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? Math Skills/Concepts: organizing data, making inferences, logical reasoning Suggested Solution: Maria—math, Edgar—science, Kim—creative writing, Tom—art Teaching Tips: ? ? ? ? ? ? ? ? ? ?
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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. § This problem is similar in nature to MIXED-UP IDENTITIES. Talk about what information is given in the problem, and what information students need to find out. Have them identify what the categories of information are. Guide students to record in an organized way all the data Jack provides. Talk about ways to do this. § You may want to have students work in pairs. Have partners discuss the inferences they make from the data given. 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: number sense, whole number operations, pattern recognition § 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. § You may find it useful to invite a volunteer to put his or her table on the overhead projector or board, and then explain how he or she used known information recorded in the table to fill in the rest of the table. Encourage students to use that same strategy to find the number of seats in the hall. Ask them to tell what information they will need in order to do so (the number of seats in the 30th row). Discuss how they can use a pattern to find that number (one way: List the number of seats in the first few rows to notice that each row has 9 more seats than the number of the row; using that pattern, they can see that row number 30 will have 39 seats). Reminding 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.) 2 3 Math Skills/Concepts: number sense, whole number operations, pattern recognition Math Skills/Concepts: organizing data, making inferences, logical reasoning Suggested Solution: Maria—math, Edgar—science, Kim—creative writing, Tom—art Teaching Tips: 93 Suggested Solution: The hall has 735 seats. Teaching Tips: § The solution to this problem involves finding sums of consecutive numbers. The most efficient way to do that is to recognize and use a pattern. To begin, you may want to start with a simpler problem, as an example. For instance, have students find the sums of the numbers from 1 to 10. Work through this simpler problem together. Guide students to recognize that it can be solved by finding five sums of 11: 1 + 10, 2 + 9, 3 + 8, and so on. § You may want to have students work in pairs. § Students may have success by guessing robbery times and then checking and adjusting those guesses. Visual learners may benefit by looking at an analog clock. Ask students to explain the method they used to figure out the time. § Review the meaning of palindromes and of prime numbers, as needed. Some students may benefit by making a list of prime numbers less than 30. Invite volunteers to explain how they used all the clues to figure out the remaining numbers of the license plate. Ask them to explain the usefulness of Nat’s final clue. § This problem is similar in nature to MIXED-UP IDENTITIES. Talk about what information is given in the problem, and what information students need to find out. Have them identify what the categories of information are. Guide students to record in an organized way all the data Jack provides. Talk about ways to do this. § You may want to have students work in pairs. Have partners discuss the inferences they make from the data given. § You may find it useful to invite a volunteer to put his or her table on the overhead projector or board, and then explain how he or she used known information recorded in the table to fill in the rest of the table. ? ?
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. 9 5 C elebrity (pause) S eating M ixed- U p W inners ? ? ? ? ? ?
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40 Fabulous Math Mysteries Scholastic Professional Books
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. 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. C elebrity (pause) S eating
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th Mysteries Scholastic Professional Books
40 Fabulous Math Mysteries Scholastic Professional Books
n a P ickle
Grade 7 I Teacher’s Guide 239
Math Skills/Concepts: organizing data, making inferences, logical reasoning
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