221 Permutations -- Counting Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Suppose you have some objects that you want to line up in a row. In how many different ways can you do it? Extensions of the problem and a complete discussion of the underlying mathematical ideas are included.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 5–8 Professional Commentary: Have students think of questions to ask about the following situation: Draw on squared paper or build with snap cubes a rectangular pool table. Trace out the path of a ball until it hits a corner.... 223 Probability Using Dice Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 4–8 Professional Commentary: What are the probabilities of rolling various sums with two dice? How can you analyze this situation? Extensions of the problem and a complete discussion of the underlying mathematical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 5–10 Professional Commentary: This activity shows how cutting geometric shapes and rearranging the pieces leads to some standard area formulas and to the Pythagorean Theorem. Complete proofs are included.... 225 Rainy Lake, aka Mirror Lake Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students use a topographical map featuring a body of water, such as a lake, pond, or river, to figure out how much the level of the water would rise after a one-inch rainfall the previous night. An extension of the problem and a discussion of the underlying mathematical ideas are included.... 226 Representation of Data -- Cholera and War Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 6–8 Professional Commentary: The object of this activity is to study excellent examples of the presentation of data. Students analyze (1) a map of cholera cases plotted against the location of water wells in London in 1854 and (2) a map of Napoleon's march on Moscow in 1812-1813 to see what inferences they can draw from the data displays.... 227 Representation of Data -- The U.S. Census Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 6–8 Professional Commentary: The object of this activity is to study an excellent example of the presentation of data. Students analyze an illustration of the 1930 U.S.... 228 Round Robin Tournament Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 5–8 Professional Commentary: Malabar Middle School is scheduling a round-robin tournament for six softball teams. In a round-robin tournament each team plays each other team exactly once.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 6–8 Professional Commentary: What would be a reasonable definition of similarity? What are sufficient conditions that two triangles be similar? Quadrilaterals? Other figures? Extensions of the problem and a complete discussion of the underlying mathematical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 5–7 Professional Commentary: The areas of what simple figures can be measured using copies of a selected unit square? Can rectangles be measured with unit squares? How about triangles? Parallelograms? Extensions of the problem and a complete discussion of the underlying mathematical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University.... |