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Lesson Plan -- Integers, Opposites, Absolute ValueChapter Resources- Lesson 3-1 Integers and the Number Line- Lesson 3-1 Integers and the Number Line Answers- Lesson 3-2 Opposites and Absolute Value- Lesson 3-2 Opposites and Absolute Value Answers- Lesson 3-3 Compare and Order Integers- Lesson 3-3 Compare and Order Integers Answers1

Name �——————LESSON3-1CaliforniaStandardsGr. 4 NS 1.8: Useconcepts ofnegative numbers(e.g., on a numberline, in counting,in temperature, in“owing”).Gr. 5 NS 1.5: Identifyand represent on anumber line decimals,fractions, mixednumbers, and positiveand negative integers.Date ————————————1V\MOMZ[ IVL \PM 6]UJMZ 4QVMWords to RememberInteger : Any positive whole number,the opposite of any positive wholenumber, or zero218, 25,Negative integer : Any integer thatis less than 02357, 242, 23Positive integer : Any integer greaterthan 01,39,0,4,122422Getting Started Previously you learned what whole numbers are andhow to graph them on a number line. You can also place integers on anumber line. On a number line positive integers are to the right of 0 andnegative integers are to the left of 0.Identifying IntegersIdentify the integers in the following list.13.3, 217, 22, 72}5Solution-PPL "IFBEFor more onopposites, seeLesson 3-2 onpage 6.3.3 is not an integer since it contains a number after a decimal point.217 is an integer since it is the opposite of a positive whole number.22 is an integer since it is a whole number.172}is not an integer since it contains a fraction, which is not a whole5number.T:A 0 1;1. Circle the integers in the following list.392, 2100.66, }, 455, 267282. Circle the negative integers in the following list.512, 215, }, 22.5, 219, 28.7592Math InterventionBook 3 Integers and Rational NumbersCopyright by McDougal Littell, a division of Houghton Mifflin Company.E@)584-

Name �——————E@)584- Date ————————————Graphing Integers on a Number LinePlace the integers 23, 4, 1, and 22 on the number line.2202Solution;\MX Determine whether each number lies to the right or to the left of 0.Negative integers lie to the left of 0: 23 and 22.Positive integers lie to the right of 0: 4 and 1.;\MX Place each integer on the number line.23 will lie 3 units tothe left of 0.221 will lie 1 unit tothe right of 0.022 will lie 2 units tothe left of 0.Copyright by McDougal Littell, a division of Houghton Mifflin Company.E@)584- 4 will lie 4 units tothe right of 0.Modeling a SituationThe high temperature on Monday in San Francisco was 83 F.The high temperature on Tuesday was 728F. Represent the changein high temperatures from Monday to Tuesday using an integer.Solution83 2 72 5 118F;\MX Find the change in temperature fromMonday to Tuesday.;\MX Determine whether the temperature change should be positiveor negative.Since the temperature decreased, the sign should be negative.ANSWER The high temperature change was 2118F.T:A 0 1;3. Place 21, 24, and 3 on the number line.04. Manuel has a piece of ribbon 63 inches long.After removing some of the ribbon for a project,the ribbon is now 44 inches long. Use an integerto represent the change in the length of the ribbon.Math InterventionBook 3 Integers and Rational Numbers3

Name �——————Date ————————————SummarizeAn integer is a positive whole number, the opposite of a positivewhole number, or zero.Positive integers are positive whole numbers and are found to the rightof zero on a number line.Negative integers are opposites of positive whole numbers and arefound to the left of zero on a number line.Modeling Situations with IntegersReal-world situations can be modeled by integers. When the situationrepresents a decrease, use a negative integer to describe it. When thesituation represents an increase, use a positive integer to describe it.8ZIK\QKMMatch the description with the integer that represents it.1. An increase of 11 pointsA. 230 ft2. A decrease of 11 pointsB.3. A decrease of 30 feetC. 211 points4. An increase of 30 feetD.30 ft6.6100.1, 0.5, 45 }, 21055, 7Circle the integers.455. 2}, 99, 122.55, 237, 14177. 676, 2932.9, 12, }43349. 2722.1, 21434, 222 } , 073338. 215, 268 }, 55.17, }45110.10,922, 3.46, 25Place the integers on a number line.11. 21, 0, 2, 2512. 26, 21, 1, 2413. 22, 3, 5, 614. 210, 4, 6, 2415.412, 5, 0, 22Math InterventionBook 3 Integers and Rational Numbers16. 213, 12, 8, 24Copyright by McDougal Littell, a division of Houghton Mifflin Company.11 points

Name �——————Date ————————————Tell if the situation represents an increase or a decrease. Then representthe amount of the increase or decrease by an integer.17. Karla has 20 to spend at a jewelry store. After buying a bracelet shehas 6 remaining.18. Hannah is building a tower of blocks with her younger brother.They currently have 14 blocks stacked in their tower. After heryounger brother knocks over the tower there are 4 blocks leftstanding.19. Jesse is filling an empty bucket with water. After he fills the bucketthere are 3 gallons of water in it.20. You and a friend order a pizza that has 10 slices in it. After you andyour friend finish eating, there are 4 slices remaining.Copyright by McDougal Littell, a division of Houghton Mifflin Company.,1, A7 / - 1 '21. Fill in the missing words. To place integers on a numberline, graph to the right of zero andgraph to the left of zero.22. Explain your reasoning. What kinds of numbers are integers?23. Describe. Give an example of a real-life increase and anexample of a real-life decrease that can be described by integers.Explain your thinking.Math InterventionBook 3 Integers and Rational Numbers5

Answer KeyAnswers to Book 3 Integers and Rational NumbersLesson 3-1, pp. 2–5Try this:1. 92, 455, 26722. 215, 2193.2432104. 219 in.Practice:1. B2. C3. A4. D5. 99, 237, 146. 21055, 77. 676, 128. 2159. 21434, 010. 10,922, 2511.2512.2613.2221 02024121035 6014.2104 6240 215.22 0512248 120 216.21317. decrease; 2 140 418. decrease; 210 blocks19. increase; 3 gal

Answer Key20. decrease; 26 slices21. positive integers; negative integers22. Sample answer: A number is an integer if it is a positive whole number,the opposite of a positive whole number, or zero.23. Sample answer: Real-life increase: Adding 8 songs to your MP3 playercan be described with the positive integer 8. Real-life decrease:A penalty in football means that a team loses yardage. Getting a 15 yardpenalty in a football game can be described with the negative integer 15.

Name �——————3-2CaliforniaStandardsGr. 7 NS 2.5: Understandthe meaning of theabsolute value of anumber; interpret theabsolute value as thedistance of the numberfrom zero on a numberline; and determine theabsolute value of realnumbers.Algebra 1 2.0: Studentsunderstand and usesuch operationsas taking theopposite, finding thereciprocal, taking aroot, and raising to afractional power. Theyunderstand and use therules of exponents.7XXW[Q\M[ IVL )J[WT]\M IT]MWords to RememberOpposites: Two numbers that are the samedistance from 0 on a number line, but onopposite sides of 07 and 27 are opposites.9 and 29 are opposites.Absolute value of a number : The distance anumber is from 0 on a number line.Remember that distance is always a positive quantity (or zero).Show absolute value with vertical bars on each side of the number, forexample z17z.Getting Started In Lesson 3-1 you learned how to place integers on anumber line. Now you will find the distance between a point and zero on thenumber line to find the opposite of a number or the absolute value of a number.E@)584- Finding the Opposite of an IntegerUse a number line to find the opposite of 3.Solution;\MX Place 3 on a number line.0 ;\MX Determine how far 3 is from 0.f0.rgehtonisu3;\MX Find the opposite of 3. The opposite of a number must be the samedistance from 0 as the original number, but in the opposite direction. So, the opposite of 3 must be 3 units to the left of 0, or at 23.ANSWER The opposite of 3 is 23.T:A 0 1;1.64Math InterventionBook 3 Integers and Rational NumbersUse a number line to find the opposite ofthe number.2. 22Copyright by McDougal Littell, a division of Houghton Mifflin Company.LESSONDate ————————————

Name �——————E@)584- Date ————————————Finding the Absolute Value of an IntegerUse a number line to find µ22µSolutionThe absolute value of a number is the distance the number is from 0.;\MX Graph 22 on a number line.0;\MX Determine how far 22 is from 0.22lf0ehtonisu.ANSWER The absolute value of 22 must be 2 because distances are alwayspositive (or 0).Finding the Opposite and Absolute Valueof an IntegerE@)584- Use a number line to find the opposite of 4 and to find µ 4µ.SolutionCopyright by McDougal Littell, a division of Houghton Mifflin Company.;\MX Place 4 on a number line.0 ;\MX Determine how far 4 is from 0.f0.rgehtonisu4;\MX The opposite of 4 must be the same distance from 0 but in theopposite direction. So, the opposite of 4 is 24. The absolute valueof 4 must be 4 because distances are always positive (or 0).ANSWER The opposite of 4 is 24, and u4u 5 4.T:A 0 1;Use a number line to evaluate the expression.3. u7u 54. The opposite of 26 5and u26u 5.Math InterventionBook 3 Integers and Rational Numbers7

Name �——————Date iteThe opposite of a number is a number that is the same distancefrom zero on a number line as the given number, but on theopposite side of zero.Absolute ValueThe absolute value of a number is the distance between 0 andthe number on a number line. Remember that distance is alwaysa positive quantity (or zero). Absolute value is shown by verticalbars on each side of the number.8ZIK\QKMMatch the description with the number that represents it. You may usesome answer choices more than once or not at all.1. Opposite of 19A. 2192. u91uB.3. u219uC. 2914. Opposite of 291D.91Evaluate the expression.85. Opposite of 276. Opposite of 68. Opposite of 229. u1u7. u29u10. Opposite of 2811. Opposite of 4412. u2199u13. Opposite of 25014. u0u15. u2762u16. Opposite of 1017. u78u18. Opposite of 9219. Opposite of 23120. Opposite of 27421. Opposite of 93622. u2302u23. u24002u24. Opposite of 7625. 2u668u26. Opposite of 6527. Opposite of 23228. 2u28701uMath InterventionBook 3 Integers and Rational NumbersCopyright by McDougal Littell, a division of Houghton Mifflin Company.19

Name �——————Date ————————————Read and solve the problem. Then explain your answer.29. Simone told you that she placed a point on a number line thathad an absolute value of 15. At what two numbers could she havegraphed her point?30. Julia and Roberto are each holding cardswith integers on them. One has a positiveinteger and the other has a negative integer.The teacher has put a number line on thefloor using tape and asks Julia and Robertoto stand on the points that represent theirnumbers. How can they determine if theirnumbers are opposites without showingeach other their cards?Copyright by McDougal Littell, a division of Houghton Mifflin Company.,1, A7 / - 1 '31. Fill in the missing words. The of a numberis the distance between and the number on anumber line.32. Explain your reasoning. What is the opposite of the oppositeof 23?33. Explain your reasoning. How are the opposite of a numberand the absolute value of a number alike? How are they different?Math InterventionBook 3 Integers and Rational Numbers9

Answer KeyLesson 3-2, pp. 6–9Try this:1.2 so, 4 unitsto the left0242.1 4 unitsto the right41 2 units to 2 so, 2 unitsthe leftto the right220; 24;223.7;704.60Practice:1. A2. D3. B4. D5. 76. 267. 98. 29. 110. 22811. 24412. 19913. 5014. 015. 76216. 21017. 7818. 29219. 31; 6; 6