NUMBER Chapter 7 Big Idea Understanding integers can help me describe the world around me. Learning Goals I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. Essential Question How can integers be used to represent real-life contexts? Important Word integer
Representing Integers Draw, build, and write to represent integers. Example: Samuel was told that the temperature today is going to be 7 C. How could you explain to Samuel what this temperature means? Josie s strategy: I showed him a thermometer and marked -7 o C on the thermometer. 1-1 Marcus s strategy: I built -7 using integer rods. -1-7 -7 Pierre s strategy: I skipped left along the number line to get from to -7. -7 11. Copy and complete each number line. a. b. c. 2 6 8 3 2 3 1 13 11 1 9 146 CHAPTER 7: Integers
Representing Integers (continued) 12. Show the following integers on a number line. a. 4 b. 6 c. 2 d. 12 e. 1 f. An integer is a negative or positive number with no fractional part. 13. Write the integer for each picture. a. b. c. d. e. 14. Write a word that means the opposite of each word below. a. win b. minus c. down d. backward e. positive f. rise 1. Write the integer opposite of each given number. a. 7 b. 2 c. 4 d. 6 16. Give an example of a negative and a positive integer you might find in each situation, and explain what each integer could mean. a. temperature b. golf c. accounting d. scuba diving CHAPTER 7: Integers 147
Representing Integers (continued) 17. Write the integer that is five less than each given number. a. 12 b. 6 c. 3 d. 1 e. 6 18. Explain the strategy you used to find the numbers in question 7. 19. Sheila recorded the daily high in her city for one week. Write an integer to show each temperature. Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 1 1 1 1 1 1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1 1. Where might you see integers in real life? 11. Explain the strategies you used to represent integers. I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. 148 CHAPTER 7: Integers
Integers in Real Life Draw, build, and write to represent integers from real-life contexts, such as board games, temperatures, golf, and accounting. Example: Merve was watching golf with his dad. He noticed that they kept talking about over par and under par. Merve s dad explained that par is the score every golfer is compared to, and that a golfer with a score under par needs fewer strokes to hit his or her ball into the hole. The first golfer finished the round at under par. How could Merve represent this score as an integer? Janice s strategy: I wrote to represent being under par. Chole s strategy: I drew a number line and represented par with. For under par I jumped left five on the number line. par Phoenix s strategy: I built the number using an integer rod. For under par I used a rod. par Fatima s strategy: If par is even, then under par would be minus, which is. 11. Several friends were playing snakes and ladders. Each time one of them landed on the tail of a snake, that person moved back spaces. Each time someone landed on the bottom of a ladder, that person moved ahead spaces. a. Hassan landed on a ladder and moved ahead 12 spaces. Write this as an integer. b. Raina landed on a snake and moved back eight spaces. Represent this as an integer. CHAPTER 7: Integers 149
Integers in Real Life (continued) 12. Some scientists were studying icebergs. One particular iceberg measured m above sea level and 17 m below sea level. a. Draw a picture to represent the iceberg and sea level. Write integers to show the measurements to the top and bottom of the iceberg. b. Explain how you know where zero is on the iceberg. c. As the iceberg travelled south, it melted. It then measured 3 m above sea level and 12 m below sea level. On the same drawing, show the new size of the iceberg. d. Explain whether the location of zero on each of the drawings would change. 13. Marnie wanted to buy a present for her mom, but had no money, so she borrowed $1 from her Dad. a. Explain why we could represent the amount of money Marnie has as 1. b. Use the strategy of your choice to show 1. 14. Pathma was driving to the University for a concert. She parked in the underground parking on level P3. a. Draw a picture to represent where Pathma might have parked. b. Describe the number of levels she will have to come up, to get back to ground level. 1 CHAPTER 7: Integers
Integers in Real Life (continued) 1. Cyndy recorded the temperature over three days in January. The temperatures she recorded were 12 C, 1 C, and 18 C. a. Draw a thermometer to represent these integers. b. Describe how the temperature changed over the three days. c. Explain whether she would be likely to record similar temperatures in July. 16. Use an integer to represent each of the following statements: a. Miles dove 2 metres below sea level while scuba diving. b. Janet scored 3 under par in golf. c. Kirsten parked 2 levels below ground. d. Samina after she lent $1 to Marcus. e. Drew had 7 goals scored against him in hockey. f. The average temperature in January is 8 degrees below zero. 17. Use what you know about integers to solve the following number riddle: I am an integer below zero. I am less than 4. I am more than 8. I am an odd integer. 18. Explain why there could be more than one answer for question 7. 19. How might drawing a picture or building a model help you understand integers? I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. CHAPTER 7: Integers 11
Comparing Conundrums Draw, build, or write to compare integers. Example: Compare the integers 4 and +2 using the symbols <, >, or =. Blaine s strategy: I compared the numbers on a number line. I know that numbers further to the right are bigger, so -4 2. -7-6 -4-3 -2-1 1 2 Marty s strategy: I showed these numbers using integer rods. -4 2-7 -6-4 -3-2 -1 1 2 I know that the more white rods there are, the bigger the number is. I also know that the more red rods there are, the smaller the number is. -4 2 Marissa s strategy: I used an egg carton. I took beans away for negative numbers, and put beans in for positive numbers. I added 2 beans to show 2. I took out 4 beans to show -4. Because I added beans to show +2, I know it is the larger number. 2-4 12 CHAPTER 7: Integers
Comparing Conundrums (continued) 11. Identify the larger of the two numbers indicated on each number line. a. b. c. d. e. 12 11 1 9 8 7 6 4 3 2 1 1 2 3 4 6 7 8 9 1 11 12 12 11 1 9 8 7 6 4 3 2 1 1 2 3 4 6 7 8 9 1 11 12 12 11 1 9 8 7 6 4 3 2 1 1 2 3 4 6 7 8 9 1 11 12 12 11 1 9 8 7 6 4 3 2 1 1 2 3 4 6 7 8 9 1 11 12 12 11 1 9 8 7 6 4 3 2 1 1 2 3 4 6 7 8 9 1 11 12 12. Identify the warmer temperature from each pair of thermometers. a. b. 1 1 1 1-1 -1-1 -1-1 -1-1 -1 c. d. 1 1 1 1-1 -1-1 -1-1 -1-1 -1 CHAPTER 7: Integers 13
Comparing Conundrums (continued) 13. Explain whether each statement is true or false. a. Zero is a positive number. b. 3 > 4 c. < d. 2 is the same distance from as 2 is from on a number line. e. 12 and 12 are opposite integers. 14. Identify the larger number in each pair of integer rods and compare the numbers using the less than (<), greater than (>), or equal to (=) symbols. a. b. c. 1. Identify the larger integer in each pair. Compare the numbers by writing an expression using the less than (<), greater than (>), or equal (=) symbols. 14 a. or b. or c. or CHAPTER 7: Integers
Comparing Conundrums (continued) 16. Compare the numbers in each pair using the symbol <, > or =. a. or Negative Positive Negative Positive b. or Negative Positive Negative Positive c. or Negative Positive Negative Positive 17. Use the strategy of your choice to compare the following sets of numbers using the symbol <, > or =. a. 3, b. 8, 8 c., 2 d., 8 18. Explain the strategy you used to compare integers. 19. Explain why is larger than 1. I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. CHAPTER 7: Integers 1
Integer Sports Draw, build, and write to compare integers from real-life contexts, such as hockey scores, golf scores, parking underground, money, and altitude. Example: Jonas is a goalie for his community hockey team. In one game, four goals were scored against him. In another game, five goals were scored against him. In which game did he play better? How do you know? Michel s strategy: I put the number of goals scored against Jonas in each game on a number line. I recorded the goals in the first game at -4 and the goals in the second game at. S F -7-6 -4-3 -2-1 1 2 Because -4 is closer to zero than, and I know that when a negative number is closer to zero it is larger, I know that -4 is the higher number. Jonas played better in the first game. Shouyang s strategy: I drew two hockey nets, and for each goal scored, I drew a hockey puck. There were four hockey pucks in the first net, and five in the second net. I know that Jonas let in more goals in the second game. He played better in the first game. 16 CHAPTER 7: Integers
Integer Sports (continued) Jinee s strategy: I used egg cartons to show the goals. For each goal scored against Jonas, I took away one bean. From one egg carton, I took out four beans, and from the other I took away five beans. I had to take fewer beans from the first egg carton, so I know Jonas let in fewer goals in the first game. He played better in the first game. 11. Mrs. Berry s class is studying professional golfers scores in 29. Sergio Garcia s average score was 13 under par and Anthony Kim s average score was 16 under par. a. How could you record each score as an integer? b. If Sergio Garcia and Anthony Kim were ranked first and second in the PGA golf tour, which of them would rank higher? How do you know? c. What does it mean to be under par? 12. Patrick and Scott went scuba diving on the Great Barrier Reef looking for stingrays. At 1 m below sea level Patrick saw his first stingray. Scott saw his first stingray at 17 m below sea level. a. How could you record each depth as an integer? b. If they were diving together, who would have seen the stingray first? How do you know? c. What integer represents the measurement at sea level? CHAPTER 7: Integers 17
Integer Sports (continued) 13. Andrei was looking at the hockey statistics for the Calgary Flames and the Edmonton Oilers. He was trying to predict which team would win the next Battle of Alberta. Calgary had had 19 losses, Edmonton had had 28 losses. a. How could you record each team s losses as a negative integer? b. If the trend continues, which team do you think will win the next Battle of Alberta? Why? 14. A team of scientists working in the Arctic studying iceberg depth measured two icebergs. The first iceberg measured 22 metres below the surface and six metres above the surface. The second iceberg measured 2 metres below the surface and four metres above the surface. a. Which iceberg extended deeper into the ocean? b. Which iceberg extended higher above the ocean? c. What strategies did you use to answer these questions? 1. Maria and Lynda were meeting at the Citadel Theatre for a play. Maria parked on level P4 in the underground parking lot. Lynda parked on level P6 in the underground parking lot. a. How could you record each girl s distance below the ground as a negative integer? b. Who had to walk further to get to the theatre? How do you know? 16. The weather channel was showing the predicted temperatures for the weekend. The forecast was 8 C for Saturday and 1 C for Sunday. a. Build a model to show which day was predicted to be warmer. b. Draw a picture to show which day was predicted to be cooler. c. Explain how each strategy showed the temperature difference. 17. Describe the strategies you use to solve problems with integers. 18. Why might we record a loss as a negative number? I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. 18 CHAPTER 7: Integers
Ordering Integers Draw, build, and write to order integers. Example: Manuel was given five cards, each showing a different integer, and asked to order them from smallest to largest. 3 2 2 Ricardo s strategy: I marked each integer on a number line. This lined them up for me automatically. -1-9 -8-7 -6-4 -3-2 -1 1 2 3 4 6 7 8 9 1 The order is, -2,, 2, 3. Anthony s strategy: I built each number using integer rods. I know that the number with the longest white integer rod is the largest number, and the number with the longest red integer rod is the smallest number. The order of the cards should be, -2,, 2, 3. -2 2 3 Hanna s strategy: I imagined each integer as a temperature, then I could order the numbers from the coldest to the warmest. The coldest temperature was and the warmest was 3. In order, they are, -2,, 2, 3. CHAPTER 7: Integers 19
Ordering Integers (continued) 11. Arrange each set of egg cartons from the smallest to the largest number. a. b. 12. Order each set of temperatures from highest to lowest. a. 1 1 1 1 1-1 -1-1 -1-1 -1-1 -1-1 -1 b. 16-1 -1-1 -1-1 -2-2 -2-2 -2-3 -3-3 -3-3 -4-4 -4-4 -4-6 -6-6 -6-6 CHAPTER 7: Integers
Ordering Integers (continued) 13. Study these sets of integer rods. Write the corresponding integers and order them from largest to smallest. a. b. 14. Use the strategy of your choice to order each set of integers from smallest to largest. a. 2, 9, 12, 16, 3 b. 41, 16, 32, 27, 9 c. 4, 43, 17, 7, 1 1. The number lines below are mixed up. Correct each number line to show the integers in order from smallest to largest. a. 2 4 6 8 1 1 2 4 6 8 b. 6 3 4 2 2 1 1 3 4 6 c. 1 1 1 1 16. How is the strategy you used to compare integers similar to the strategy you used to order integers? 17. Explain, in your own words, what an integer is. I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. CHAPTER 7: Integers 161
Interesting Integers Draw, build, and write to order integers from real-life contexts, such as skiing, diving, money, hockey, and golf. Example: The record low temperatures in some Saskatchewan cities are shown in the table. How might you order these temperatures? City Temperature Date La Ronge 48 Jan., 1973 Lloydminster 42 Jan. 8, 1991 Moose Jaw 46 Jan. 23, 1943 Saskatoon Feb. 1, 1893 Swift Current 42 Dec. 23, 1983 Sheila s strategy: I drew a number line from to -4 and plotted each temperature on the number line. -4 Lloydminster, Swift Current I'd order these temperatures from coldest to warmest as: Saskatoon, La Ronge, Moose Jaw, Lloydminster, and Swift Current. -4 Moose Jaw La Ronge Saskatoon 162 CHAPTER 7: Integers
Interesting Integers (continued) 11. Denver is looking at the yards scored against his favourite team, the Edmonton Eskimos, for the last four games. They are: 4, 3, 1,. Denver determined that the Eskimos best game was the third game when their yards-against score was 1. a. Is he right? How do you know? b. What would mean in this situation? 12. Purvi has been taking diving classes. She is quite excited because she is managing to get deeper with almost every dive. Her last five dives were to depths of metres, 9 metres, 6 metres, 12 metres, and 8 metres. a. What was her deepest dive? How do you know? b. Order her dives from deepest to shallowest. c. Which dive was most likely her first? How do you know? 13. Palehswan is taking money from her bank account. Her last five withdrawals were $1, $2, $1, $, and $3. a. How would you record these withdrawals as integers? b. What was the largest amount of money she took out? How do you know? CHAPTER 7: Integers 163
Interesting Integers (continued) 14. Habitat for Humanity is building houses in New Orleans. New Orleans has many neighbourhoods where the land is close to sea level. The 9th Ward is 2 m below sea level, Metairie is 3 m below sea level, Terrytown is 1 m above sea level, and St. Bernard Parish is 1 m below sea level. a. Write these numbers as integers. b. Use the strategy of your choice to determine the best community to live in. 1. After reading about New Orleans, Emma researched other places in the world that had land below sea level. She recorded the elevations of some locations in the table below. Location Laguna del Corbón, Argentina Elevation 1 m Brawley, United States 34 m Turfan Depression, China 14 m Lammefjord, Denmark 7 m Tiberias, Israel 27 m a. Which location is the furthest below sea level? b. Order the locations from lowest elevation to highest elevation. c. What strategy did you use to compare the elevation of the locations? d. Research elevations of other areas above or below sea level. 16. Jaden has different groups of numbers from different situations. The first group of numbers she has is 4, 2, 12, 8, 1. a. Order the integers from smallest to largest. b. Describe a situation these numbers might represent. 17. Write a problem that includes ordering integers in the solution. Exchange problems with a classmate and solve each other s problem. 18. Explain the strategy you find the most helpful for ordering integers. I can use manipulatives to show my understanding of integers. I can use drawings to show my understanding of integers. I can use symbols to show my understanding of integers. 164 CHAPTER 7: Integers