LESSON 24Overview Order Positive and Negative NumbersSTANDARDS FOR MATHEMATICALPRACTICE (SMP)ObjectivesVocabularySMP 1, 2, 3, 4, 5, and 6 are integrated into theTry-Discuss-Connect routine.*Content Objectives Math VocabularyThis lesson provides additional support for: 2 Reason abstractly and quantitatively.* See page 1q to learn how every lesson includesthese SMP. Compare and order positive and negativenumbers.Interpret numerical inequalities asstatements about position of numbers ona number line.Write and interpret inequalities in real-world contexts.Language Objectives Use lesson vocabulary and direction andcomparison words, such as left, right, up,down, farther, best, and worst, to talkabout ordering and comparing positiveand negative numbers.Read and interpret word problems toidentify key quantities and comparethem using words and inequality statements in discussion and writing.Prior Knowledge Locate positive and negative numbers onthe number line.Compare and order positive rationalnumbers.Use positive and negative numbers torepresent real-world quantities andexplain the meaning of 0 in context.There is no new vocabulary. Review thefollowing key terms.compare to describe the relationshipbetween the value or size of two numbersor quantities.inequality a mathematical statement thatuses an inequality symbol (,, ., #, ) toshow the relationship between values ofexpressions.negative numbers numbers that are lessthan 0. They are located to the left of 0 on ahorizontal number line and below 0 on avertical number line.positive numbers numbers that aregreater than 0. They are located to the rightof 0 on a horizontal number line and above0 on a vertical number line.rational number a number that can beexpressed as the fraction ba or the··opposite of a , where a and b are wholeb·· numbers and b Þ 0. Rational numbers canalso be expressed as a decimal.Academic Vocabularyinterpret to explain the meaning ofsomething.lesser less or smaller in value.relative to compared to something orsomeone else.Learning ProgressionIn earlier grades, students located andlabeled positive whole numbers,fractions, and decimals on the numberline and compared them usinginequality symbols and words. Theyordered positive rational numbers.In the previous lesson, studentslocated positive and negative wholenumbers, fractions, and decimals andtheir opposites on the number line. Theydescribed the value of positive andnegative rational numbers in relation to0 and in real-world contexts.553aLESSON 24 Order Positive and Negative NumbersIn this lesson, students compare andorder positive and negative rationalnumbers. They interpret inequalities asstatements about the relative positionof numbers on the number line.They also write inequalities torepresent and interpret inequalities inreal-world contexts.Later in Grade 6, students will extendtheir understanding of locatingnumbers on the number line tointerpret the absolute value of anumber. They will also write and graphinequalities with variables andunderstand that these inequalities haveinfinitely many solutions.In Grade 7, students will writeinequalities with a variable to representreal-world situations with unknowns.They will solve inequalities that includea variable and graph solutions toinequalities on the number line. Curriculum Associates, LLCCopying is not permitted.
LESSON 24OverviewPacing GuideItems marked withSESSION 1 are available on the Teacher Toolbox.MATERIALSDIFFERENTIATIONExplore Ordering Positive and Negative Numbers (35–50 min)Start (5 min)Try It (5–10 min)Discuss It (10–15 min)Connect It (10–15 min)Close: Exit Ticket (5 min)Math Toolkit algebra tiles, numberlines, two-color countersPresentation SlidesPREPARE Interactive TutorialRETEACH or REINFORCE Hands-On ActivityMaterials For each pair: 1 sticky noteAdditional Practice (pages 557–558)SESSION 2 Develop Comparing Positive and Negative Numbers (45–60 min)Start (5 min)Try It (10–15 min)Discuss It (10–15 min)Connect It (15–20 min)Close: Exit Ticket (5 min)Math Toolkit graph paper,number linesPresentation Slides REINFORCE Fluency & Skills PracticeEXTEND Deepen UnderstandingAdditional Practice (pages 563–564)SESSION 3RETEACH or REINFORCE Hands-On ActivityMaterials For each pair: 1 two-color counter,1 number cube, Activity Sheet Number LinesRefine Ordering Positive and Negative Numbers (45–60 min)Start (5 min)Monitor & Guide (15–20 min)Group & Differentiate (20–30 min)Close: Exit Ticket (5 min)Math Toolkit Have items fromprevious sessions available forstudents.Presentation SlidesRETEACH Hands-On ActivityMaterials For each pair: 20 index cardsREINFORCE Problems 4–8EXTEND ChallengePERSONALIZELesson 24 Quiz orDigital Comprehension CheckRETEACH Tools for InstructionREINFORCE Math Center ActivityEXTEND Enrichment Activity Curriculum Associates, LLCCopying is not permitted.LESSON 24 Order Positive and Negative Numbers553b
LESSON 24Overview Order Positive and Negative NumbersConnect to Culture Use these activities to connect with and leverage the diverse backgroundsand experiences of all students. Engage students in sharing what theyknow about contexts before you add the information given here.SESSION 1Try ItAsk students if they have ever played or watched American football. Thereare many decisions a coach has to make regarding the team in every football game.People are working on technology that can predict what play a team will run next.In certain circumstances, the predication is over 90% accurate. Some people may beconcerned with how this power of predicting will change how football is played.Ask students if they think football will become a game of beating the computermore than beating the opponent.SESSION 2Try ItThere are many places that typically have very cold climates. The coldesttemperature ever recorded was in Antarctica, which was 2128.6 degreesFahrenheit, or 289.2 degrees Celsius. Another place that has experienced a recordlow temperature is a town in Canada called Snag, in the Yukon province. In 1947 itreached 281 degrees Fahrenheit. The average annual high temperature is 32degrees Fahrenheit. Survey students about the coldest temperatures they haveexperienced and discuss the locations where these temperatures occurred.Carrier1:00 PM100%OshkoshCurrent Temperature2.5 FAppletonCurrent Temperature–3.5 FGreen BayCurrent Temperature–5.0 FApply It Problem 9 One interesting sea creature is the sixgill shark. Most sharkshave five gills, but this one has six. It is also one of the largest sharks, excluding theones that feed on plankton like whales do. The sixgill shark can grow to be up to 18feet long! These sharks can be found at depths around 8,000 feet below sea level.Another unique fact about them is that they have only the back dorsal fin, so theirback is flat in the middle, where other sharks have the iconic large dorsal fin thatmight stick out of the water as they circle their prey. Encourage a discussion aboutvarious sea creatures with which students are familiar.SESSION 3Apply It Problem 2 Survey students to determine how often they purchaseitems from a vending machine. When we think of vending machines, typically wethink of buying drinks or snacks. However, there are some vending machines thatare much more unique. For example, there is a vending machine in Dubai whereyou can buy gold. Other examples include vending machines that sell real crabs,mashed potatoes, hair extensions, books, and dog toys and treats. If you are lookingfor a meal, there is even a vending machine that serves hot pizza, ready to eat!553cLESSON 24 Order Positive and Negative Numbers Curriculum Associates, LLCCopying is not permitted.
LESSON 24OverviewConnect to Family and Community After the Explore session, have students use the Family Letter to let theirfamilies know what they are learning and to encourage family involvement.LESSON 24 ORDER POSITIVE AND NEGATIVE NUMBERSActivity Thinking AboutComparing Positive and NegativeNumbers Around YouLESSON24This week your student is learning how to compare positive and negative numbers.The farther to the left a number is located on a horizontal number line, the lesserthe value of that number.increasing values25242322 21012345decreasing valuesYou can write an inequality to show which of two numbers has the greater or lesservalue. For example, 2 . 23 means that 2 is greater than 23.Your student will be learning to solve problems like the one below.A town well extends to an elevation of 255 ft below ground level. Jesse’shouse well extends to an elevation of 2260 ft. Which well is deeper? ONE WAY to compare the elevationsis to use words to describe theirrelationship in context. ANOTHER WAY is to use symbols towrite an inequality.Look at the positions of 2260 and2255 on a vertical number line.HolePar14positive and negative numbers in the real world.24Did you know when you play golf, the lowest score wins?In fact, your final score could even be negative!4654 Do this activity together to investigate comparingOrder Positive and Negative NumbersDear Family,DUS T Y HILL S GOLF COURSE3A score of 24 means a person used four fewer strokes thanwas expected in order to complete the golf course. A scoreof 14 means a person used four more strokes than wasexpected in order to complete the golf course. Using fewerstrokes is better, so a score of 24 is better than 14!6StrokesScore55758694Where else do you compare positive andnegative numbers in the world around you?224022452250260 ft2255255 ft2260A point 260 ft underground is deeperthan a point 255 ft underground.2260 is below 2255.2260 , 2255Both models show that Jesse’s well is deeper than the town well.Use the next page to start a conversation aboutpositive and negative number comparisons. Curriculum Associates, LLC Copying is not permitted.LESSON 24 Order Positive and Negative Numbers553554LESSON 24 Order Positive and Negative Numbers Curriculum Associates, LLC Copying is not permitted.Connect to Language For English language learners, use the Differentiation chart to scaffold thelanguage in each session. Use the Academic Vocabulary routine for academicterms before Session 1.DIFFERENTIATION ENGLISH LANGUAGE LEARNERSUse with Session 1Connect ItLevels 1–3: Speaking/WritingLevels 2–4: Speaking/WritingLevels 3–5: Speaking/WritingUse Act It Out to support the problemcontext before students write a responseto Connect It problem 1. Display an arrowbeginning with the word worst and endingwith best. Explain that best means really goodor better than all others and worst meansreally bad or worse than all others. Write fourmovie titles from worst to best on the arrow.Point as you ask questions to help studentscompare: Which movie is the worst? Whichmovies are better than this? Is this movie betterthan this? Is this movie worse than this? Whichmovie is the best? Next, read the problem.Have students use a similar arrow to orderthe plays. Then have them work in pairs toexplain in writing. Ask: Which is the worstresult? Which plays are better?Use Act It Out to support the problem contextbefore students write a response to ConnectIt problem 1. Display the words worst, worse,best, and better. Ask: Which words compare twothings? Which words compare more than twothings? Call on volunteers to explain worst andbest. Then invite students to order four movietitles with an arrow on the board. Guide otherstudents to use the words to compare the titles.Ask: Which word describes the favorite movie?[best] And the movie nobody liked? [worst]Read the problem with students. UseStronger and Clearer Each Time to supportwriting. During partner review, encouragestudents to check whether they listed theplays in the correct order. Monitor as theyreview comparison words in the explanations.Help students discuss before they write aresponse to Connect It problem 1. Display thewords worst, worse, best, and better. Call onvolunteers to explain or provide examples.Have students read the problem. Invitevolunteers to use the meanings of worstand best to Say It Another Way. Then useStronger and Clearer Each Time to supportwriting. During partner review, encouragestudents to ask each other questions to makesure they listed the plays in the correct order,and to check whether they used correctcomparison words in their explanations. Curriculum Associates, LLCCopying is not permitted.LESSON 24 Order Positive and Negative Numbers553–554
LESSON 24 SESSION 1Explore Ordering Positive and Negative NumbersPurpose Explore the idea that you can use a number line tocompare positive and negative numbers.Understand that the greater of two numbers lies to theright of the other number on a horizontal number lineand above the other number on a vertical number line.STARTCONNECT TO PRIOR KNOWLEDGEStartLESSON 24 SESSION 1Explore Ordering Positiveand Negative NumbersPreviously, you learned about positive and negativenumbers. In this lesson, you will learn about orderingand comparing positive and negative numbers.Sweep Left Use what you know to try to solve theproblem below.A diagram of a football playSame and Different4A youth football team tries several different plays. The goal of each play is to gainyards. The coach records the result of each play. List the plays from worst to best.–3A BC DName of PlayResult: Yards Gained (1)or Lost (2)–215WedgeHookFlagDrawSweepToss23142512024 Curriculum Associates, LLC Copying is permitted.TRYITPossible SolutionsAll are whole-number integers.Math Toolkit algebra tiles, number lines, two-color countersSAMPLE AA and C are greater than 0.Possible work:A loss of 5 yd is worse than a loss of 4 yd and a loss of 4 yd is worse than a loss of 3 yd.A gain of 4 yd is better than a gain of 2 yd.B and D are less than 0.The value 0 comes between the losses and gains.A and D are even integers.Worst to best: Flag, Toss, Wedge, Sweep, Draw, HookB and C are odd integers.SAMPLE BFlagWHY? Support students’ facility with positiveand negative numbers.DISCUSS ITTossWedge25 24 23 22 21DrawHo