5-1 Integers and Graphing

Transcription

1 Write an integer for the situation. Explain the meaning of zero in the situation miles below sea level The words "below sea level" indicate an integer less than zero so the integer is 3. Sea level is represented by the integer earning $45 The word "earning" indicates a positive integer, so 45 represents the situation. The integer 0 represents neither earning nor spending. 3. moving back 5 spaces on a game board The words "moving back" indicate an integer less than zero, so the integer 5 represents the situation. The integer 0 represents neither moving backward nor moving forward. Graph the integer or set of integers on a number line The integer 5 is located 5 units to the left of zero. Place a point at 5. esolutions Manual - Powered by Cognero Page 1

2 5. {2, 3, 0, 1} Place the integers in order from least to greatest. 3, 0, 1, 2 Graph the integers. 3 is located 3 units to the left of 0. 0 is located at 0. 1 is located 1 unit to the right of 0, and 2 is located 2 units to the right of The data set {+4, 1, 2, 0} shows a change in number of state representatives for four states after the last census. Graph the change in number of representatives. Explain the meaning of zero in this situation. The integer 0 represents neither a gain or loss in number of representatives. esolutions Manual - Powered by Cognero Page 2

3 7. Use Math Tools The table shows the record low temperatures for several states. Graph the temperatures on a number line. Order the integers from least to greatest. 34, 32, 30, 29, 27. esolutions Manual - Powered by Cognero Page 3

4 8. Use Math Tools The table shows the number of points earned for each action in a video game. While playing the video game, Kevin fell in water, jumped over a rock, touched a cactus and climbed a mountain. Graph the number of points he earned for each action on the number line. Order the integers associated with falling in water, -10, jumping over a rock, +5, touching a cactus, 15, and climbing a mountain, +10 from least to greatest. 15, 10, 5, 10 esolutions Manual - Powered by Cognero Page 4

5 9. Model with Mathematics Complete the graphic organizer by writing words or symbols used to represent positive and negative integers. 10. Persevere with Problems A football team receives the ball on the10 yard line. a. They make a gain of 15 yards in the first play. What yard line is the ball on? b. What represents zero in this situation? Explain. a. "A gain" means adding a positive integer. Since the team starts on the 10 yard line, add = 25 The ball is on the 25 yard line. b. Zero is represented by the starting point. The 10 yard line represents neither a gain nor a loss in yards. 11. Justify Conclusions The temperature outside is 15 F. If the temperature drops 20, will the outside temperature be represented by a positive or negative integer? Explain your reasoning. A drop of 20 is represented by the integer 20 so the temperature is 20 less than 15. A drop of 15 would result in a temperature of 0 F. Since the drop of 20 is greater than 15, the temperature is below zero and will be represented by a negative integer. 12. Identify Structure Describe the characteristics of each set of numbers that make up the set of integers. Negative integers are to the left of zero on the number line, positive integers are to the right of zero on the number line, and zero is neither positive nor negative. 13. Reason Inductively Explain how to find the distance between -2 and 3 on a number line. Sample answer: Locate 2 and 3 on a number line. Count the number of units between each integer and 0. 2 is 2 units to the left of zero and 3 is 3 units to the right. So, the number of units between 2 and 3 is or 5 units. esolutions Manual - Powered by Cognero Page 5

6 Write an integer for the situation. Explain the meaning of zero in the situation below zero "Below zero" indicates a negative integer. So, 13 below zero is represented with 13. The integer 0 represents zero degrees. 15. spending $25 "Spending" indicates a negative integer. So, spending $25 is represented by 25. The integer 0 represents neither spending nor earning yard gain "Gain" indicates a positive integer. So, 13-yard gain is represented by 13. The integer 0 represents neither a gain nor a loss. Graph the integer or set of integers on a number line Graph 8 on the number line. 18. {0, 3, 1, 1} Order the integers from least to greatest. 3, 1, 0, 1 esolutions Manual - Powered by Cognero Page 6

7 19. { 1, 1, 2} Order the integers from least to greatest. 2, 1, 1 esolutions Manual - Powered by Cognero Page 7

8 20. {3, 5, 4, 1} Order the integers from least to greatest. 5, 1, 3, 4 esolutions Manual - Powered by Cognero Page 8

9 21. {4, 2, 2} Order the integers from least to greatest. 2, 2, 4 esolutions Manual - Powered by Cognero Page 9

10 22. The data set {+3, 1, 2, +1} shows the moves a player made forward or backward in a board game. Graph the moves the player made. Explain the meaning of zero in this situation. Order the integers from least to greatest. 2, 1, 1, 3 Graph the integers on a number line. The integer 0 represents a move neither forward nor backward. 23. Model with Mathematics The table shows the overnight low temperatures for 5 days in Minneapolis. Graph the temperatures on a number line. Order the integers from least to greatest. 6, 1, 0, 1, Jackson owes his sister Monica $15. Monica has a $10 bill in her pocket. Explain the meaning of zero in this situation. The integer 0 represents neither owing money nor having money. esolutions Manual - Powered by Cognero Page 10

11 25. On Monday Kennedy spent $2 on lunch. On Tuesday she spent $1 on a snack. On Wednesday, her sister gave her $3. "Spent" indicates a negative integer. "Gave" indicates a positive integer. Order the integers from least to greatest. 2, 1, 3 Fill in the 26. with < or > to make the inequality true. Since the tens digit is the same for each number, compare the ones digit. 6 is greater than 2 So, 27. Since the tens digit is the same for each number, compare the ones digit. 1 is less than 3 So, esolutions Manual - Powered by Cognero Page 11

12 28. Compare the ones digit in each number. 2 is less than So, 44 has a number in both the tens and ones place. 4.4 has a number in the ones and tenths place, but no number in the tens place. 30. So, 15 has a number in both the tens and ones place. 6.8 has a number in the ones and tenths place, but no number in the tens place. 31. So, The ones digit is the same in each number so compare the tenths place. 8 is less than 9 So, esolutions Manual - Powered by Cognero Page 12

13 32. Ally bought pound of cashews and pound of granola. Plot the fractions on the number line. Which quantity is greater? Explain. The number line is divided into 6 sections. Graph on the fifth tick mark. so graph half way between 0 and the first tick mark. is greater; It is closer to 1 and greater than. is less than. 33. The number of raffle tickets the student council sold over three days is shown in the table. How many total raffle tickets did they sell? Add the total for each day = 104 They sold 104 raffle tickets. esolutions Manual - Powered by Cognero Page 13