C arlotta’s C oins
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:
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9 5 § Students’ weighings and calculations should show that a pound of quarters has about 80 quarters, that a pound of dimes has about 192 dimes, and that a pound of nickels has about 88 nickels. So, 10 pounds of quarters is worth about $200, 10 pounds of dimes is worth $192, and 10 pounds of nickels is worth $44. § 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.) § 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 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.
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 40 Fabulous Math Mysteries Scholastic Professional Books ? ? ? ? ? ?
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: § 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. § As needed, review with students how to find the probability of an event occurring. Discuss that a problem such as this one involves conditional prob- ability, since a particular condition has reduced the size of the sample space. In this case, the sample space has been reduced by the fact that Victor already knows that the book he has selected is a fantasy. § Guide students to see that if their task were simply to find the probability of choosing a book with money inside, they would multiply the probability of choosing a fantasy ( , or ), by the probability of choosing a fantasy with a bill inside ( ). Then elicit that since Victor already knows he has selected a fantasy, to find the probability that the book has money inside, he needs to divide by the probability of choosing a fantasy: ( x ) ÷ = . 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. § You may want to discuss with students the kinds of conditions that will reduce a sample space. Ask them to explain what happens to the probability of an event occurring when the sample space is reduced in size. (It increases.) 5 2 20 60 1 3 1 3 1 3 1 5 1 5 1 5 105 U nder P articular C o nditions Math Skills/Concepts: probability and conditional probability ? ? U nder P articular C o nditions
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th Skills/Concepts: ebraic representation and modeling, fractions ggested Solution: by—$12,000; Hector—$30,000; Dave—$60,000 aching Tips: Suggested Solution: The probability is . Teaching Tips: An rritating nheritance 1 5
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.
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th Mysteries Scholastic Professional Books
Math Skills/Concepts: whole-number operations, mental math, distributive property Suggested Solution:
Grade 7 I Teacher’s Guide 245
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