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Board / Authority Authorized Courses (Locally Developed) Course Name: Mathematical Puzzles, Problems and Games District Name: Okanagan Skaha District Number: 67 Developed by: Mike Cooke Date Developed: November 2012 School Name: Princess Margaret Secondary Principal's Name: Terry Grady Board/Authority Approval Date: Board/Authority Signature: Grade Level of Course: 11 or 12. Number of Course Credits: 4 Number of Hours of Instruction: 100-110 Prerequisite(s): None Special Training, Facilities or Equipment Required: A computer lab will be needed for some parts of the course. Origami paper will be needed for unit 2. Course Synopsis: This course is intended to be a chance for students to see some of the more interesting and fun topics in math. We will look at historical problems and the branches of math that developed as a result of these problems. The topics in the course will develop students’ creativity, research skills, reasoning skills, and perseverance in solving the puzzles and problems. Rationale: To expose students to a variety of beautiful and interesting topics in math. To change the culture and attitudes towards mathematics. To develop numeracy and logical reasoning through games, puzzles and problems. Organized Structure: (units, topics, modules) Unit Title Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Graph Theory Mathematics of Origami Japanese Logic Puzzles Mathematical Problems Mathematical Games Math Fair Projects Arithmetic to Algebra to Arithmetic Estimated Time (hours) 10-15 10-15 15 20 10-15 10-15 15 Total Hours 100 Unit/Topic/Module Descriptions: Unit 1: Overview: Beginning with a famous problem in math, students will see how this branch of mathematics came to be and how it is used today. Sample topics Bridges of Konigsberg Travelling Salesman Problem Bridges game Maze Games Exam Schedules at Universities Utilities Problem Connections to Polyhedra (edges, faces and vertices) Unit 2: Overview: The mathematics of paper folding. Students will create three dimensional objects. They will also see connections to geometry and surface area. Students’ creations will be presented to parents and the general public at an exhibition. Sample objects to be built Platonic Solids Prisms Archimedean Solids Torus Intersecting Squares Unit 3: Overview: Students will learn of 15-20 engaging games and puzzles that develop logic and reasoning skills. Sample puzzles Sudoku and variations Kakuro KenKen Skyscrapers Futoshiki Tents Lightup Unit 4: Overview: Students will see a wide variety of interesting and challenging problems. Students will also be exposed to some unsolved problems in mathematics at an age-appropriate level. Sample problems Painting the Cube Shaded Area Problem Staircase Towers Hunger Games Problem Exeter Reunion Problem Taxicab Problem Pythagorean Path Problem Crossing the River Problems Word Additions Unit 5: Overview: Students will learn to develop strategies in old and new mathrelated games. Sample games Go Nim Mancala Othello Mastermind Gobblet Rush Hour Anti-Virus Set Unit 6: Overview: Individual students will focus on a problem in order to become an expert at the problem. Students could then be involved in the Math Fair that is organized by Okanagan College. Topics will vary based on student interest Unit 7: Overview: Students will see how having knowledge of algebra can help them do mental math easily. They will learn a number of mathematical tricks and the algebra that explains why they work. Sample topics Distributive Law applications Five Squares Multiplying by Five Difference of Squares (i.e. 23x17, or 38x42) Instructional Component: Students will be taught material as needed. However, learning through discovery will be a focus throughout the course. Assessment Component: One of the purposes of this course is to improve students’ attitudes towards math. For that reason, I will not have unit tests in this course. The intent is to allow students to play with the math in a structured way. Having formal tests would take away from this goal. Assessment will be mainly based on projects, group work, rubrics, quizzes and self-assessment (in conjunction with teacher assessment). Learning Resources: Students will not have a textbook for this course. Instead, a teacher library of resources would be needed. I already have access to a number of books and websites that would be helpful in developing the course (including books on Origami, algebraic math tricks, Japanese logic puzzles) I would also need to purchase copies of some board games (anti-Virus, Gobblet, Set). I have copies of some of the games listed while some of the other games could easily be made by the class.