Patterns of Problem Solving
Calendar (quizzes have 1-2 problems, students share unique solutions)
This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any apocalyptic events that may occur during the semester .
1:
Tuesday
Introductions
assign groups & syllabus quiz
discussion [+ ]
What is a problem? an exercise?
What is problem solving (PS)?
What are major phases of PS? (understanding, plan and execute, reflect)
intro problems: 1-5 (p. 7-8), 16 (p. 23)
model presentation (name, strategy, solution)
Thursday
Read Introduction and Chapter 1
Chapter 1: Drawing diagrams
discuss problems from last class
discuss strategy and evidence
represent information spatially to reduce cognitive load
diagrams need explanation, a picture is work 1000 words, but the words need to be the same
chapter 1: 2, 5, 7, 9, 12, 15, 16
2:
Tuesday
Complete problems from last class
Read Chapter 2
Chapter 2: Systematic lists
present chapter 1: 2, 5, 7, 9, 12, 15, 16
(name, strategy, solution, review key points)
discuss strategy and evidence
describe system
where is answer? (number of possiblities, last possible, etc.)
chapter 2: 1, 5, 7, 9, 10, 13, 14
Thursday
Complete problems from last class
Read Chapter 3
Chapter 3: Eliminate possibilities
present chapter 1: 16
present chapter 2: 1, 5, 7, 9, 10, 13, 14
(name, strategy, solution, review key points)
discuss strategy and evidence
chapter 3: 1, 3, 4, 5, 7, 15
Homework reminder (due in one week)
Friday*
* Last day to drop full-semester courses with no record.
3:
Tuesday
start next homework
Chapter 3: Eliminate possibilities
homework questions
work time
present chapter 3: 1, 3, 4, 5, 7, 15
(name, strategy, solution, review key points)
Thursday
Chapter 3b: 1, 2, 3 ,4, 5 (hints , scoring )
3b.1 - A 2x4 indicates the width and height of the lumber. Not the length. When done, the garden will touch the sidewalk.
Read Chapter 4
Chapter 4: Use Matrix Logic
collect homework
previous: 3.5
discuss: strategy and evidence
requires 1-1 correspondence
convention X=not and O=success
adjunct lists also helpful
chapter 4: 1, 8, 11, 16
4:
Tuesday
Chapter 4: Use Matrix Logic
return homework and present (volunteers)
homework questions?
work time (hints on 4.16)
volunteers to present Chapter 4: 1, 8, 11, 16
(name, strategy, solution, review key points)
Thursday
Chapter 4b: 1, 2, 3, 4, 5 (hints , scoring )
4b.1 - Be careful when copying the 4-digit numbers.
4b.3 - Less than 20 ways.
4b.4 - There are two solutions.
Read Chapter 5
Chapter 5: Look for patterns
discuss strategy and evidence
sequences: 0, 1, 1, 2, 3, 5, _, _, _
sequences: 3, 3, 5, 4, _, _, _
how to find patterns?
chapter 5: 2, 7, 8, 9, 10, 14, 18
5:
Tuesday
Chapter 5: Look for patterns
return homework and present (volunteers)
work time
present chapter 5: 2, 7, 8, 9, 10, 14, 18
(name, strategy, solution, review key points)
Thursday
Exam 1
chapters 1-5
one page of notes (1 sided, handwritten)
6:
Tuesday
read Chapter 6
New groups
Chapter 6: Guess and check
discuss strategy and evidence
chapter 6: 4, 8, 9, 11, 15, 19
Thursday
start next homework
Chapter 6: Guess and check
discuss homework
work time
present chapter 6: 4, 8, 9, 11, 15, 19
(name, strategy, solution, review key points)
7:
Tuesday
Chapter 5b: 2, 4 (notes , scoring )
5b.1 - Read pronouns carefully.
5b.3 - The course is NOT 200 feet, but is 100 feet with a turn around.
5b.4 - If the square description is confusing, just remember that the partners stand next to each other while facing their opponents.
Chapter 6b: 1, 3, 5 (notes , scoring )
6b.1 - Sandwich must be complete before eating it. Back at the dock, consider the choice of hands (left versus right), but order does not matter as he picks them up at the same time.
6b.3 - March has 31 days.
read chapter 7
Chapter 7: Identify subproblems
discuss strategy and evidence
chapter 7: 2, 3, 7, 11, 12, 14, 17 (see 16 for hints)
Thursday
start next homework
Chapter 7: Identify subproblems
discuss homework
work time
present chapter 7: 2, 3, 7, 11, 12, 14, 17 (see 16 for hints)
8:
Tuesday
Chapter 7b: 1, 2, 3, 4, 5 (notes , scoring )
Problem 2 - Part of a section is not allowed. Answer will be a whole number.
Problem 3 - Algebra not allowed. Only use strategies we have discussed so far.
Group project introduction
Chapter 8: Analyze units
chapter 7: 17 (see 16 for hints)
discuss strategy and evidence
chapter 8: 1, 7, 10, 13, 15
Thursday
start next homework
read chapter 9
Chapter 8: Analyze Units
discuss homework
present chapter 8: 1, 7, 10, 13, 15
Chapter 9: Easier related problem
discuss strategy and evidence
for example, using 7.16 to help with 7.17
chapter 9: 1, 2, 5, 7, 8, 9, 10, 11, 14
9:
Tuesday
Chapter 8b: 1, 2, 3, 4, 5 (notes , scoring )
Problem 3 - Use 365.25 days per year to account for leap years.
Problem 4 - It may be important to notice that the received letter is mailed out with each generation.
Problem 5 - We will not question the business ethics of hiring two people who always lie.
Exam 2 schedule
Chapter 9: Easier related problem
present chapter 9: 1, 2, 5, 7, 8
continue chapter 9: 9, 10, 11, 14
Thursday
Group project proposals due via dropbox
Chapter 9: Easier related problem
present homework
work time
present chapter 9: 9, 10, 11, 14
10:
Tuesday
Class canceled (Wisconsin Dells grant meeting)
Thursday
Exam 2 (proctored)
Friday*
Deadline to register for Math Retreat
* Last day to withdraw from individual full-semester classes.
11:
Tuesday
Read Chapter 10
New groups
Chapter 10: Physical representation
discuss strategy and evidence
chapter 10: 5, 7, 17a, 17b, 18, 20, 21
Coke vs Sprite problem (alternate version of #18)
Thursday
start next homework
Chapter 10: Physical representation
discuss homework
present chapter 10: 5, 7, 17a, 17b, 18, 20, 21
Friday*
Math Retreat applications due (see email for link)
12:
Tuesday
Chapter 9b: 1, 3, 5 (notes , scoring )
Problem 2 - I know there is a formula for this. You may only use it if you use the "Find a pattern" strategy to develop the formula.
Problem 4 - Double-check your conversions.
Problem 5 - (i) Assume the track is 120 feet. How fast is each person moving? (ii) Looking for a measure of time.
Chapter 10b: 2, 4 (notes , scoring )
Problem 1 - Similar to Chapter 9a:11. It may help to look for patterns involving powers of 2.
Problem 2 - The clue "For each sheet she was able to get a towel and a washcloth" can be misleading. It refers to price, not quantity as she was "able" to do it, which does not mean she did.
Problem 2 - Guess and check can be a useful strategy.
Problem 4 - See pages 465-466 for conversions.
Problem 5 - Please describe the location of all seven merchants using the point of view given.
Read Chapter 11
Chapter 11: Work backwards
discuss strategy and evidence
chapter 11: 1, 3, 5, 7, 9, 11, 15 change 11 to 12
Thursday
Finish Chapter 11 problems
Read Chapter 12
Chapter 12: Venn diagrams
discuss strategy and evidence
chapter 12: 10, 11, 12, 14
14:
Tuesday
Chapter 11b: 3, 5 (notes , scoring )
Problem 3 - I suggest using capital letters for adults and lowercase letters for the corresponding dogs.
Problem 5 - The question asks how long it takes to get out, which means to the edge of the forest.
Chapter 12b: 2, 4 (notes , scoring )
Problem 2 - Each clue is very dense. For example, on my first pass Clue #1 allowed me to eliminate three spaces.
Chapter 13b: 1 (notes , scoring )
Problem 1 - Answer is greater than 1000. Also 25! is an interesting example because it has 6 ending zeroes.
Chapter 14: Finite differences
discuss strategy and evidence
work problem 14.1c
example
chapter 14: 4, 5, 6, 8
Thursday
Class canceled (WMC conference )
15:
Tuesday
Chapter 14: Finite differences
present homework
present chapter 14: 4, 5, 6, 8
chapter 15: 3, 6, 11
chapter 16: 2, 3, 4, 7, 13
Evaluations
Thursday
Finish chapters
present chapter 15: 3, 6, 11
present chapter 16: 2, 3, 4, 7, 13