Patterns of Problem Solving

Calendar

This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any unforeseen events that may occur during the semester.

1:

### Tuesday #### Introductions #. assign groups & [syllabus scavenger hunt](handouts/syllabus-quiz.html) #. discussion - What is a problem? what is 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, problem #, strategy name, solution)
### Thursday Due today
- Read Introduction and Chapter 1 - continue work on 16 (p. 23)?
#### Chapter 1: Drawing diagrams #. if needed, discuss problems from last class #. discuss [strategy and evidence](handouts/homework.html) - represent information spatially to reduce cognitive load - diagrams need explanation, a picture is worth 1000 words, but words are needed to keep interpretations consistent #. Chapter 1: 2, 5, 7, 9, 12, 15, 16? #. present problems (name, problem #, strategy name, solution)

2:

### Tuesday Due today
- Complete problems from last class - read Chapter 2
#### Chapter 2: Systematic lists #. if needed, discuss problems from last class #. discuss [strategy and evidence ](handouts/homework.html) - describe system - where is answer? (number of possibilities, last possible, etc.) #. Chapter 2: 1, 5, 7, 9, 13, 14, 10 (if time)
### Thursday Due today
- Complete problems from last class - read Chapter 3
#### Chapter 3: Eliminate possibilities #. present problems from last class (name, problem #, strategy name, solution) #. discuss [strategy and evidence ](handouts/homework.html) #. Chapter 3: 1, 3, 4, 5, 15, 7

Homework reminder (due in one week)

3:

### Tuesday Due today
- start next Homework
#### Chapter 3: Eliminate possibilities #. homework questions #. work time #. individual presentations (name, problem #, strategy name, solution) #. extra, [cryptogram puzzle](https://datagenetics.com/blog/march32017/index.html) (DataGenetics)
### Thursday Due today
• Chapter 3b: 1, 2, 3 ,4, 5 ([scoring](handouts/homework.html)) - 3b.1 hint - A 2x4 indicates the width and height of the lumber, not the length. When done, the garden will touch the sidewalk.
#### Chapter 4: Use Matrix Logic #. collect homework #. discuss: [strategy and evidence](handouts/homework.html) - requires 1-1 correspondence - convention X=not and O=success - adjunct lists also helpful - explain at least 3 key steps #. Chapter 4: 1, 8, 11, 16 #. extra: [Puzzle Baron's Logic Puzzles](https://logic.puzzlebaron.com/) #. individual presentations (name, problem #, strategy name, solution)

4:

### Tuesday Due today
- start next Homework - read Chapter 5
#### Chapter 5: Look for patterns #. return homework and present #. next homework questions? #. discuss [strategy and evidence](handouts/homework.html) #. how to find patterns? - [0, 1, 1, 2, 3, 5, _, _, _](https://oeis.org/search?q=0%2C+1%2C+1%2C+2%2C+3%2C+5%2C&sort=&language=english&go=Search) - [3, 3, 5, 4, _, _, _](https://oeis.org/search?q=3%2C+3%2C+5%2C+4%2C+&language=english&go=Search) #. Chapter 5: 2, 7, 8, 10, 17, [18](https://duckduckgo.com/?q=tower+of+hanoi&ia=web), 14
### Thursday Due today
• Chapter 4b: 1, 2, 3, 4, 5 ([scoring](handouts/homework.html)) - 4b.1 hint - Be careful when copying the 4-digit numbers. - 4b.3 hint - Less than 20 ways. - 4b.4 hint - There are two solutions.
#### Chapter 5: Look for patterns #. finish Chapter 5 #. individual presentations (name, problem #, strategy name, solution)

5:

### Tuesday #### Review #. discuss [strategy and evidence](handouts/homework.html) #. Chapter 5b: 1, 2, 3, 4, 5 - 5b.1 - Read pronouns carefully. - 5b.3 - The course is *not* 200 feet, but is 100 feet with a turn around. - 5b.4 hint - If the square description is confusing, just remember that the partners stand next to each other while facing their opponents. #. extra: [Harry Potter potion riddle](https://hpread.scholastic.com/activities/DecJan/HPRC_Activity_2_DecJan.pdf) #. extra: [false patterns?](https://researchinpractice.files.wordpress.com/2010/05/newsletter_march06_print-version.pdf)
### Thursday #### Exam 1 - Chapters 1-5 - one page of notes (one-sided, handwritten)

6:

### Tuesday Due today
Discuss exam, plan [Math Retreat presentations](handouts/group-project.html), new groups #### Chapter 6: Guess and check #. discuss [strategy and evidence](handouts/homework.html) #. Chapter 6: 4, 8, 9, 11, 15, 19
### Thursday Due today
- start next homework - read Chapter 7
#### Chapter 6: Guess and check #. individual presentations (name, problem #, strategy name, solution) #. next homework questions? #### Chapter 7: Identify subproblems #. discuss [strategy and evidence](handouts/homework.html) #. example 7a.1 #. Chapter 7: 2, 3, 11, 12, 13, 16, 17 (if time permits)

7:

### Tuesday Due today
• Chapter 6b: 1, 2, 3, 4, 5 ([scoring](handouts/homework.html)) - 6b.1 hint - Sandwich must be complete before eating it. Back at the dock, consider the choice of hands: left first or right first. - 6b.3 hint - March has 31 days.
• Proposal for [Math Retreat](handouts/group-project.html)
#### Chapter 7: Identify subproblems #. continue Chapter 7 problems #. individual presentations (name, problem #, strategy name, solution)
### Thursday Due today
- start next homework
#### Work day #. return proposals for [Math Retreat](handouts/group-project.html); submit [abstracts](https://uweauclaire.qualtrics.com/jfe/form/SV_0IZ9KOwJzU0gEYK) #. discuss Chapter 7.17 #. work on homework for next class #. read for next class

8:

### Tuesday Due today
• Chapter 7b: 1, 2, 3, 4, 5 ([scoring](handouts/homework.html)) - 7b.2 hint - Part of a section is not allowed. Answer will be a whole number. - 7b.3 hint - Algebra not allowed. Only use strategies we have discussed so far.
#### Chapter 8: Analyze units #. discuss [strategy and evidence](handouts/homework.html) #. example 8a.1 #. Chapter 8: 7, 10, 13, 15, 19? #. individual presentations (name, problem #, strategy name, solution)
### Thursday Due today
- start next homework - read Chapter 9
Review homework and next homework questions? #### Chapter 9: Easier related problem #. example 8a.19 #. discuss [strategy and evidence](handouts/homework.html) #. Chapter 9: 1, 2, 6, 7, 9, 10, 11, 14 #. individual presentations 9: 1, 2, 6, 7 (name, problem #, strategy name, solution)

9:

### Tuesday Due today
• Chapter 8b: 1, 2, 3, 4, 5 ([scoring](handouts/homework.html)) - 8b.3 hint - Use 365.25 days per year to account for leap years. - 8b.4 hint - It may be important to notice that the received letter is mailed out with each generation. - 8b.5 hint - We will not question the business ethics of hiring two people who always lie.
#### Chapter 9: Easier related problem #. continue Chapter 9 #. individual presentations 9: 9, 10, 11, 14 (name, problem #, strategy name, solution)
### Thursday Due today
Discuss homework #### Chapter 10: Physical representations #. discuss [strategy and evidence](handouts/homework.html) #. Chapter 10: 5, 7 (see #4), 18, 20, 21, [17?](handouts/365-10a17.html) #. individual presentations (name, problem #, strategy name, solution) #. extra: [Coke vs Sprite](https://vimeo.com/20628942) problem (alternate version of #18)

10:

### Tuesday Due today
- n/a
#### Review day
1. Chapter 9b: 1, 2, 3, 4, 5
- 9b.2 hint - 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. - 9b.4 hint - Double-check your conversions. - 9b.5 hint - (i) Assume the track is 120 feet. How fast is each person moving? (ii) Looking for a measure of time.
2. individual presentations (name, problem #, strategy name, solution)
### Thursday #### Exam 2 - Chapters 1-10 - one page of notes (one-sided, handwritten)

11:

### Tuesday Due today
Discuss exam & new groups #### Chapter 11: Work backwards #. discuss [strategy and evidence](handouts/homework.html) #. example 11a.1 #. Chapter 11: 3, 5, 7, 9, 12, 15 #. individual presentations (name, problem #, strategy name, solution) #. prepare for Math Retreat
### Thursday Due today
#### Chapter 12: Venn diagrams #. discuss [strategy and evidence](handouts/homework.html) #. examples 12a.2 and 12a.3 #. Chapter 12: 10, 11, 12, 14 #. individual presentations (name, problem #, strategy name, solution) #. prepare for Math Retreat

12:

### Monday #### [Math Retreat presentations](handouts/group-project.html) - recommend at least 20 handouts for presentations
### Tuesday #### No class to make up for Math retreat yesterday!
### Thursday Due today
• Chapter 11b: 1, 2, 3, 4, 5 ([scoring](handouts/homework.html)) - 11b.5 hint - a diagram may be helpful
Student evaluations & Email group project collaboration issues #### Chapter 13: Algebra #. discuss [strategy and evidence](handouts/homework.html) #. Chapter 13: 5, 7, 11, 12, 15, 18 #. Chapter 16: 12 #. individual presentations (name, problem #, strategy name, solution)

13:

### Tuesday Due today
- [Math Retreat solutions](handouts/group-project.html) - read Chapter 14
Discuss homework #### Chapter 14: Finite differences #. work problem 14.1c #. discuss [strategy and evidence](handouts/homework.html) #. [example](/math302/handouts/finite-differences2.html) #. Chapter 14: 4, 5, 6, 8
### Thursday Due today
- n/a
#### Chapter 14: Finite differences #. continue Chapter 14 problems #. Chapter 14b: 1, 2, 3, 4, 5 #. individual presentations (name, problem #, strategy name, solution)

14:

### Tuesday Due today
- prepare for final exam
#### Review #. Chapter 13b: 1, 2, 3, 4, 5 #. Chapter 16: 12 #. individual presentations (name, problem #, strategy name, solution)
### Thursday Due today
- prepare for final exam
#### Review
1. Chapter 12b: 1, 3, 4, 5, 2
2. individual presentations (name, problem #, strategy name, solution)

Exam 3

- [scoring](handouts/homework.html) - one page notes (one-sided, handwritten) - calculator allowed