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Solutions for Session 10, Grades 6-8, Part C
See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6
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Problem C1 | |
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The answer is 33 trips: 4 trips to bring over each adult plus 1 more trip for the 2 children.
Possible responses for questions (a)-(d), which apply to all the problems in Part C, are as follows:
a. | Answers will vary. Most people draw a diagram showing the number of trips to get 1 or 2 adults across the river and then generalize to 8 adults. |
b. | Answers will vary. The problem requires students to find a way to represent the problem, look for a pattern, and generalize. The problem can be thought of as a recursive pattern. |
c. | Answers will vary. Most students draw a diagram with arrows showing people crossing the river in each direction. This arrow representation allows students to "see" the number of trips required for each adult. |
d. | Answers will vary. For example: What sequence of events must happen to get 1 adult across the river? Where are the 2 children at the end of this sequence? How many trips does the sequence require? What must happen so that 1 adult and 2 children are across the river? How does this change if there are 2 adults? Think of "undoing" your sequence to find out the number of adults with 2 children that required 13 trips to cross the river. |
<< back to Problem C1
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Problem C2 | |
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The answer is 25 trips: 4 trips to bring over each adult, plus 1 more trip for the 2 children.
a. | Answers will vary. Most people draw a diagram showing the number of trips to get 1 or 2 adults across the river and then generalize to 8 adults. |
b. | Answers will vary. The problem requires students to find a way to represent the problem, look for a pattern, and generalize. The problem can be thought of as a recursive pattern. |
c. | Answers will vary. Most students draw a diagram with arrows showing people crossing the river in each direction. This arrow representation allows students to "see" the number of trips required for each adult. |
d. | Answers will vary. For example: What sequence of events must happen to get 1 adult across the river? Where are the 2 children at the end of this sequence? How many trips does the sequence require? What must happen so that 1 adult and 2 children are across the river? How does this change if there are 2 adults? Think of "undoing" your sequence to find out the number of adults with 2 children that required 13 trips to cross the river. |
<< back to Problem C2
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Problem C3 | |
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The answer is 61 trips: 4 trips to bring over each adult, plus 1 more trip for the 2 children.
a. | Answers will vary. Most people draw a diagram showing the number of trips to get 1 or 2 adults across the river and then generalize to 8 adults. |
b. | Answers will vary. The problem requires students to find a way to represent the problem, look for a pattern, and generalize. The problem can be thought of as a recursive pattern. |
c. | Answers will vary. Most students draw a diagram with arrows showing people crossing the river in each direction. This arrow representation allows students to "see" the number of trips required for each adult. |
d. | Answers will vary. For example: What sequence of events must happen to get 1 adult across the river? Where are the 2 children at the end of this sequence? How many trips does the sequence require? What must happen so that 1 adult and 2 children are across the river? How does this change if there are 2 adults? Think of "undoing" your sequence to find out the number of adults with 2 children that required 13 trips to cross the river. |
<< back to Problem C3
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Problem C4 | |
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The answer is 93 trips: 4 trips to bring over each adult, plus 1 more trip for the 2 children.
a. | Answers will vary. Most people draw a diagram showing the number of trips to get 1 or 2 adults across the river and then generalize to 8 adults. |
b. | Answers will vary. The problem requires students to find a way to represent the problem, look for a pattern, and generalize. The problem can be thought of as a recursive pattern. |
c. | Answers will vary. Most students draw a diagram with arrows showing people crossing the river in each direction. This arrow representation allows students to "see" the number of trips required for each adult. |
d. | Answers will vary. For example: What sequence of events must happen to get 1 adult across the river? Where are the 2 children at the end of this sequence? How many trips does the sequence require? What must happen so that 1 adult and 2 children are across the river? How does this change if there are 2 adults? Think of "undoing" your sequence to find out the number of adults with 2 children that required 13 trips to cross the river. |
<< back to Problem C4
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Problem C5 | |
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The answer is 401 trips: 4 trips to bring over each adult, plus 1 more trip for the 2 children.
a. | Answers will vary. Most people draw a diagram showing the number of trips to get 1 or 2 adults across the river and then generalize to 8 adults. |
b. | Answers will vary. The problem requires students to find a way to represent the problem, look for a pattern, and generalize. The problem can be thought of as a recursive pattern. |
c. | Answers will vary. Most students draw a diagram with arrows showing people crossing the river in each direction. This arrow representation allows students to "see" the number of trips required for each adult. |
d. | Answers will vary. For example: What sequence of events must happen to get 1 adult across the river? Where are the 2 children at the end of this sequence? How many trips does the sequence require? What must happen so that 1 adult and 2 children are across the river? How does this change if there are 2 adults? Think of "undoing" your sequence to find out the number of adults with 2 children that required 13 trips to cross the river. |
<< back to Problem C5
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Problem C6 | |
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The answer is (4N + 1) trips: 4 trips to bring over each adult, plus 1 more trip for the 2 children.
a. | Answers will vary. Most people draw a diagram showing the number of trips to get 1 or 2 adults across the river and then generalize to 8 adults. |
b. | Answers will vary. The problem requires students to find a way to represent the problem, look for a pattern, and generalize. The problem can be thought of as a recursive pattern. |
c. | Answers will vary. Most students draw a diagram with arrows showing people crossing the river in each direction. This arrow representation allows students to "see" the number of trips required for each adult. |
d. | Answers will vary. For example: What sequence of events must happen to get 1 adult across the river? Where are the 2 children at the end of this sequence? How many trips does the sequence require? What must happen so that 1 adult and 2 children are across the river? How does this change if there are 2 adults? Think of "undoing" your sequence to find out the number of adults with 2 children that required 13 trips to cross the river. |
<< back to Problem C6
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