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Session 10 Session 10 Grades K-2 Part A Part B Part C Part D Part E Homework
 
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A B C D E

Video

Solutions for Session 10, Grades 6-8, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6


Problem C1

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


 

Problem C2

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


 

Problem C3

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


 

Problem C4

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


 

Problem C5

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


 

Problem C6

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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