Yes; on Mercury, Kenneth would be 20 years old. Teaching Tips:
? § This mystery requires students to suspend their sense of disbelief long enough to tackle a problem filled more with fantasy and fun than with middle-school mathematics. If needed, point out to students that there are (as of this writing) no signs of life on the planet Mercury, and that even if there were, the likelihood that life would have a close physical resemblance to that on Earth would be minimal, at best. Students shouldn’t have too much trouble accepting the idea that “Mercurians” can drive a car and even have automotive preferences! ? ? ? ? ? ? ? ? ? ? ?
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92 Although the graphs show the same information, they differ in appearance due to differences in the horizontal and vertical scales and to differences in incre- ments shown on the vertical scales. Augie’s graph shows a more gradual increase in prices for two reasons; (1) there is more space between the years along the horizontal axis, and (2) there are greater increments along the vertical scale. Teaching Tips: § Help students interpret these graphs, as needed. Have them describe the Math Skills/Concepts: proportional reasoning, measurement (time), prime numbers, palindromes Suggested Solution: The robbery took place at 7:45 A . M . The license plate number is 64946. Teaching Tips: § There are two problems for students to solve in this story. Make sure they understand the information presented. Guide students to first figure out the time of the robbery and then to determine the license plate number. Math Skills/Concepts: correspondence between data sets and graphical representation of the data Suggested Solution: Math Skills/Concepts: number sense, fractions Suggested Solution: Each server should get $18 in tips. There was a total of $54 in tips to start. Teaching Tips: § Tell students that using real data about the solar system can help them solve the perplexing mystery in this story. They can use an almanac or other source to see that Mercury, which is closer to the sun than the earth is, has an orbit of about 88 days—about one-fourth of the time it takes the earth to make one revolution. By deduction, 1 year on Earth is equal to about 4 years on Mercury. That 1:4 ratio explains how Kenneth “aged” 8 years in the two years he was away. § Review with students the information that is given in the problem and what they can infer from it. For instance, begin by eliciting from them how much money was in the jar when Danielle reached in ($24, since she left $16 after taking her third—$8). Make sure students understand that each of the other servers took and left of what was in the jar when she or he reached in. § Guide students to work backwards to determine how much money was in the jar before each of the other two servers reached in. For instance, they can go next to Felix, who was the second one to take his tips. Students can know that he left $24. Ask, “How much money did Felix take if he took a third, which left $24 in the jar? ($12) How much was in the jar when he reached in for his share?” ($36) Students can use these answers to determine how much Ellie took and left. With those final pieces of information, they can figure out how much money was in the jar to begin with. § Have students explain how they reached their solutions. Invite them to suggest ways for the servers at Carla’s to avoid this problem in the future. § Discuss why, in Lucia’s case, the mean more accurately describes her test results than the mode does. Ask students to give the median of her scores (66), and to explain why that is or is not a useful measure of her test performances. 91 The mode of Lucia’s test scores is 91; the mean of the scores is about 73.14. The mean is the more reasonable representation of her performance on the tests. Teaching Tips: § This debate over the interpretation of test scores is a good starting point for a discussion about the different measures of center and spread, and the usefulness of each measure in analyzing given situations. Talk, for instance, about real-life situations for which the mode is a more appropriate measure than the mean, or for when it is the median that is the most useful measure of average. Discuss times when knowing the range of data is very important. § Challenge students to list two sets of seven test scores for Lucia, one for which the mode is the most accurate description of the data, and one for which the median works best. Discuss their choices. ? ?
A T icklish T ip P roblem ggested Solution: was not a cold day. 15ºC is equivalent to about 59ºF, which is a mild tempera- e by most standards. The witness would not have been freezing, and the thief uld not have been wearing a down coat. aching Tips: You may want to briefly discuss the roles (defense and prosecution) of the different attorneys, and of other participants in a courtroom during a trial like his one. Explain any courtroom procedures or court-related language used in his story, as needed. 1 3 Also, as needed, review the distinction between Celsius and Fahrenheit emperature scales. Discuss a formula to use (here’s one: ºF = x ºC + 32) o convert a temperature given in one scale to the equivalent temperature in he other. You may wish to use this opportunity to review other relationships between Celsius and Fahrenheit scales. You may also find it useful to discuss benchmark temperatures students can easily use to compare temperatures in he two scales. 2 3 Math Skills/Concepts: statistical measures of average Suggested Solution: 9 5 40 Fabulous Math Mysteries Scholastic Professional Books 95 ? ? ? ? ? ? G rappling o ver G rades
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An rritating nheritance
th Skills/Concepts: ebraic representation and modeling, fractions ggested Solution: by—$12,000; Hector—$30,000; Dave—$60,000 aching Tips:
The B ad A rt B urglary Make sure students understand the relationships between the sizes of the hree inheritances. Then guide them to represent each of the inheritances using an algebraic expression, and then to write and solve an equation to solve the problem. One possible equation to use is x + x + 5 x = 102,000, where x represents the smallest inheritance, the amount of money Libby will receive. Invite students to suggest other equations to use. Some students may guess and then adjust their guesses to solve the problem. Ask them to explain their reasoning. One way: First determine which of the nephews or nieces gets the smallest part of the inheritance; choose a reason- able money amount for that niece or nephew; use that amount to find the others; adjust it as needed to fit the requirements of the problem. A C ase of A ppearances 5 2
th Mysteries Scholastic Professional Books
Grade 7 I Teacher’s Guide 241
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