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

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

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

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 

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)

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

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

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?

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?

Shikaku Puzzle 11 Design symmetry Where would you start?

The Columbus 500 race #1

the Columbus 500 Each driver picks a starting position from 1-49 (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

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

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

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?

The Columbus 500 race #2

the Columbus 500 Each driver picks a starting position from 1-49 (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

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

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

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?

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?

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?

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

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

Feel free to contact us at: wankojj@muohio.edu hawkg@piqua.org