Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Solutions for Session 3, Part E

See solutions for Problems: E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | E10 | E11
E12 | E13 | E14 | E15 | E16

Problem E1

In each case there are clear reasons that there can only be one answer. For example, a state can have only one capital city. A word can only have one first letter.

 Integer Odd or Even 1 odd 2 even 3 odd 4 even 5 odd 10 even 15 odd

 SSN DOB 590-14-6017 6/2/75 024-33-3467 10/27/70 024-33-3568 10/27/70 024-33-7146 8/10/74 036-89-0831 6/8/84

 State Capital Massachusetts Boston Texas Austin Washington Olympia North Dakota Bismarck West Virginia Charleston

 Side Length Area 1 1 2 4 3 9 4 16 5 25 10 100 15 225

 Word First Letter Word W Hey H Wow W Math M Is I Very V Cool C

 Problem E2 Sure, but not always. The odd-or-even, date of birth, and letter functions have the possibility of matching outputs.

Problem E3

More tables!
For certain (not necessarily all!) inputs, there can be more than one correct output. Note how different this is from Algorithms A and B.

 Number Smaller Number 10 7 10 8 15 10 17 12 21 12 21 -5 0 -100

 Number Factor 15 3 20 5 24 3 24 4 30 10 45 9 100 20

 Person Grandparent Abbey Mary Abbey John Megan Mary Megan Alice Brian Henry

 City Name State Name New York New York Chicago Illinois Salem Massachusetts Salem Oregon Portland Oregon Portland Maine

 Side Length Area 5 20 10 20 20 20 1 1/4 5 15 10 50 100 250000

 Word Anagram ear are ear era mare ream toilets T. S. Eliot relation oriental listen silent Elvis lives

 Problem E4 Other functions: a circle's circumference is a function of its radius; the average temperature is a function of the time of year; a TV program's rating is a function of the number of people watching the show. For each function, there can only be one output for a given input, while a non-function may have more than one output for the same input. For example, people of more than one age can wear size 11 shoes.

Problem E5

 a. The output is yes, 3 is a prime number. b. The output is yes, 2 is a prime number. c. No, 100 is not a prime (it has lots of factors). d. No, 1 is not a prime (it needs to have exactly two factors).

 Problem E6 It could be any prime number: 2, 3, 5, 7, 11, 13, 17, 19, ... .

 Problem E7 It's a function because there is exactly one output. The answer is always "yes" or "no," never both.

 Problem E8 There is no such function. The outputs are only "yes" or "no," so if such a function existed, it would have to guarantee the specific prime number picked from "yes," which is impossible. Put another way, the undoing rule cannot be a function, because "yes" would return all the prime numbers, and "no" would return all the non-primes.

Problem E9

 a. The output is 3. b. The output is 3. c. The output is still 3.

 Problem E10 It could be any number at all. Since the output is always 3, telling us that the output is 3 doesn't give any new information. This is the same situation as Problem D5.

 Problem E11 There is exactly one value for the output. It's always 3, but that doesn't keep it from being a function.

 Problem E12 No such function exists.

 Problem E13 The output is a triangle whose sides are 1/2 the sides of the original and parallel to the original sides.

 Problem E14 All the sides are half as long, and the new triangle's area is one-fourth of the original.

 Problem E15 All the formed quadrilaterals are parallelograms.

 Problem E16 Yes, because there is exactly one output polygon for any starting polygon.

 Session 3: Index | Notes | Solutions | Video