Patterns of Problem Solving

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.

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1. Introductions and Drawing

### Monday #### Introductions #. assign groups (note: new groups for each chapter) #. syllabus scavenger hunt & Canvas introductions #. 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) #. present: student name, problem #, strategy name, solution Volunteer for Math Meet (Feb 17)?
### Wednesday Due today #### Chapter 1: Drawing diagrams #. if needed, discuss problems from last class #. discuss [strategy and evidence](handouts/homework.html#1) - 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, 12, 15, 9, 16? #. present: student name, problem #, strategy name, solution

2. Lists and Elimination

### Monday Due today #### Chapter 2: Systematic lists #. if needed, discuss problems from last class #. discuss [strategy and evidence ](handouts/homework.html#2) - describe system, e.g., 2d6 - where is answer? (number of possibilities, last possible, etc.) #. Chapter 2: 1, 5, 7, 9, 13, 14, 10 (if time) #. present: student name, problem #, strategy name, solution
### Wednesday Due today #### Chapter 3: Eliminate possibilities #. discuss [strategy and evidence ](handouts/homework.html#3) #. Chapter 3: 1, 3, 4, 5, 15, 7 #.! extra? [cryptogram puzzle](https://datagenetics.com/blog/march32017/index.html) (DataGenetics) #. present: student name, problem #, strategy name, solution PStart next homework assignment

3. Matrix logic and Patterns

### Monday Due today Collect homework #### Chapter 4: Use Matrix Logic #. matrix logic example ([Puzzle Baron](https://logic.puzzlebaron.com/)) #. discuss: [strategy and evidence](handouts/homework.html#4) - 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 #. present: student name, problem #, strategy name, solution
### Wednesday Due today Return homework and present #### Chapter 5: Look for patterns #. discuss [strategy and evidence](handouts/homework.html#5) #. 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 PStart next homework assignment

4. Review

### Monday Due today #### Chapter 5: Look for patterns #. finish Chapter 5 #. present: student name, problem #, strategy name, solution #### Review #. 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://web.archive.org/web/20220520023037/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) #.
### Wednesday Return homework and present #### Review #. finish problems from last class #. if time, WMC state contest sample problem #. present : student name, problem #, strategy name, solution

5. Exam and Problem-posing project

### Monday Due today - create note sheet #### Exam 1 - Chapters 1-5 - note sheet (1 page, 1-sided, handwritten)
### Wednesday Due Today - preview Problem-posing project #### Plan problem-posing project #. introduce Problem-posing project #. teams? resources? #. Proposals

6. Guess & check and Subproblems

### Monday Due today Discuss exam, new groups #### Chapter 6: Guess and check #. discuss [strategy and evidence](handouts/homework.html#6) (Goldilocks?) #. Chapter 6: 4, 8, 9, 11, 15, 19 #. present: student name, problem #, strategy name, solution
### Wednesday Due today #### Chapter 7: Identify subproblems #. discuss [strategy and evidence](handouts/homework.html#7) #. example 7a: 1 #. Chapter 7: 2, 3, 11, 12, 13, 16, 17 (if time permits) Start next homework assignment

7. Analyze units

### Monday Due today Return Proposals #### Chapter 8: Analyze units #. discuss [strategy and evidence](handouts/homework.html#8) #. example 8a: 1 #. Chapter 8: 7, 10, 13, 15, 19 #. present: student name, problem #, strategy name, solution Old business, 7a: #17
### Wednesday Due today #### Work day #. homework present: student name, problem #, strategy name, solution #. submit Math Retreat proposal for problem-posing project #. homework for next class #. reading for next class Start next homework assignment

Spring break

8. Easier related problems

### Monday Due today #### Chapter 9: Easier related problems #. creates different problem where as subproblems break big problem into smaller problems #. start 9.1 #. discuss [strategy and evidence](handouts/homework.html#9) #. Chapter 9: [1](https://www.wolframalpha.com/input?i=number+of+diagonals+in+a+25-gon), 2, 6, 7, 9, 10, 11, 14 - 9.11: order doesn't matter because "combinations" #.
### Wednesday Due today Present homework problems #### Chapter 9: Easier related problems (continued) #. 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 240 feet. How fast is each person moving? (ii) Looking for a measure of time. #. present: student name, problem #, strategy name, solution Start next homework assignment

9. Physical representations

### Monday Due today #### Chapter 10: Physical representations #. discuss [strategy and evidence](handouts/homework.html#10) #. Chapter 10: 5, 7 (see #4), 18, 20, 21, [17?](handouts/365-10a17.html) #. present: student name, problem #, strategy name, solution #. extra: [Coke vs Sprite](https://vimeo.com/20628942) problem (alternate version of #18) Present problems from 9b?
### Wednesday Due today - n/a #### Review #. Chapter 10b: 1, 2, 3, 4, 5 - 10b.1 - Similar to Chapter 9a:11. - 10b.2 - (i) 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. (ii) Guess and check can be a useful strategy. - 10b.4 - See pages 465-466 for conversions. - 10b.5 - Please describe the location of all seven merchants using the point of view given. #. present: student name, problem #, strategy name, solution

10. Exam and Working backwards

### Monday Due today #### Exam 2 - Chapters 1-10 - note sheet (1 page, 1-sided, handwritten)
### Wednesday Due today Discuss exam, new groups #### Chapter 11: Work backwards #. discuss [strategy and evidence](handouts/homework.html#11) #. example 11a.1 #. Chapter 11: 3, 5, 7, 9, 12, 15 #. present: student name, problem #, strategy name, solution

11. Venn diagrams and Algebra

### Monday Due today #### Chapter 12: Venn diagrams #. discuss [strategy and evidence](handouts/homework.html#12) #. see language differences between 12a.2 and 12a.3 #. tip: universal set #. Chapter 12: 2, 3, 10, 11, 12, 14 #. present: student name, problem #, strategy name, solution Math Retreat planning?
### Wednesday Due today #### Chapter 13: Algebra #. discuss [strategy and evidence](handouts/homework.html#13) #. Chapter 13: 5, 7, 11, 12, 15, 18 #. present: student name, problem #, strategy name, solution Math Retreat planning?

12. Math Retreat and Finite differences

### Monday #### Math Retreat #. Problem-posing presentation
### Wednesday Due today Discuss homework #### Chapter 14: Finite differences #. work problem 14.1c #. discuss [strategy and evidence](handouts/homework.html#14) #. another example #. Chapter 14: 4, 5, 6, 8 #. present: student name, problem #, strategy name, solution

13. Change focus

### Monday Due today Collaboration scores & student evaluations #### Chapter 16: Change focus #. discuss [strategy and evidence](handouts/homework.html#16) #. Chapter 16: 1, 2, 3, 4, 6, 11, 13, 12 #. present: student name, problem #, strategy name, solution
### Wednesday Due today #### Review #. Chapter 13b: 1, 2, 3, 4, 5 #. present: student name, problem #, strategy name, solution

14. Review

### Monday Due today #### Review #. Chapter 14b: 1, 2, 3, 4, 5 #. present: student name, problem #, strategy name, solution
### Wednesday Due today #### Review #. "Exit" ticket

Finals week

### Final Exam 3 - [scoring](handouts/homework.html#16) - one page notes (one-sided, handwritten) - calculator allowed
University finals schedule