teaching students to invent puzzles scott kim shufflebrain.com math fair workshop april 21, 2007
TRANSCRIPT
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Teaching Students to
Invent Puzzles
Scott Kim • shufflebrain.comMath Fair Workshop • April 21,
2007
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SNAP
Fun math Present puzzles Puzzles are assigned
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Next step: inventing puzzles
Like creating art Like writing stories Like math research
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But how do you invent them?
Where do you get started? How do you get new ideas? What makes a good puzzle?
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I design puzzles
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Outline
What makes a good puzzle?
Inventing new puzzles
Adapting old puzzles
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WHAT MAKES A GOOD PUZZLE?
A bit of theory from game design
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1. Definition of “Puzzle”
A puzzle is fun and has a right answer.
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1. Definition of “Puzzle”
A puzzle is fun and has a right answer.
As opposed to everyday “problems”
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1. Definition of “Puzzle”
A puzzle is fun and has a right answer.
As opposed to everyday “problems”
As opposed to a game (no answer) or a toy (no goal)
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2. Medium
Spoken Paper and pencil Manipulative Computer
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3. Goal
Put together Take apart Fill in the blanks Matching Get from here to there Unscramble order Satisfy conditions
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4. Parts
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4. Parts
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4. Parts
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4. Parts
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4. Parts
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5. Rubric
Attractive (familiar, intriguing) Simple rules (harmonious, few pieces)
Fun to play (manipulative, unfamiliar)
Good feedback (sense of progress) Clear goal (pleasing, checkable) Solvable (deducible, maybe unique)
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ADAPTING OLD PUZZLES
You too can invent puzzles
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5 levels of originality
1. Present2. Adapt3. Compose4. Vary5. Invent
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1. PRESENT
…an old puzzle
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Presenting a puzzle
Play lots of puzzles Choose a puzzle Present it to someone else Offer hints as needed
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2. REVAMP
…an old puzzle in a new way
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Revamp appearance
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Revamp theme
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Revamp context
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3. COMPOSE
…within an existing form
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Sudoku
Fill the grid so every row, column and outlined region contains the numbers 1 to 5.
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Sudoku
Fill in solution Remove numbers Solve it Unique answer?
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Sudoku — Lessons Learned
Fewer numbers = harder (usually)
May be more than one solution
May be no solution at all Better if the puzzle has a theme
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Make a sequence: easy to hard
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Groups of Levels
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Levels
Go from easy to hard Common in computer games Help player learn the game Levels work in physical games too
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Tangrams
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Logic puzzles
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Rush Hour
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Rush Hour
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Rush Hour
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Rush Hour
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Rush Hour
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Rush Hour
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Rush Hour
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Rush Hour
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4. VARY
…an existing game
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Start with an existing game
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Vary difficulty
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Vary scale
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Vary scale
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Vary size
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Vary the rules
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Vary the medium
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INVENTING NEW PUZZLES
Creative mathematics
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Getting started
Art — doodle Writing — what have I experienced?
Machines — what is needed? Music — what do I care about?
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Asking the right question
1. What can this do?2. What’s wrong?3. What’s the question?4. How can I generalize?5. What happens if?6. How can I make this fun?
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1. What can this do?
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1. What can this do?
Hint: It’s not the letter L.
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1. What can this do?
Answer: The letter F.
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1. What can this do?
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2. What’s wrong?
…with Sudoku?
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2. What’s wrong?
Too abstract…make it physical
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2. What’s wrong?
Too much time…make it smaller
Too repetitive…make shaped regions
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2. What’s wrong?
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3. What’s the question?
The word TEN is made of 9 sticks.
That’s the answer. What’s question?
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3. What’s the question?
Remove six matches and leave ten.
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4. How can I generalize?
Place 8 queens so none attack each other
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4. How can I generalize?
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4. How can I generalize?
What about 9 queens? What about other chess pieces?
What about other size boards?
What if queen attacks n others?
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4. How can I generalize?
Queens are in pairs Each pair uses up 3 ormore rows/columns
16 rows/columns 16/3=5.33 pairs Therefore, maximum queens=10
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4. How can I generalize?
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5. What happens if?
Roll the ball to the end of the maze.
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5. What happens if?
What if there were 2 balls instead of 1?
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5. What happens if?
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6. How can I make it fun?
Marcy Cook tiles
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6. How can I make it fun?
Attractive (tiles) Simple rules (place all the tiles)
Fun to play (moving tiles) Good feedback (use every tile) Clear goal (use all ten digits) Solvable (unique solution)
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Example: Mind Games in Discover
Monthly puzzle for science magazine
One page, three puzzles About a topic in science or math
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Creative Process
1. Choose a topic2. Make it work in print3. Make a range of difficulties
4. Address a range of thinking styles
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Topic: Manipulatives
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1. Choose a topic
Cuisenaire Rods Pattern Blocks Geoboards
Topic: Manipulatives
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print
Build the figure with the ten rods
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print
Rods: 10
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print
Rods: 10, 9
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print
Rods: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print3. Make a range of difficulties
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print3. Make a range of difficulties
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Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print3. Make a range of difficulties4. Address a range of thinking styles
Numerical Spatial Logical
![Page 86: Teaching Students to Invent Puzzles Scott Kim shufflebrain.com Math Fair Workshop April 21, 2007](https://reader035.vdocuments.site/reader035/viewer/2022062314/56649ed35503460f94be33df/html5/thumbnails/86.jpg)
Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print3. Make a range of difficulties
4. Address a range of thinking styles
![Page 87: Teaching Students to Invent Puzzles Scott Kim shufflebrain.com Math Fair Workshop April 21, 2007](https://reader035.vdocuments.site/reader035/viewer/2022062314/56649ed35503460f94be33df/html5/thumbnails/87.jpg)
Hands-On Math (Dec 2002)
1. Choose a topic2. Make it work in print3. Make a range of difficulties
4. Address a range of thinking styles
![Page 88: Teaching Students to Invent Puzzles Scott Kim shufflebrain.com Math Fair Workshop April 21, 2007](https://reader035.vdocuments.site/reader035/viewer/2022062314/56649ed35503460f94be33df/html5/thumbnails/88.jpg)
SUMMARY
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Summary
What makes a good puzzle?
Definition
Medium
Goal
Parts
Rubric
Adapting old
puzzles
1. Present2. Revamp3. Compose4. Vary5. Invent
Inventing new puzzles
What can this do?What’s wrong?What’s the question?How can I generalize?
What happens if?How can it be fun?
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
![Page 90: Teaching Students to Invent Puzzles Scott Kim shufflebrain.com Math Fair Workshop April 21, 2007](https://reader035.vdocuments.site/reader035/viewer/2022062314/56649ed35503460f94be33df/html5/thumbnails/90.jpg)
Puzzles = nutritious + delicious
Nutritious
Nutritious +
Delicious
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Puzzles = fun math
MATH PUZZLEApproachableSimple rulesPhysicalEasy to checkMeaningful
MATH PROBLEMIntimidating
Complex rulesAbstract
Hard to checkMeaningless
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Puzzles = pop math
Puzzles : Math :: Pop songs : music
Short and accessible At worst they’re time-wasters
At best they’re art
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Puzzles = art form
“A good puzzle can give you all the pleasures of being duped that a mystery story can. It has surface innocence, surprise, the revelation of a concealed meaning, and the catharsis of solution.”
— Stephen Sondheim
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Thank You
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Thank You
Exploring Math Through Puzzles (keypress.com) Brainteasers Page-a-day Calendar (pageaday.com)
Discover Magazine (discovermagazine.com) Railroad Rush Hour, Sudoku 5x5 (thinkfun.com) ThinkFun teacher guides (puzzles.com) Math dance (mathdance.org)
scottkim.com shufflebrain.com
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Math Fairs
Like Science Fairs, Reading Fairs
Fun Big Public
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Puzzles = writing math
Goal of math education is literacy
Literacy = reading + writing
What’s missing: creative writing
Inventing puzzles = writing math