1. Challenge Your Mind: Puzzles for Your Classroom
Jeffrey Wanko
Miami University
Greg Hawk
Piqua High School
OCTM Annual Conference October 18, 2012

2. About the Puzzles U.S. Popularity began with Sudoku in 2005
Dozens of other language independent logic puzzles have been created - some based on number sense, others based on geometry or spatial sense - all building on reasoning and sense-making

3. Big Ideas in Middle School Geometry
What big ideas come to mind when you think of geometry for the middle grades?

4. NCTM Principles and Standards: Geometry (6-8)
Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships
Specify locations and describe spatial relationships using coordinate geometry and other representational systems 
Apply transformations and use symmetry to analyze mathematical situations
Use visualization, spatial reasoning, and geometric modeling to solve problems 

5. Common Core State Standards
Classify two-dimensional figures into categories based on their properties (grade 5)
draw, construct and describe geometrical figures and describe the relationships between them (Grade 7)
Understand congruence and similarity using physical models, transparencies, or geometry software (Grade 8)
experiment with transformations in the plane (High School)

6. Today’s puzzles
Shapedoku
Shape
Rep-Tiles
Similarity
Shikaku
Area

7. Shikaku
Goal: divide the grid into rectangles and squares such that every grid square is used exactly once
Rules:
Each rectangle or square contains exactly one circled number
Each circled number represents the area of the corresponding rectangle

8. Shikaku Puzzle 1
Shikaku Puzzle 2
Work on these individually or with a partner. Consider:
Where did you start?
Where did you encounter difficulties?
Where is the mathematics?
How can you use these in your classroom?

9. Shikaku Puzzle 3
Shikaku Puzzle 4
Are these puzzles more challenging? If so, why?
Is there more than one place to start?
What do you notice about the placements of the circled numbers?

10. Shikaku Puzzle 11
Design symmetry
Where would you start?

11. The Columbus 500
race #1

12. the Columbus 500
Each driver picks a starting position from (inclusively) for your car
The smallest starting position chosen by only one person is the winner
Write down your starting position on a piece of paper
After all starting positions have been recorded, you must show your number to someone else for verification

13. the Columbus 500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

14. Rep-Tiles
Goal: Use copies of a shape to create a larger shape that is mathematically similar to the original

15. Small L
Large L
Right
Trapezoid
Isosceles
Trapezoid
P Pentomino
Show that each of these shapes is a rep-4 polygon
Can a rep-tile be created with more than 4 copies of any of these shapes?

16. The Columbus 500
race #2

17. the Columbus 500
Each driver picks a starting position from (inclusively) for your car
The smallest starting position chosen by only one person is the winner
Write down your starting position on a piece of paper
After all starting positions have been recorded, you must show your number to someone else for verification

18. the Columbus 500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

19. Shapedoku Goal: Place numbers to complete the grid Rules:
Quadrilateral
Parallelogram
Rectangle
Isosceles right triangle
Goal: Place numbers to complete the grid
Rules:
Each number occurs once in each row and each column
The center of the square containing each non-circled number forms a vertex of the shape indicated

20. Work on this individually or with a partner. Consider:
Square
Rectangle
Rhombus
Parallelogram
Right Triangle
Shapedoku Puzzle 5
Work on this individually or with a partner. Consider:
Where did you start?
Where did you encounter difficulties?
Where is the mathematics?
How can you use these in your classroom?

21. Work on this individually or with a partner. Consider:
Right Trapezoid
Square
Parallelogram
Isosceles Triangle
Rectangle
Shapedoku Puzzle 7
Work on this individually or with a partner. Consider:
Where did you start?
Where did you encounter difficulties?
Where is the mathematics?
How can you use these in your classroom?

22. Work on this individually or with a partner. Consider:
Isosceles Triangle
Isosceles Right Triangle
Rhombus
Square
Shapedoku Puzzle 2
Work on this individually or with a partner. Consider:
Where did you start?
Does a smaller size mean an easier puzzle?
How might you use a puzzle of this size differently than the 5x5 puzzles in your classroom?

23. Creating your own! Sizes - what are your needs? Three Approaches:
Shape-oriented
Row-oriented
Combination

24. Creating your own! Shapedoku Puzzle 6 Square Isosceles Trapezoid
Parallelogram
Rectangle
Shapedoku Puzzle 6

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