Patterns of Problem Solving

### Tuesday #### Introductions #. assign groups & syllabus quiz #. 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, strategy, solution)

### Thursday Due today

- 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 worth 1000 words, but words are needed to keep interpretations consistent #. chapter 1: 2, 5, 7, 9, 12, 15, 16

### Tuesday Due today

- Complete problems from last class - Read Chapter 2

#### Chapter 2: Systematic lists #. present chapter 1 (name, strategy, solution, review key points) #. discuss strategy and evidence - describe system - where is answer? (number of possibilities, last possible, etc.) #. chapter 2: 1, 5, 7, 9, 10, 13, 14

### Thursday Due today

- Complete problems from last class - Read Chapter 3

#### Chapter 3: Eliminate possibilities #. present chapter 2 (name, strategy, solution, review key points) #. discuss strategy and evidence #. chapter 3: 1, 3, 4, 5, 7, 15

Homework reminder (due in one week)

### Tuesday Due today

- 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 Due today

• Chapter 3b: 1, 2, 3 ,4, 5 (scoring) - 3b.1 hint - 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 - Puzzle Baron's Logic Puzzles #. chapter 4: 1, 8, 11, 16

### 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 Due today

• Chapter 4b: 1, 2, 3, 4, 5 (scoring) - 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.
• Read Chapter 5

#### Chapter 5: Look for patterns #. discuss strategy and evidence #. sequence: 0, 1, 1, 2, 3, 5, _, _, _ #. sequence: 3, 3, 5, 4, _, _, _ #. how to find patterns? #. chapter 5: 2, 7, 8, 9, 10, 14, 18

### Tuesday #### Chapter 5: Look for patterns #. return homework and present (volunteers) #. work time #. present chapter 5 (name, strategy, solution, review key points) #. Harry Potter potion riddle #. false patterns?

### Thursday #### Exam 1 - chapters 1-5 - one page of notes (1 sided, handwritten)

### Tuesday Due today

- read Chapter 6

New groups & discuss exam #### Chapter 6: Guess and check #. discuss strategy and evidence #. chapter 6: 4, 8, 9, 11, 15, 19

### Thursday Due today

- start next homework

#### Chapter 6: Guess and check #. discuss homework #. work time #. present chapter 6 (name, strategy, solution, review key points)

### Tuesday Due today

• Chapter 5b: 2, 4 (scoring) -! 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.
• Chapter 6b: 1, 3, 5 (scoring) - 6b.1 hint - 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 hint - 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 Due today

- 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)

### Tuesday Due today

• Chapter 7b: 1, 2, 3, 4, 5 (scoring) - 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.

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 Due today

- 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 #. example, using 7.16 to help with 7.17 #. chapter 9: 1, 2, 5, 7, 8, 9, 10, 11, 14

### Tuesday Due today

• Chapter 8b: 1, 2, 3, 4, 5 (scoring) - 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.

Exam 2 schedule #### Chapter 9: Easier related problem #. present chapter 9: 1, 2, 5, 7, 8 #. continue chapter 9: 9, 10, 11, 14

### Thursday Due today

- Group project proposals due via dropbox

#### Chapter 9: Easier related problem #. present homework #. work time #. present chapter 9: 9, 10, 11, 14

### Tuesday #### Flex day

### Thursday #### Exam 2

### Friday Deadline to register for Math Retreat???

### Tuesday Due today

- Read Chapter 10

New groups & discuss exam #### 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 Due today

- read Chapter 11

#### Chapter 11: Work backwards #. discuss homework and Group project #. discuss strategy and evidence #. chapter 11: 1, 3, 5, 7, 9, 12, 15

### Monday #### Math retreat #. Present Group projects

### Tuesday #### No class to make up for Math retreat yesterday!

### Thursday Due today

• Chapter 9b: 1, 3, 5 (scoring) -! 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.
• Chapter 10b: 2, 4 (scoring) -! 10b.1 - Similar to Chapter 9a:11. It may help to look for patterns involving powers of 2. - 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.
• Read Chapter 11
• Finish Chapter 11 problems
• Read Chapter 12

#### Chapter 12: Venn diagrams #. discuss strategy and evidence #. chapter 12: 10, 11, 12, 14 #. present chapter 12

### Thursday Due today

- Group project solutions - Group project collaboration scores - Read Chapter 13

#### Chapter 13: Algebra #. review last homework #. discuss strategy and evidence #. chapter 13: 5, 11, 12, 13, 15 #. chapter 16: 12

### Tuesday Due today

- Complete problems from last class - read Chapter 14

#### Chapter 13: Algebra #. discuss homework #. present chapter 13 #. present chapter 16 #. discuss strategy and evidence #. work problem 14.1c #. example

### Thursday Due today

- Read Chapter 14

#### Chapter 14: Finite differences #. chapter 14: 4, 5, 6, 8 #. present chapter 14