Lesson 8: Ordering Integers and Other Rational Numbers

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1 Name Date Period Unit 2: Negative Numbers and the Number Line Test Review 1. Jane completes several example problems that ask her to find the opposite of the opposite of a number, and for each example, the result is positive. Jane concludes that when she takes the opposite of the opposite of any number, the result will always be positive. Is Jane correct? Explain, on the lines below, why or why not. (Before you answer this question, find the opposite of the opposite of a few numbers. See what happens and then determine if Jane is correct or not correct. Use your examples to help you explain your decision about Jane. Remember that opposite of the opposite sounds confusing but it just means to find the opposite of a number and then the opposite of that.) the opposite is the opposite of the opposite is the opposite is the opposite of the opposite is 6 Jane is not correct. All of Jane s problems must have started with a positive number because those all have positive answers whereas if she had started with a negative Name number she would have ended with a negative number. Jane should Date have done some more examples before she made the conclusion that she did. Lesson 8: Ordering Integers and Other Rational Numbers Exit 2. Ticket Order the following set of rational numbers from least to greatest. Then explian how you determined their order. Order the following set of rational numbers from least to greatest, and explain how you determined their order. 0, 1 2, 1, 3 1 3, 6, 5, 1, 21 5, 4-1, 0, 1, 4, 5, 6 To order these numbers from least to greatest I pictured their position on a number line. Once the numbers were on a number line I was able to correctly write the order by copying the numbers from the far left to the far right.

2 Name Date Lesson 4: The Opposite of a Number 3. In a recent Exit Ticket survey, a magazine reported that the recommended room temperature in the summer is 68 F. A wall thermostat, like the ones shown below, tells a room s In a recent survey, a magazine reported that the recommended room temperature in the summer is temperature 68 F. A wall in thermostat, Fahrenheit. like the ones shown below, tells a room s temperature in Fahrenheit. Sarah s Upstairs Bedroom Downstairs Bedroom a. Which bedroom is warmer than the recommended room temperature? a. Which bedroom is warmer than the recommended room temperature? Sarah s upstairs bedroom is warmer than recommended. b. Which bedroom is cooler than the recommended room temperature? 0 b. Which bedroom is cooler than the recommended room temperature? c. Sarah notices that her room s temperature is 4 F above the recommended temperature and the downstairs bedroom s temperature is 4 F below the recommended temperature. She graphs 72 and 64 on a vertical number line and determines they are opposites. Is Sarah correct? Explain. The downstairs bedroom is cooler than recommended. c. Sarah notices that her room s temperature is 4 F above the recommended d. After determining relationship between the temperatures, Sarah now decides to temperature and the downstairs bedroom s temperature is 4 F below the represent 72 F as 4 and 64 F as 4 and graphs them on a vertical number line. Graph 4 and recommended 4 on the vertical temperature. number line on the She right. graphs Explain 72 what and zero 64 represents on a vertical in this situation. number line and Name determines they are opposites. Is Sarah correct? Explain. Date Lesson 1: Positive Sarah is not correct. and Negative 72 and 64 are Numbers not opposites. on For the numbers Number to opposite Line they have to be the same number of units (or jumps) away from zero, one moving towards the positive and the other moving towards the negative. What Opposite Direction and Value 10/15/13 Sarah noticed, and incorrectly called opposites, is that both numbers are 4 units (or jumps) away from the recommended temperature of 68 F. Exit Ticket 4. If zero lies between a and d, give one set of possible values for a, b, c and d. Answers will vary for this question. You needed to pick a spot for zero somewhere between 1. If zero a and lies d between and then and label, give the one rest set of of the possible lines values accordingly. for,, My, and answer. is one of many possible correct answers a = -1 b = 2 c = 4 d = 7 2. Below is a list of numbers in order from least to greatest. Use what you know about the number line to complete the list of numbers by filling in the blanks with the missing numbers. 6, 5,, 3, 2, 1,, 1, 2,, 4,, 6

3 5. In math class, Christina and Brett are debating the relationship between two rational numbers. Read their claims below, and then write an explanation of who is correct. Use a number line to support your answer. Christina s Claim: I know that 3 is greater than than., so -3 must be greater Brett s Claim: Yes, 3 is greater than, but when you look at their opposites, their order will be opposite. That means that is greater than -3. Brett is correct. He is correct because, on a number line, Name is further to the right than -3 and Date the further a number is to the right the higher the value it is. Lesson 9: Comparing Integers and Other Rational Numbers Exit Ticket 6. Interpret 1. the Interpret number the number line line diagram shown shown below and below write a and statement write about an the inequality temperature for statement Tuesday compared to Monday at 11:00 p.m. about the temperature for Tuesday compared to Monday at 11:00pm. Inequality Statement: 40 F > -10 F OR -10 F < 40 F 2. If the temperature at 11:00 p.m. on Wednesday is warmer than Tuesday s temperature, but still below zero, what is a possible value for the temperature at 11:00 p.m. Wednesday?

4 Lesson 10: Writing and Interpreting Inequality Statements Involving Rational Numbers 7. Kendra Exit Ticket collected data for her Middle School Science Fair project. She surveyed people by asked them how many hours they sleep during a typical night. The chart below shows 1. Kendra how collected each data person s for her Science response project. compares She surveyed to people 8 hours asking (which them how is the many amount hours they of sleep hours during a typical night. The chart below shows how each person s response compares to 8 hours (which is the answer she doctors suggest people get) expected most people to say). Name Number of Hours (usually slept each night) Compared to 8 hours Frankie Mr. Fields Karla Louis 8 0 Tiffany a. Plot and label each of the numbers in the right-most column of the table above on the number line below. a. Plot and label each of the numbers in the right-most column of the table above on the number line below. b. List the numbers from least to greatest. b. List the numbers from the right-most column from least to greatest. c. Using your answer from part (b) and inequality symbols, write one statement that shows the relationship among all of the numbers. -1.0, 0, 0.5, 1.5 c. Using your answer from part b, write one inequality statement that shows the relationship among all of the numbers. Numbers 10/15/13 There are many possible answers for this question. You need to pick two of the numbers and use an inequality to represent their relationship.

5 3. Complete the number line scale. Explain and show how to find 2 and the opposite of 2 on a number line. 8. Complete the number line scale. Explain, on the lines below, how to find 2 and the opposite of 2 on a number line. To find 2 on a number line you should move two units to the right of zero. To find the opposite of two you should move two units to the left of zero. Opposites will always be symmetrical on a number line to zero. 2 Direction and Value 10/14/13

6 1: Absolute Value Magnitude and Distance 9. Jessie and his family drove to a picnic area on a mountain in Berkshires. In the morning, they followed a trail that led to the mountain summit, which was 2,000 feet above the is family drove up to a picnic area area. on a mountain. They then In returned the morning, to they picnic followed area a trail for that lunch. led to After the lunch, they hiked on ummit, which was 2,000 feet a trail above that the led picnic to the area. mountain They then overlook, returned to which the picnic was area 3,500 for feet lunch. below the picnic area., they hiked on a trail that led to the mountain overlook, which was 3,500 feet below the picnic area. a. Locate and label the elevation of the Mountain Summit and the Mountain e and label the elevation of the mountain Overlook summit on a and vertical mountain number overlook line. on The a vertical picnic number area represents line. The zero. Write a area represents zero. Write a rational rational number number to represent to represent each location. each location. Picnic area: 0 area: 0 Mountain Summit: 2,000 tain summit: Mountain Overlook: -3,500 tain overlook: bsolute value to represent the distance on the number line of each location from the area. ce from the picnic area to the mountain summit: ce from the picnic area to the mountain overlook: is the distance between the elevations b. Use absolute of the summit value and to overlook? represent Use the absolute distance valueon the number line from each our number line from part (a) to explain location your from answer. the picnic area. Distance from the picnic area to the Mountain Summit: 2,000 feet Distance from the picnic area to the Mountain Overlook: 3,500 feet c. What is the distance between the elevations of the Summit and Overlook? Use absolute value and your number line from part a to explain your answer. This distance from the Mountain Summit to the Mountain Overlook is 5,500 feet. To find the total distance 2,000 feet had to be added to the absolute value of -3,500 feet. Absolute value had to be used because the question asked for a total distance to be found and distance is always positive. 10/14/13

7 10. Mason was ordering the following rational numbers in math class: -3.3, -15, a. Order the numbers from least to greatest. -15, -3.3, b. List the order of their absolute values. 3.3, 15 c. Explain why the orderings in parts a and b are different. The order of the answers for part a and part b are reversed because when dealing with positive Name numbers the smaller numbers are closer to zero but with negative numbers Date the smaller numbers are father away from zero. This is why when ordering negative numbers and absolute Lesson 13: Statements of Order in the Real World values the answers are reversed. Exit Ticket 11. Loni and Daryl call each other from opposite sides of Watertown. Their locations are shown on the number line below using miles. Use absolute value to explain who is further distance (in miles) from Watertown. How much closer is one than the other? 1. Loni and Daryl call each other from opposite sides of Watertown. Their locations are shown on the number line below using miles. Use absolute value to explain who is a further distance (in miles) from Watertown. How much closer is one than the other? Daryl and Loni are both outside of Watertown but Daryl is father away. He is ten miles away whereas Loni is only 6 miles away. Even though Loni s distance is expressed as -6 on the number line it represents 6 miles because distance is always positive. Absolute value is how distance is dealt with when a negative number is being used. By using the absolute value of the numbers we can subtract 10 and to find a difference of 4 miles. 2. Claude recently read that no one has ever scuba-dived more than 330 meters below sea level. Describe what this means in terms of elevation using sea level as a reference point.

8 12. The picture below is a flood gauge that is used to measure how far (in feet) a river s water level is above or below its normal level. a. Explain what the number 0 on the gage represents and explain what the numbers above and below 0 represent. On the rain gague, zero represents the normal level of the water in the river. The numbers above zero represent when the river has more water in it than normal and the numbers below zero represent when the river has less water in it than normal. b. Describe what the picture indicates about the river s current water level. The picture shows that the current water level is below the regular level by two feet. c. What number represents the opposite of the water level shown in the picture, and where is it located on the gauge? What would it mean if the river water were at that level? 2.0 feet would represent the opposite of the current water level shown in the picture. It would be above the normal level and the riverbank would probably be flooded. d. If heavy rain is forecast for the area for the next 24 hours, what reading might you expect to see on the gauge tomorrow? Explain your reasoning. If it were to rain heavily for the next 24 hours I would expect the river level to rise up to the normal level. It would bring the river back to the expected level. Depending on how severe the rain is, it could even cause a flooding to occur.

9 13. Cole, Joachim and Austin play on the same soccer team. So far this season, Cole has scored 3 times as many goals as Austin and Joachim combined. If Austin has scored 2 goals and Joachim has scored 4 goals, how many goals has Cole scored? Write and simplify an expression to determine the number of goals that Cole has scored. 18 goals 14. During a family reunion last summer, 7 adults and 17 children from the Nakai family went to a water park. Admission was $16 per adult and $9 per child. What was the total cost of the admission? Write and simplify an expression to determine the cost of admission to the water park. $ The table shows the grams of protein for several food items. Food (Single Serving Size) Protein (g) Low-fat Yogurt (8 ounces) 4 Low-fat Pudding (8 ounces) 6 Low-fat Cottage Cheese (8 ounces) 4 Hard Cheese (1.5 ounces) 12 Write and simplify an expression that gives the total grams of protein in 2 servings of hard cheese and 2 servings of yogurt. 32 grams of protein 16. Place one pair of parentheses in the expression so that its value is 25. Then show the steps for simplifying the expression.