261 The Cereal Box Problem Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students explore the Cereal Box Problem first by estimating an answer, then modeling the problem with manipulatives and collecting data for the class, and finally using a computer program to model the problem and determine the theoretical expected value. This mathematically rich problem was prepared by the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools developed by the Ohio Department of Education.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: The "Folded Triangle" problem is rich by virtue of its connections to so many different levels of secondary school mathematics. Students in a first-year algebra or geometry course can investigate the problem just as meaningfully as students enrolled in a senior-level calculus course.... 263 Fireworks: The Localized Big Bang Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 Professional Commentary: Commercial fireworks must be carefully timed to ignite as intended. The process involves projectile motion that can be modeled with the quadratic function (ignoring air resistance), as found in the study of dynamics in physics: h = –16t2 + v0t + h0.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students begin by graphing data points presented in unusual formats. They then construct the graph that fits those points. Using a creative technique, they are able to find the function rule that relates the data points even when the function is not a simple linear relationship.... 265 How Many Gifts Did My True Love Give to Me? Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: This problem asks us to find the total number of gifts my true love gave to me during the twelve days of Christmas. The fact that there are two distinct methods to find the solution makes this problem interesting.... 266 If They Test Positive, Are They Using Drugs? Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: In this problem, students develop a mathematical model that enables them to determine the fraction of the population that is using performing-enhancing substances based upon the parameters of the testing, parameters of the population, and the fraction of the tests that have positive results. From this, they can help determine whether or not authorities should test all athletes.... 267 Caffeine in the Body: Get the Lead Out Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 Professional Commentary: Students explore the use of exponential decay models in the context of eliminating caffeine and lead from the body. The problem starts with generalizing the relationship between time and the amount of chemical left in the body to writing an explicit rule and connecting it to the graphical representation.... 268 E. coli Bacteria: Can't Live Without Them Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 Professional Commentary: This problem uses a contextual situation of E. coli bacteria in the stomach.... Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 10–12 Professional Commentary: Land has been donated to River City. Students must decide how to split the land use between development and recreation in a way that will minimize the cost to the city of the necessary improvements, while adhering to restrictions agreed on by the River City Council.... 270 Generating Trig Tables Resource Type: Rich Problem, Inquiry, or Exploration Discipline: Mathematics Ohio Standards Alignment: Grades 10–12 Professional Commentary: Students compare trigonometric ratios for a unit and non-unit circle with the goal of observing that the ratios are independent of the radius. They thus see the benefit of using a radius of one unit.... |