1 Venn Diagrams and Logic: A Visual Approach to Deductive Reasoning Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: This lesson focuses on using Venn diagrams to explore direct, indirect, and transitive reasoning. For each activity, students construct arguments based on Venn diagrams, and conversely, create Venn diagrams for a particular argument.... 2 Circle Packing 2: Soda Rack Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: In this second lesson (in a unit of three), students consider the arrangement of soda cans placed in a bin with two vertical sides, discover an interesting result, and prove that the result is true. This lesson utilizes an on-site applet.... Resource Type: Content Supports Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: This resource offers 72 proofs of the Pythagorean Theorem. Each is well illustrated and most provide links to other sites for further information and/or Java applets to allow for exploration of the proof.... Resource Type: Content Supports -- Activities and rich problems Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: This problem is the best-known simple example of a knight-knave problem, in which you come to a fork in the road and you do not know which way to go. In one direction lies happiness; in the other, disaster.... 5 Fibonacci Nim 2: Static Nim Resource Type: Content Supports Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Static Nim is the classic game in which two players take turns removing a specified range of tokens from a pile of tokens, the winner being the player who removes the last token. This "lesson" presents a detailed analysis of the strategies underlying Nim and several variations of the game. Several proofs of the strategies are... 6 Intermediate Value Theorem Resource Type: Content Supports -- Reference materials Discipline: Mathematics Grades: Grades 12–Postsecondary Professional Commentary: This website poses and solves the classic hiker problem: A hiker starts on a path from the bottom of a mountain at 6:00 a.m. and arrives at the top of the mountain at 6:00 p.m.... |