1 Time-Axis Fallacy and Bayes' Theorem Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 10–12 Professional Commentary: Most students understand that the probability of an event occurring can be influenced by another event that has already occurred. However, many students cannot understand that the probability of an event occurring can actually be dependent on an event that occurred later.... 2 Venn Diagrams and Logic: A Visual Approach to Deductive Reasoning Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 4–12 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 create Venn diagrams for a particular argument.... 3 Circle Packing: Soda Rack Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 Professional Commentary: In this lesson, 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.... 4 Hooked on Problem Solving Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 3–7 Professional Commentary: Students use each of the digits 1–9 exactly once to form addition problems consisting of two three-digit addends and a three-digit sum and look for patterns in the solutions. Guiding questions, summary questions, assessment tasks, and extensions are included.... 5 Understanding Ratios of Areas of Inscribed Figures Using Interactive Diagrams Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–10 Professional Commentary: This NCTM E-Example features four student tasks along with teacher support material about using interactive figures with students to explore the connections between algebra and geometry. This site features an applet that students can use to explore an interesting quantitative relationship between the area of a polygon and the area of an inscribed figure formed by... Career Fields: Arts & Communication, Construction Technologies, General Career Skills Projects: COR, Standards First 6 Looking Through the Algebraic Lens, Grades 3-5 Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 2–7 Professional Commentary: This lesson has two parts, both of which foster algebraic thinking across content strands. Part I, from the number and operations strand, has students explore the addition and subtraction of odd and even numbers.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: We assume that all the points in the plane have been colored either red or blue. It is then required, without knowing anything further about the distribution of the colors, that we find: (a) a line segment whose endpoints and midpoint are the same color, (b) three points of the same color that determine a right angle, (c) an equilateral triangle whose vertices are the same color, and (d) a parallelogram whose vertices are the same color.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: 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.... 9 Fibonacci Nim: Static Nim Resource Type: Content Resource Discipline: Mathematics Ohio Standards Alignment: 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 provided.... Resource Type: Content Resource Discipline: Mathematics Ohio Standards Alignment: 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.... |