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Solutions for Session 10, Grades 3-5, 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 one 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 one or two adults across the river and then generalize to eight 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 one adult across the river? Where are the two children at the end of this sequence? How many trips does the sequence require? What must happen so that one adult and two children are across the river? How does this change if there are two adults? Think of "undoing" your sequence to find out the number of adults with two 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 one or two adults across the river and then generalize to eight 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 one adult across the river? Where are the two children at the end of this sequence? How many trips does the sequence require? What must happen so that one adult and two children are across the river? How does this change if there are two adults? Think of "undoing" your sequence to find out the number of adults with two 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 one or two adults across the river and then generalize to eight 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 one adult across the river? Where are the two children at the end of this sequence? How many trips does the sequence require? What must happen so that one adult and two children are across the river? How does this change if there are two adults? Think of "undoing" your sequence to find out the number of adults with two 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 one or two adults across the river and then generalize to eight 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 one adult across the river? Where are the two children at the end of this sequence? How many trips does the sequence require? What must happen so that one adult and two children are across the river? How does this change if there are two adults? Think of "undoing" your sequence to find out the number of adults with two children that required 13 trips to cross the river. |
<< back to Problem C5
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Problem C6 | |
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(4N + 1) trips: Four trips to bring over each adult plus one more trip for the two children.
a. | Answers will vary. Most people draw a diagram showing the number of trips to get one or two adults across the river and then generalize to eight 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 one adult across the river? Where are the two children at the end of this sequence? How many trips does the sequence require? What must happen so that one adult and two children are across the river? How does this change if there are two adults? Think of "undoing" your sequence to find out the number of adults with two children that required 13 trips to cross the river. |
<< back to Problem C6
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