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Number System Chapter QuestionsExplain what absolute value represents.Create an owing money example for comparing two negative numbers.What is the Cartesian (Coordinate) plane?How is the Cartesian plane divided?How are ordered pairs graphed?6th Grade Number System Chapter ProblemsAbsolute ValueClassworkFind:│-12││25││-47││13│Which numbers have the number given as their absolute value?15075141250How would you explain to a new student how to find the absolute value of -10 and +10?HomeworkFind:│32││-35││-55││3│Which numbers have the number given as their absolute value?72281552500How would you explain to a new student how to find the absolute value of 27 and -27?Comparing and Ordering IntegersClassworkPlace the appropriate inequality symbol between the following pairs of integers:3-7-8-1012-1177-4005Draw a number line and mark and label points for these numbers: 4, -7, 5, 0, -2, 1, -4Draw a number line and mark and label points for these numbers: -15, 0, 7, 4, -3, -1, 9If the temperature reading on a thermometer is 12°C, what will the new reading be if the temperature:Falls 15°Rises 3°Falls 12°If the temperature reading on a thermometer is -7°C, what will the new reading be if the temperature:Falls 3°Rises 5°Rises 9°HomeworkPlace the appropriate inequality symbol between the following pairs of integers:25-25-30-30-17-15-99-100-500-1Draw a number line and mark and label points for these numbers: 15, -3, 0, 5, -9, 7, 11Draw a number line and mark and label points for these numbers: -9, 1, 0, -3, 9, -1, -8If the temperature reading on a thermometer is 5°C, what will the new reading be if the temperature:Falls 15°Rises 3°Falls 12°If the temperature reading on a thermometer is -10°C, what will the new reading be if the temperature:Falls 3°Rises 5°Rises 9°Comparing and Ordering Rational NumbersClassworkPlace the appropriate inequality symbol between the following pairs of integers:270.3- 512-0.420.21425-0.3- 78-0.8-0.535Draw a number line and mark and label points for these numbers: 0, 34, -0.25, 134, -2.5Draw a number line and mark and label points for these numbers: 0.26, - 27, -3.1,1 23, -278 Homework Place the appropriate inequality symbol between the following pairs of integers:58-0.6-0.12- 1927-0.15120.55-0.75- 3400.36Draw a number line and mark and label points for these numbers: 212, -5, 2.26, 0, -327, 8.1, -3.5Draw a number line and mark and label points for these numbers: -0.73, 0, 2.53, 4.3, -0.39, -0.85 Cartesian PlaneClasswork1397020447000Label the quadrants, the origin, and the x-axis and y- axis. In what quadrant or axis is each point located? 247175969000A ____D ____ B ____E ____ C ____F ____Homework?Label the quadrants, the origin, and the x-axis and y- axis. 139705969000In what quadrant is each point located?1397010033000A ____D ____B ____E ____C ____F ____Graphing Ordered PairsClassworkPlot a point and label it with the letter in each location indicated.-3414191900A Quadrant III B Quadrant IC Quadrant IID Quadrant IVE OriginF x – axisG y – axisWrite the coordinates of each point on the graph. 8890889000Label the point in quadrant I, A ____Label the point in quadrant IV, B ____Label the point in quadrant II, C____Label the point on the x – axis, D____What is the point that is not labeled? ____Plot and label the following points:0000 A (2, 1.5) F (0, 4)B (1, 2) G (4, 0.25) C (-4, -2 1/2) H (-2, 0) D (-3, 1) I (0, - 3) E (5, -2) J (3, - 3)Name the coordinates of each point.031305500 A _____ D _______ B _____ E _______ C ______ F _______Reflect each of the coordinates (in the previous problem) over the x and y axis. Write the new coordinates below. A _____ _____ B _____ _____ C _____ _____ D _____ _____ E _____ _____ F _____ _____ HomeworkPlot a point and label it with the letter in each location indicated.-685806921500A Quadrant IB Quadrant IIIC Quadrant IVD Quadrant IIE OriginF y – axisG x - axisWrite the coordinates of each point on the graph.05842000Label the point in quadrant I, A ______Label the points in quadrant IV, B & C____________Label the points in quadrant II, E & F______ ______Label the point in quadrant III, D ______Label the origin, O ______Plot and label the following points: 0952500 A (-2, 1.25) F (0, 1)B (2, 2) G (1, 0.5) C (4, -2 1/2) H (0, -3) D (3, -1) I (-3, 0) E (-5, -2) J (2, -2)Name the coordinates of each point.76200-6985000 A _____ D _______ B _____ E _______ C ______ F _______Reflect each of the above coordinates (in the previous problem) over the x and y axis. Write the new coordinates below.A _____ _____ D _____ _____ B _____ _____ E _____ _____ C _____ _____ F _____ _____ Cartesian Plane ApplicationsClassworkWhat is the distance between the two graphed points?1562108255 Find the distance between each pair of points. (20,-10), (20,6)(-3,17), (15 1/4, 17)(5,1), (5,-6.5)(4,6), (4,-3)(6,-3), (6,-7)Use the following map to answer questions the next three questions.Each unit on the graph represents ? mile. What is the total distance driven, if Sebastian drives from his house, to Ulysses’ house and then to Rodger’s house?If the town library is at the map origin, describe the trip Tara would have to make to get to the library.What quadrant is Sebastian’s house in?Homework15621043180What is the distance between the two graphed points? Find the distance between each pair of points.(6,2), (0,2)(-3,-1), (-3,0.5)(-2,3), (-2,7)(-7 1/2, 8), (2,8)(6,-2), (-8, -2)Use the following map to answer the next three questions. If each unit on the graph represents 2/3 mile, what is the distance from Cutler to Dixon?Describe the trip a traveler would have to make to get from Edison to Brookdale.When asked what quadrant Fischer Lake is in, Sammy says it is in Quadrant II. George says that answer is not correct? Who do you agree with? Explain your answer.Number System Multiple Choice ProblemsWhat is the opposite of -15? 15-150 What is I-36I? 36-360What is I27I?27-27064198511049000-3 0>=<641985-6667500-5 -7>=<80010013525500– 57 -0.45>=< A point that lies on the y axis between quadrants I and II could have the following for the x and y-coordinates:(0, 5)(5, 0)(0, -5)(-5, 0)A point that lies on the x axis between quadrants I and IV could have the following for the x and y-coordinates:(0, 7)(7, 0)(0, -7)(-7, 0)Use this Cartesian plane to identify the coordinates for each point for #9 - #1113716003810ABC00ABCPoint A(-2,2)(0,2)(2, 2)(2,0)Point B(4, 3)(-4, 3)(4, -3)(3, 4)Point C(3, 2)(-3, -2)(-3, 2)(3, -2)Find the distance between the two points for #12 - #13(-5, 3.5) (-5, 7)4.5 units4 units3 units3.5 units(-7, 5) (-7, -4)1 unit9 units12 units3 unitsWhich of the following points would be located in the first quadrant?(-3, -1)(3, 1)(3, -1)(-3, 1)Which of the following points would be located in the fourth quadrant?(-4, 5)(-4, -5)(4, 5)(4, -5)A sunken ship is 150 feet below sea level. Which statement is expressed correctly?150 feet below sea level can be represented by the integer -150.The depth of the sunken ship is -150 feet below sea level.Both A & BThe temperature dropped by 10° F when the sun went down. Which statement is expressed correctly?The integer -10 represents the change in temperature in degrees Fahrenheit.The temperature decreased by 10° F.Both A & BNumber System Short Constructed Response QuestionsWhich numbers have 23 as their absolute value?Put the following numbers in order on a number line: -313, 4.7, 0, -2.58, 78, -5.2Explain how to plot (-3 ? , -6) on the coordinate plane.192405017843500Label the quadrants, x-axis, y-axis, and origin.5. Plot the following points on the coordinate grid:3143251079500A (0, 4)B (2 1/4, -3)C (-4, 0)D (-2, -3.25)E (-4, 4)F (1.5, -2)Number System Extended Constructed Response QuestionsEach unit on the coordinate grid represents 1 kilometer. Plot the following cities on the county map: Smithville (-3.5, 2), Horton (4, -1.5), Marina (2, 2), Fair Hills (-3, -1 1/2).What is the distance in kilometers from Smithville to Marina?What is the distance in kilometers from Horton to Fair Hills?108585013335000Below is a map of Lake County. Use the map to answer the following questions.If each unit on the graph represents 1/3 mile, what is the distance from Cutler to Dixon?Describe the trip a traveler would have to make to get from Brookdale to Edison.Marcus thinks that the train tracks are in Quadrant IV. Is he correct? Explain your answer.It is well known that Antartica has freezing temperatures. The chart below shows the average monthly temperature from 1958-1020, at Vostok Station in Antartica.MonthJanFebMarAprilMayJuneJulyAugSeptOctNovDecAverage Temp F(rounded to nearest ? number.)-26-48-72-85-86-85-88-90-87-71-45-25Plot these temperatures on a number line.Hannah wrote the inequality -72 > -85 to compare the average temperatures for March and April. Explain what this comparison means about the temperatures for these two dates.A scuba diver is on an expedition to view whales in their natural habitat. The diver begins his journey on a boat, at 10 feet above the surface of the water. He spots his first whale at 100 feet below the surface.Write an integer to represent the diver’s depth.Draw and plot these points on a number line to show the distance from the diver’s position on the boat to the location where he spots his first whale.The diver views a school of fish on his way back to the surface, 30 feet above the spot where he viewed his first whale. What integer represents the diver’s depth during this sighting? Add this location to the number line.Answer Key12254713-150, 150-75, 75-14, 14-1250, 1250Absolute value is the distance from zero on the number line, regardless of direction. -10 and 10 are both 10 units from zero, so │-10│=10 and │10│=10.3235553-72, 72-28, 28-155, 155-2500, 2500Absolute value is the distance from zero on the number line, regardless of direction. -27 and 27 are both 27 units from zero, so │-27│=27 and │27│=27.3>-7-8>-1012>-117=7-4<00<5Order on number line: -7, -4, -2, 0, 1, 4, 5Order on number line: -15, -3, -1, 0, 4, 7, 9-3°C15°C0°C-10°C-2°C2°C25>-25-30=-30-17<-15-99>-100-5<00>-1Order on number line:-9, -3, 0, 5, 7, 11, 15Order on number line: -9, -8, -3, -1, 0, 1, 9-10°C8°C-7°C-13°C-5°C-1°C27 < 0.3- 512 > -0.420.2 < 1425 < -0.3- 78 < -0.8-0.5 35Order on number line: -2.5, -0.25, 0, 34, 134Order on number line: -3.1, - 278, - 27, 0.26, 12358 > -0.6-0.12 < - 1927 > -0.1512 < 0.55-0.75 = - 340 < 0.36Order on number line: -5, -3.5, -327, 0, 2.26, 212, 8.1Order on number line: -0.85, -0.73, -0.39, 0, 2.53, 4.3457200103505IIIIIIIVy-axisx-axis00IIIIIIIVy-axisx-axis170688016510origin00origin IIIy-axisIIIVIIV41910045720IIIIIIIVy-axisx-axis00IIIIIIIVy-axisx-axis 1706880101600origin00originIIIIIIIIIIVIV4864101905 a. A(-3,-2)b. B(2,2)c. C(-3,2)d. D(2,-2)e. E(0,0)f. F(2,0)g. G(0,2)199453512065The origin is not labeled. 52768546990001912620137160F020000F191262085725002514600133985A00A221742090170B020000B2225040901700024892006413500308610045085G00G105918011430D020000D10591804191000304292043180001333500132080H020000H1348740132080003383280128270E020000E332994012827000800100114935C00C80010089535002773680102870J020000J194818057150I020000I2773680571500019126205715000 1912620137160020000 (-4, -5)(0, 3)(-2, 1)(1, -2)(5, 3)(5, -4) (-4, 5) (4, -5) (4, 5)(0, -3) (-2, -1) (2, 1) (2, -1)(1, 2) (-1, -2) (-1, 2)(5, -3) (-5, 3) (-5, -3)(5, 4) (-5, -4) (-5, 4)285750106045Answers will vary. 556260-126365a. A(5,2)b. B (2, -1)c. C (3, -4)d. D(3, -2)e. E(-3,1)f. F(-1, 3)g. O(0,0) (-2, 3)(-4, 0)(0, -2)(1, 4)(3, -2)(-1, -4) (-2, -3) (2, 3) (2, -3)(4, 0)(0, 2)(1, -4) (-1, 4) (-1, -4)(3, 2) (-3, -2) (-3, 2)(-1, 4) (1, -4) (1, 4) 31618 ?7.59410 ? miles She would have to travel 4 units (or 3 miles) down.Quadrant II461.549 ?142 2/3 milesA traveler would have to travel 3 units (or 2 miles) up and 5 units (or 3 1/3 miles) to the left, in either order.George is correct, because Fischer Lake is in all four quadrants.Number System Multiple Choice Questions1. a2. a3. a4. c5. a6. c7. a8. b9. c10. c11. b12. d13. b14, b15. d16. a17. cNumber System Short Constructed Response1. 23, -232. Order on the number line: -5.2, -3 13, -2.58, 0, 78, 4.73. Start at the origin and go left to -3 ? on the x axis, then go down 6 from that position.50482572390IIIIIIIVy-axisx-axisorigin00IIIIIIIVy-axisx-axisorigin4. 5. Number System Extended Constructed Responsesee grid below.5.5 kilometers7 kilometers 1 1/3 milesA traveler would have to travel 2 ? units (or 5/6 of a mile) and 5 units (or 1 2/3 miles) to the right, in either order. His answer is not complete. The train tracks are in quadrants III and IV.a.b. It means that the average temperature for March (-72) is warmer than the average temperature for April (-85).-100b and c.c. -70 ................
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