Number System Chapter Questions

Transcription

1 Number System Chapter Questions. What is an integer?. Explain what absolute value represents.. Create an owing money example for comparing two negative numbers.. What is the Cartesian (Coordinate) plane? 5. How is the Cartesian plane divided? 6. How are ordered pairs graphed? NJ Center for Teaching and Learning ~ ~

2 Integers Homework 6 th Grade Number System Chapter Problems. Write an integer to represent each situation: a. The temperature rises degrees. b. The submarine dives 5 feet below sea level. c. The team loses 5 yards. d. You earn $5 babysitting. e. A company loses $,000 in a month. f. A fee of $.50 is charged. g. You deposit $00 in your bank account. h. Sea level.. Using the scoring system in the game of Jeopardy (you earn points for correct responses and lose points for incorrect responses) what would be the final score after the following 5 responses: a. Player answers a 00 point question correct, a 50 point question wrong, a 50 point question correct, a 50 point question wrong, and 50 point question correct. b. Player answers a 00 point question wrong, a 00 point question correct, a 00 point question wrong, a 00 point question wrong and 50 point question correct. c. Player gets a 50 point question correct, a 00 point question wrong, a 50 point question wrong, a 00 point question correct and a 50 point question correct.. Use the Jeopardy scoring system and create a sequence of 5 answers that would give you a score of: a. -50 points b. 00 points c. 0 points Comparing and Ordering Integers Homework. Place the appropriate inequality symbol between the following pairs of integers: a. 5-5 b c d e f Draw a number line and mark and label points for these numbers: 5, -, 0, 5, -9, 7, 6. Draw a number line and mark and label points for these numbers: -9,, 0, -, 9, -, If the temperature reading on a thermometer is 5 C, what will the new reading be if the temperature: a. Falls 5 b. Rises c. Falls NJ Center for Teaching and Learning ~ ~

3 8. If the temperature reading on a thermometer is -0 C, what will the new reading be if the temperature: a. Falls b. Rises 5 c. Rises 9 Absolute Value Homework 9. Find: a. b. -5 c. -55 d. 0. Which numbers have the number given as their absolute value? a. 7 b. 8 c. 55 d How would you explain to a new student how to find the absolute value of 7 and -7?. What is the opposite of -50?. What is the opposite of?. What is the opposite of? 5. What is the opposite of -7? Comparing and Ordering Rational Numbers Homework 6. Place the appropriate inequality symbol between the following pairs of integers: a.!! -0.6 b !!! c d.!!! 0.55 e !! f Draw a number line and mark and label points for these numbers:!, -5,.6, 0, -!, 8., -.5!! NJ Center for Teaching and Learning ~ ~

4 8. Draw a number line and mark and label points for these numbers: -0.7, 0,.5,., -0.9, NJ Center for Teaching and Learning ~ ~

5 Cartesian Plane Homework 7. Label the quadrants, the origin, and the x-axis and y- axis In what quadrant or axis is each point located? y A D B E B C E F E C x D A - F 9. Label the quadrants, the origin, and the x-axis and y- axis NJ Center for Teaching and Learning ~ 5 ~

6 y 0. In what quadrant is each point located? B A A B D E x C - E C F D F Graphing Ordered Pairs homework y. Plot a point and label it with the letter in each location indicated x A Quadrant III B Quadrant I C Quadrant II D Quadrant IV E Origin F x axis G y axis - - y. Write the coordinates of each point on the graph. Label the point in quadrant I, A x 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? NJ Center for Teaching and Learning ~ 6 ~

7 . Plot and label the following points: A (,.5) F (0, ) B (, ) G (, 0.5) C (-, - /) H (-, 0) D (-, ) I (0, - ) E (5, -) J (, - ) - - y. Name the coordinates of each point A D B E B E E C x C F A D F 5. Reflect each of the above coordinates over the x and y axis. Write the new coordinates below. A B C D E F NJ Center for Teaching and Learning ~ 7 ~

8 Homework y x 6. Plot a point and label it with the letter in each location indicated A Quadrant I B Quadrant III C Quadrant IV D Quadrant II E Origin F y axis G x - axis - - y 7. Write the coordinates of each point on the graph. Label the point in quadrant I, A x 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 - 8. Plot and label the following points: A (-,.5) F (0, ) B (, ) G (, 0.5) C (, - /) H (0, -) D (, -) I (-, 0) E (-5, -) J (, -) - - NJ Center for Teaching and Learning ~ 8 ~

9 y 9. Name the coordinates of each point A D A D B E B x C F - - C E F Reflect each of the above coordinates over the x and y axis. Write the new coordinates below. A B C D E F Cartesian Plane Applications Classwork What is the distance between the two graphed points? 5. Find the distance between each pair of points. 5. (0,-0), (0,6) 5. (-,7), (5 /, 7) 5. (5,), (5,-6.5) 55. (,6), (,-) 56. (6,-), (6,-7) NJ Center for Teaching and Learning ~ 9 ~

10 Use the following map to answer questions Each unit on the graph represents ¾ mile. What is the total distance driven, if Sebastian drives from his house, to Ulysses house and then to Rodger s house? 58. If the town library is at the map origin, describe the trip Tara would have to make to get to the library. 59. What quadrant is Sebastian s house in? Homework What is the distance between the two graphed points? 60. Find the distance between each pair of points. 6. (6,), (0,) 6. (-,-), (-,0.5) 6. (-,), (-,7) 6. (-7 /, 8), (,8) 65. (6,-), (-8, -) NJ Center for Teaching and Learning ~ 0 ~

11 Use the following map to answer questions If each unit on the graph represents / mile, what is the distance from Cutler to Dixon? 67. Describe the trip a traveler would have to make to get from Edison to Brookdale. 68. 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. NJ Center for Teaching and Learning ~ ~

12 Number System Multiple Choice Problems. What is the opposite of -5? a. 5 b. -5 c. 0. What is I-6I? a. 6 b. -6 c. 0. What is I7I? a. 7 b. -7 c a. > b. = c. < a. > b. = c. < 6.!! a. > b. = c. < A point that lies on the y axis between quadrants I and II could have the following for the x and y-coordinates: a. (0, 5) b. (5, 0) c. (0, -5) d. (-5, 0) 8. A point that lies on the x axis between quadrants I and IV could have the following for the x and y-coordinates: a. (0, 7) b. (7, 0) c. (0, -7) d. (-7, 0) NJ Center for Teaching and Learning ~ ~

13 Use this Cartesian plane to identify the coordinates for each point for #9 - # A C B - 9. Point A a. (-,) b. (0,) c. (, ) d. (,0) 0. Point B a. (, ) b. (-, ) c. (, -) d. (, ). Point C a. (, ) b. (-, -) c. (-, ) d. (, -) Find the distance between the two points for # - #. (-5,.5) (-5, 7) a..5 units b. units c. units d..5 units NJ Center for Teaching and Learning ~ ~

14 . (-7, 5) (-7, -) a. unit b. 9 units c. units d. units. Which of the following points would be located in the first quadrant? a. (-, -) b. (, ) c. (, -) d. (-, ) 5. Which of the following points would be located in the fourth quadrant? a. (-, 5) b. (-, -5) c. (, 5) d. (, -5) 6. A sunken ship is 50 feet below sea level. Which statement is expressed correctly? a. 50 feet below sea level can be represented by the integer -50. b. The depth of the sunken ship is -50 feet below sea level. c. Both A & B 7. The temperature dropped by 0 F when the sun went down. Which statement is expressed correctly? a. The integer -0 represents the change in temperature in degrees Fahrenheit. b. The temperature decreased by 0 F. c. Both A & B Number System Short Constructed Response Questions. Which numbers have as their absolute value?. Put the following numbers in order on a number line: -!!,.7, 0, -.58,!!, -5.. Explain how to plot (- ½, -6) on the coordinate plane. NJ Center for Teaching and Learning ~ ~

15 . Label the quadrants, x-axis, y-axis, and origin Plot the following points on the coordinate grid: A (0, ) B ( /, -) C (-, 0) D (-, -.5) - E (-, ) - - F (.5, -) - NJ Center for Teaching and Learning ~ 5 ~

16 Number System Extended Constructed Response Questions. Each unit on the coordinate grid represents kilometer. a. Plot the following cities on the county map: Smithville (-.5, ), Horton (, -.5), Marina (, ), Fair Hills (-, - /). b. What is the distance in kilometers from Smithville to Marina? c. What is the distance in kilometers from Horton to Fair Hills? Below is a map of Lake County. Use the map to answer the following questions. NJ Center for Teaching and Learning ~ 6 ~

17 a. If each unit on the graph represents / mile, what is the distance from Cutler to Dixon? b. Describe the trip a traveler would have to make to get from Brookdale to Edison. c. Marcus thinks that the train tracks are in Quadrant IV. Is he correct? Explain your answer. NJ Center for Teaching and Learning ~ 7 ~

18 . It is well known that Antartica has freezing temperatures. The chart below shows the average monthly temperature from , at Vostok Station in Antartica. Month Jan Feb Mar April May June July Aug Sept Oct Nov Dec Average Temp F (rounded to nearest ½ number.) a. Plot these temperatures on a number line. b. Hannah wrote the inequality -7 > -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 0 feet above the surface of the water. He spots his first whale at 00 feet below the surface. a. Write an integer to represent the diver s depth. b. 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. c. The diver views a school of fish on his way back to the surface, 0 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. NJ Center for Teaching and Learning ~ 8 ~