed.

Why should you extend each decimal place to the thousandths? because each pair has the sametenths and hundredths values

How do you know just by looking at the numbers 3.44 and 3.4 which one is greater? Sample answer:3.4 repeats the digit 4 forever. Even if it just repeated the digit to the thousandths place, 3.444 > 3.44.

Is a terminating decimal, repeating decimal, or neither? Explain. Neither; is a non-terminating,non-repeating decimal.

Need Another Example?

Order the set from least to greatest.

5. Order a set of rational numbers.

In what form can we compare these numbers? Sample answer: decimal form

Could you use another form to compare? If so, which form? yes; Sample answer: percent

What are the fractional values for each number? decimal values? percentage values? , ,

; 0.67, 0.64, 0.60, 0.69; 67%, 64%, 60%, 69%,

Which form do you prefer to use to compare the numbers? See students’ preferences.Need Another Example?Maddie is a guard on the basketball team. She made 70% of her field goals in the first game. She

made 0.62, , and 66% of her field goals in the next three games. List Maddie’s made field goal

statistics from least to greatest. 0.62, 66%, 70%,

Alternate Teaching Strategy students have trouble finding the LCD of the fractions,If

use one of these reteach options:Then, pp. 153-155Quick Review Math Handbook

, Unit B: Rational NumbersProblem-Based Learning Book 2 , Investigation 2: Order and CompareRational NumbersHave students write equivalent fractions for each fraction until they find fractions with a common




3.

denominator. For example, to compare and , students would write , , , ,

and , , , . Since and have a common denominator, they can be used for

the comparison. and . , so .

Formative Assessment Use these exercises to assess students' understanding of the concepts inthis lesson.

If some of your students are not ready for assignments, use the differentiated activitiesbelow.

Have students work together to complete Exercises 1-4. Give themPairs Discussionblank number lines for Exercises 3 and 4. Students should place values on a decimal or fractionnumber line. 1, 5

Numbered Heads Together Provide a list of varying fraction, decimal, and percentagevalues. Have students work in groups generate equivalent values of remaining forms for each givenvalue. Call on one group member to share the group’s responses. 1, 7

Tips for New Teachers Help students remember the definition of numbers by pointing out that Rational Numbers rational

numbers can be written as a of integers (provided the second integer is not 0). You mayrational ratioalso wish to remind students that terminating decimals can be written as fractions.

Teach with Tech Draw a number line on the IWB to compare and order rational numbers. HaveInteractive WhiteBoard

students use the highlighter tool to show the placement of various rational numbers as suggested byother students in the class. Have students decide on the order of value of the rational numbers. Repeatwith different sets of rational numbers.

Have students write a song, rap, or poem about rational numbers, integers, whole numbers,Podcastand natural numbers. Included should be what type of number is in each set and how the different setsof numbers relate to each other. Have students record the result using software and share it by way ofa podcast.

ResourcesVirtual ManipulativesFractions as DecimalsFractions as DecimalsMixed Numbers as DecimalsWrite a Fraction as a Decimal Using DivisionWrite a Fraction as a Decimal Using DivisionWrite a Fraction as a Repeating DecimalReal-World Example: Write a Decimal as a FractionCompare Rational NumbersCompare Rational NumbersOrder Rational Numbers




Real-World Example: Order Rational NumberseToolkitProblem-Based Learning Book 2, Unit B, Student Edition: Rational NumbersProblem-Based Learning Book 2, Unit B, Teacher Edition: Rational NumbersHot Topic 2-9: Fraction, Decimal, and Percent RelationshipsCompare and Order Whole Numbers, Fractions, and PercentsSimplifying Fractions and ExpressionsManipulative Masters: Number LinesCompare with Percents




3 Practice & Apply

Engage Explore Explain Elaborate EvaluateIndependent Practice and Extra PracticeThe Independent Practice pages are meant to be used as the homework assignment. The ExtraPractice page can be used for additional reinforcement or as a second-day assignment. Levels of ComplexityThe levels of the exercises progress from 1 to 3, with Level 1 indicating the lowest level of complexity.

Suggested AssignmentsYou can use the table below that includes exercises of all complexity levels to select appropriateexercises for your students' needs.

Differentiated Homework Options

Approaching Level 1–9, 11, 12, 14, 15, 24, 25

On Level 1–7 odd, 9–12, 14, 15, 24, 25

Beyond Level 9–15, 24, 25

can provide additional remediation support with personalized instruction andpractice. Create Your Own Homework OnlineeSolutionsManual™ can be used to create worksheets for the suggested assignments above, or tocreate your own worksheets for differentiated homework or review.

The following worksheets are also available for additional homework practice:The editable worksheet provides students with additional practice in the skills taught inSkills Practicethis lesson.The editable worksheet helps students practice skills in this lesson and use thoseHomework Practiceskills to solve problems.The editable worksheet helps students become better problem solvers byProblem-Solving Practiceproviding frequent opportunities to solve real-world problems.The worksheet provides additional practice for the skills taught in this lesson.Extra Practice

The provide a worked out solution for selected exercises from the Step-by-Step SolutionsIndependent Practice in the Student Edition.

Students may have trouble comparing fractions with unlike denominators because theyCommon Error




may only compare the numerators. Have students circle the denominators and remind them to rewritethe fractions using the LCD. Then compare the numerators.

ResourcesStep by Step Solutions: Compare and Order Rational NumbersSkills Practice: Compare and Order Rational NumbersSkills Practice Answers: Compare and Order Rational NumbersHomework Practice: Compare and Order Rational NumbersHomework Practice Answers: Compare and Order Rational NumbersProblem-Solving Practice: Compare and Order Rational NumbersProblem-Solving Practice Answers: Compare and Order Rational NumbersExtra Practice: Compare and Order Rational NumbersExtra Practice Answers, Chapter 4Homework Practice: Compare and Order Rational NumbersProblem-Solving Practice: Compare and Order Rational NumbersSkills Practice: Compare and Order Rational NumbersExtra Practice: Compare and Order Rational NumberseSolutions, Glencoe Math Course 2




Additional Activities for Differentiated Instruction

Differentiated Instruction activities for Approaching Level, On Level, and Beyond Level Learners canalso be found at point-of-use in the Launch the Lesson and Teach the Concept sections. The followingare additional activities that can be used with this lesson.

The provides additional examples and practice for students who may have Reteach Worksheetdifficulty in grasping the math concepts in this lesson.

The provides students with valuable opportunities for extending this lesson.Enrich Worksheet

ResourcesReteach: Compare and Order Rational NumbersReteach Answers: Compare and Order Rational NumbersEnrich: Intersection and Union of SetsEnrich Answers: Intersection and Union of SetsReteach: Compare and Order Rational NumbersEnrich: Intersection and Union of Sets




Additional Activities for English Learners

Differentiated Instruction activities for English Learners can also be found at point-of-use in the Launchthe Lesson and Teach the Concept sections. The following are additional activities that can be usedwith this lesson.

Option 1: Use Chapter 4, Lesson 2: Compare and Order Rational Numbers from the Interactive Guide for English Learners.

Place students in groups of four. Give each group twelve cards,Option 2: Kinesthetic Learners each of which shows a fraction or a decimal.Each member of the group draws one card. Then have students order the cards from least togreatest. Repeat the activity several times.

Create a word wall with examples of GCF, LCM, andOption 3: Verbal/Linguistic Learners LCD.Explain what each term is, how it is used, and whether the terms are related in any way. Be sureto give examples of all three. Word Wall Printable English/Spanish Word Wall cards are available for the following vocabularywords in this lesson: common denominatorleast common denominatorrational number

ResourcesWord Wall CardsInteractive Guide for English Learners, Student Edition, Course 2, Lesson 4-2: Compare and Order RationalNumbersInteractive Guide for English Learners, Teacher Edition, Course 2, Lesson 4-2: Compare and Order RationalNumbersInteractive Guide for English Learners, Course 2, Teacher EditionInteractive Guide for English Learners, Course 2, Student EditionVisual Kinesthetic Vocabulary, Course 2, Student EditionVisual Kinesthetic Vocabulary, Course 2, Teacher Edition




25.

24.

Assessment

Formative AssessmentUse this activity as a closing formative assessment before dismissing students from your class.

Write the following on the board: and ; and and . Have each

student explain out loud to a partner how they would compare each pair of rational numbers. Then havethem summarize the process by writing it on a piece of paper to hand in at the end of class. Seestudents' work.

The online for this lesson allows students to review concepts from each lesson.Self-Check Quiz

Exercises 24 and 25 prepare students for more rigorous thinking needed when taking the CCSSassessment.

This test item requires students to explain and apply mathematical concepts andsolve problems with precision, while making use of structure.

Depth of Knowledge DOK2

CCSS Content Standard 7.EE.3

Mathematical Practices MP1

Online Experience Students will be required to type theirresponses in the boxes.

Scoring Rubric

2 points Students correctly order 4 counties, list the salestax rate for each, and determine the county withthe lowest sales tax.

1 point Students correctly order 4 counties, list the salestax for each, but fail to determine the county withthe lowest sales tax OR students correctly orderthe counties, but fail to list the correct sales taxrate for each and may or may not identify thecounty with the lowest sales tax.

This test item requires students to reason abstractly and quantitatively when problemsolving.

Depth of Knowledge DOK1

CCSS Content Standard 7.EE.3

Mathematical Practices MP1

Online Experience Students will be required to click on thebubbles to select all answers that arecorrect.




Scoring Rubric

1 point Students correctly answer each part of thequestion.

Quick CheckAre students continuing to struggle with comparing and ordering rational numbers?If Yes

Reteach WorksheetIf No

Skills Practice WorksheetEnrich Worksheet

ResourcesSelf-Check Quiz: Compare and Order Rational Numbers




Documents

Chapter 4: Rational Numbers Numbers... · Chapter 4: Rational Numbers Lesson 2: Compare and Order Rational Numbers ... rational numbers in any form (whole numbers, fractions, and