Suggested Solution: It was not a cold day. 15ºC is equivalent to about 59ºF, which is a mild tempera- ture by most standards. The witness would not have been freezing, and the thief would not have been wearing a down coat. Teaching 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 this one. Explain any courtroom procedures or court-related language used in this story, as needed. § Also, as needed, review the distinction between Celsius and Fahrenheit temperature scales. Discuss a formula to use (here’s one: ºF = x ºC + 32) to convert a temperature given in one scale to the equivalent temperature in the 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 the two scales. 9 5 9 5 94 Math Skills/Concepts: organizing data, making inferences, logical reasoning Suggested Solution: toaster—Ankers, blender—Reids, candlesticks—Wixteds, salad bowl—Motts Teaching Tips: students of the simpler problem above, ask, “What is the sum of seats in rows 1 and 30?” (49) “In rows 2 and 29?” (49) Then ask, “How many pairs of rows with sums of 49 are there?” (15) Lastly, ask, “How can you use this information to find the total number of seats in rows 1 through 30?” (Multiply 49 by 15.) § Recognize and support other expressions of this pattern or other patterns stu- dents find and use to solve this problem. Extend by challenging students to use a pattern to find the sums of the numbers 1-100 or 1-1,000. ? ? ? ? ? ? ? ? ? ? ? ? ? § This problem is similar in nature to MIXED-UP IDENTITIES and MIXED-UP WINNERS. Once again, have students begin by identifying what information is given in the problem and what information they need to find out. Guide them again to record in an organized way all the data the Picketts provide. Discuss ways to do this. § You may want to have students work in pairs. Have partners discuss the inferences they make from the data they’ve recorded. § Ask a volunteer to put his or her table on the overhead projector or board. Ask the volunteer to explain how he or she used what the table shows to fill in the missing data. Invite discussion. ?
Teaching Tips I Math Mysteries (cont.)
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Math Skills/Concepts: algebraic representation and modeling, fractions Suggested Solution: Libby—$12,000; Hector—$30,000; Dave—$60,000 Teaching Tips: Math Skills/Concepts: ratios, critical (and imaginative!) thinking Suggested Solution: Yes; on Mercury, Kenneth would be 20 years old. Teaching Tips: 5 2 § Make sure students understand the relationships between the sizes of the three 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. Math Skills/Concepts: algebraic representation and modeling, fractions Suggested Solution: Libby—$12,000; Hector—$30,000; Dave—$60,000 Teaching Tips: AC ase from S pace Suggested Solution: It was not a cold day. 15ºC is equivalent to about 59ºF, which is a mild tempera- ture by most standards. The witness would not have been freezing, and the thief would not have been wearing a down coat. Teaching 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 this one. Explain any courtroom procedures or court-related language used in this story, as needed. § Also, as needed, review the distinction between Celsius and Fahrenheit temperature scales. Discuss a formula to use (here’s one: ºF = x ºC + 32) to convert a temperature given in one scale to the equivalent temperature in the 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 the two scales. n a P ickle ? ? ? ? ? ? ? An rritating nheritance § 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. An rritating nheritance
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40 Fabulous Math Mysteries Scholastic Professional Books
91 § 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. § Make sure students understand the relationships between the sizes of the three 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. 91 5 2 § 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!
40 Fabulous Math Mysteries
240 Scholar Zone Summer: Math
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