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1 LESSON 98 Temperature Power Up facts mental math Power Up I a. Number Sense: Simplify the improper fractions 6 4, 7 4, and , 1 4, 2 b. Number Sense: What is the reciprocal of 4?... of 1 4? 4 or 1 1 ; 4 1 or 4 c. Percent: What is 5% of $2?... 25% of $2?... % of $2? $; $5; $2 d. Powers/Roots: e. Estimation: Choose the more reasonable estimate for the capacity of a coffee cup: ml or L. ml f. Time: The movie began at 6:45 p.m. It ended 1 hour 5 minutes later. At what time did the movie end? 8:5 p.m. g. Calculation: 1 of 21, 2, + 1,, 6, + 2, 4 8 h. Roman Numerals: Write 18 in Roman numerals. XVIII problem solving Choose an appropriate problemsolving strategy to solve this problem. Sasha used 1-inch cubes to build this rectangular soild. How many 1-inch cubes did Sasha use? 6 1-inch cubes 4 in. in. in. New Concept Numbers that are greater than zero are positive numbers. Numbers that are less than zero are negative numbers. Zero is neither positive nor negative. On the number line on the following page, we show both positive and negative numbers. We write negative numbers with a minus sign in front of the number. Point A is at, which we read as negative three. 68 Saxon Math Intermediate 5

2 Thinking Skill Compare What is the freezing point of water on the Celsius scale? On the Fahrenheit scale? ºC; 2ºF A negative positive One place we might see negative numbers is on a thermometer. On a very cold day the temperature may drop below zero. If the temperature is four degrees below zero, we might say the temperature is minus four. Example 1 The high temperature for the day was 6 C. The thermometer shows the low temperature during the night. How many degrees are there between the high and low temperatures? The distance between tick marks is two degrees. Counting down from, we find that the thermometer indicates a temperature of 12 C. The high temperature was 6 C above zero, so the difference between the high and low temperatures is 18. C 2 C 2 Example 2 The highest temperature recorded in Death Valley is 14 F. The lowest temperature recorded is 15 F. Estimate the difference in the temperatures. We can use compatible numbers to estimate the difference = 12 There is about a 12 F difference. Lesson 98 69

3 Example Julius recorded the daily high and low temperatures in the desert for a week in the table below. Daily Temperatures ( C) Day Sun Mon Tues Wed Thurs Fri Sat High ( C) Low ( C) a. What was the median high temperature for the week? b. What was the mode of the low temperatures recorded? c. What was the range of temperatures for the week? a. To find the median high temperature, we first list the high temperatures in numerical order. 2, 25,, 2, 2, 4, 45 The middle number is 2, so the median is 2 C. b. The most frequently recorded low temperature is 15 C. c. The range of temperatures for the week is the difference between the highest high (45) and the lowest low (11). When we subtract, we find that the range is 4 C. Evaluate Could these temperatures represent a week in your community? Why or why not? See student work. Lesson Practice a. Use digits and symbols to write the temperature that is twelve degrees below zero on the Fahrenheit scale. 12 F b. What temperature is shown on this thermometer? 5 C c. If the temperature shown on the thermometer is 14 lower than the high temperature for the day, then what was the high temperature? 9 C C d. If the temperature falls º from the temperature shown, what will the temperature be? 8 C Refer to the table in Example to answer problems e and f. e. What is the median of the low temperatures for the week? 15 F f. What is the mean (average) of the high temperatures for the week? 2 F 64 Saxon Math Intermediate 5

4 Written Practice Distributed and Integrated * 1. (97) Justify There were 12 dogs and 8 cats at the class pet show. What was the ratio of cats to dogs at the show? Explain how you found your 2 answer ; sample: I created the ratio 8 to 12 and reduced to (8) a. Conclude What is the name of this solid? pyramid b. How many faces does it have? 5 faces. (7) Logan lives 1.2 miles from school. How far does he travel going from home to school and back home? 2.4 miles 4. (98) One day in January, the temperature at 9: p.m. in Juneau, Alaska, was 2 F. By 11: p.m. the temperature had dropped 5. What was the temperature at 11: p.m.? F * 5. (8, 98) Connect Refer to this number line to solve parts a and b. A B C D a. Which arrow could be pointing to 2 1 on the number line? D b. Which arrow is pointing to negative three? A 6. (49) A person who is a fast swimmer can swim at a rate of about 5 mph. A trout can swim about mph faster, and a sailfish can swim about 45 mph faster than a trout. About how fast can a sailfish swim? about 6 mph * 7. (1, 61) Multiple Choice If LN is perpendicular to JM, then which of these angles is obtuse? C A JNK C KNM B KNL D LNM J K N L M Lesson

5 8. (7) (7) (7) (7) (17) $ $ (56) , * 14. (94) R (54) $7.2 2 $ (59) (41) (6) (86) (86) of 25 2 * (96) (79) (9) Reduce: * 24. (98) a. The thermometer at left shows the highest temperature in Madison in December. What is the temperature shown? 79 F 9 b. The thermometer at right shows the lowest temperature in Madison in December. What is the temperature shown? 1 F 8 7 c. What is the range of the two temperatures shown? 8 F F 25. (78) * 26. (82, 9) a. Find the common factors of 7 and. 1, 2, 5, b. Use the GCF of 7 and to reduce (76) Compare: a < b < Saxon Math Intermediate 5

6 * 28. (88) Multiple Choice This regular hexagon contains 12 congruent right triangles. Look at one triangle and a second triangle right next to it. Which transformation moves the first triangle to the position of the second triangle? C A translation C reflection B rotation D slide * 29. (8) Multiple Choice Which of these numbers is a composite number? D A B 5 C 7 D 9 *. (69) Arrange these decimal numbers in order from least to greatest:.7,.67,.76, Early Finishers Real-World Connection Maria went scuba diving off the coast of Florida and stayed close to the shore. The deepest she dove was 8 feet below sea level, or 8 feet. Now she is standing on a dune that is 6 feet above sea level, or +6 feet. a. Draw a number line and label the two elevations Maria visited. See student work. b. What is the difference between the two points Maria has visited? 14 feet Lesson 98 64