? § Challenge small groups of students to practice using this kind of code to create and decode messages of their own. Invite them to use the tic-tac-toe code format to respond to the thief. § Have students introduce, talk about, and demonstrate other types of codes they know. ? ? ? ? ? ? ? ? ? ? ? ? by a unique cell shape. You may wish to have students practice the code by deciphering a word or two, or even a brief message. Then ask a volunteer to show how to decode the crook’s message.
Teaching Tips I Math Mysteries (cont.)
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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. Math Skills/Concepts: logical thinking, number sense Suggested Solution: Coded message—You were lucky this time. Teaching Tips: AB rief R eply ? ? ? ? ? ? ?
91 most and the least. You may wish to have students work with partners. § Since it is unlikely that students will have 10 pounds of any of these coins handy, guide them to measure lesser weights, and then use proportional reason- ing to find out how many of each coin are needed to make a weight of 10 pounds. § 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. Math Skills/Concepts: number sense (money amounts), proportional reasoning, measurement (weight) Suggested Solution: Carlotta should take the quarters; she wins about $200 by doing so. Teaching Tips: § Provide a scale, like a postal scale; students will need to weigh coins to solve the problem. Encourage them to first guess which coins will be worth the 91 § Have students describe their weighing strategies and why they chose them. (One reasonable approach to selecting a weight is to use a factor of 16— there are 16 ounces in a pound; students might find the number of coins that weigh 4 ounces, or even 2 ounces or 1 ounce.) § Students’ weighings and calculations should show that a pound of quarters 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. § Students will soon recognize the difficulty inherent in deciphering messages that use the telephone number pad code—there are three or more letters for each number (some number pads have the letters Q and Z). Therefore, it will be useful to discuss other clues that can help kids decode messages, such as § 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 (1) noticing the number of letters a word has, (2) recognizing digits that repeat in a message, (3) knowing which letters appear most often in words, and (4) understanding where certain letters are often found or not found in words. To give an example of this last form of clue, point out to students that if the number 8 appears at the end of a word, it is much more likely to repre- sent a t than either a u or a v . § Students will have an easier time deciphering this coded message if they have a telephone number pad to look at. You may wish to have a student copy one from a telephone onto the board or onto an overhead projector screen. § Invite students to make their own reply to the sleuths, or to the crook, using this code. Now students can solve the problem. If 4 flavors weren’t available for Gilbert to serve that day, then the store only had 8 flavors on hand. The symbol 8 C 2 represents the combination of 8 flavors of ice cream taken 2 at a time; (8 x 7) ÷ 2! = 28. Math Skills/Concepts: algebraic representation and modeling, fractions Suggested Solution: Libby—$12,000; Hector—$30,000; Dave—$60,000 Teaching Tips: 101 C arlotta’s C oins An rritating nheritance Students can work backwards to figure this out. Here’s how: They can use the symbol n C r to represent the combination of some number of flavors of ice cream taken 2 at a time. They can infer that some number divided by 2!, or 2, yields 66. That number is 132. Then they can deduce that 12 x 11 gives 132 permutations. They can use the symbol 12 C 2 to represent the combina- tion of 12 flavors of ice cream taken 2 at a time. ?
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An rritating nheritance
Math Skills/Concepts: algebraic representation and modeling, fractions Suggested Solution: Libby—$12,000; Hector—$30,000; Dave—$60,000 Teaching Tips: 40 Fabulous Math Mysteries Scholastic Professional Books
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. 5 2 § 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.
40 Fabulous Math Mysteries
244 Scholar Zone Summer: Math
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