In this first of five lessons related to football, students identify geometric shapes on a football field. Some of the shapes are overlapping or rotated in orientation. ORC notes that the overview of this multi-lesson site does not match the content of the site. Nevertheless, the activities are creative enough to interest some reluctant mathematics students. Activity sheets and Internet extensions are included. This site is adapted from an article that appeared in the January 1993 issue of Arithmetic Teacher. (author/sw)

In this second of five lessons related to football, students look at four pictures and make up one or more story problems to go with each picture. Classmates share and compare the problems they have made up. ORC notes that the overview of this multi-lesson site does not match the content of the site. Nevertheless, the activities are creative enough to interest some reluctant mathematics students. Activity sheets and Internet extensions are included. This site is adapted from an article that appeared in the January 1993 issue of Arithmetic Teacher. (author/sw)

In this third of five lessons related to football, students look for different combinations of points that could be scored in a football game to result in specified scores. ORC notes that the overview of this multi-lesson site does not match the content of the site. Nevertheless, the activities are creative enough to interest some reluctant mathematics students. Activity sheets and Internet extensions are included. This site is adapted from an article that appeared in the January 1993 issue of Arithmetic Teacher. (author/sw)

In this second of five lessons related to football, students look at four pictures and make up one or more story problems to go with each picture. Classmates share and compare the problems they have made up. ORC notes that the overview of this multi-lesson site does not match the content of the site. Nevertheless, the activities are creative enough to interest some reluctant mathematics students. Activity sheets and Internet extensions are included. This site is adapted from an article that appeared in the January 1993 issue of Arithmetic Teacher. (author/sw)

This lesson capitalizes on students' interest in sports to integrate instruction on fractions, decimals, percents, rounding, Cartesian coordinates, probability, and statistics. Students create their own game board using baseball card statistics and then play a simulated baseball game. The game board worksheet, suggested enhancements, and Internet extensions are included. This lesson is based on an article that appeared in the May 1996 issue of Mathematics Teaching in the Middle School. (author/sw)

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. Students formulate questions that can be asked about this situation. A discussion of the underlying mathematical ideas is 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. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)

This two-lesson unit explores the meaning of constant rate of change with an interactive simulation of one or two runners racing along a track. Students can control the speeds and starting points of the runners, watch the races, and examine a graph of the time-versus-distance relationship. Activities like these can help students in the upper elementary and middle grades understand ideas about functions, constant rates, and change over time. Activity sheets and discussion questions are included. Go to ORC#1444 for a resource designed to introduce the teacher to the use of the simulation. (author/sw/js)

Students construct charts to examine number patterns and use these patterns to generate a graph. The story of Tortisha and Harry is presented to the class: Harry is so sure that he can run faster than Tortisha, that he will give her a 2 mile head start in a race. Harry runs at the rate of 3/4 mile in 6 minutes and Tortisha runs at the rate of 1/2 mile in 5 minutes. Will Harry ever catch Tortisha? Students first map the progress of Tortisha and Harry using the Dream Track worksheet. Finding this to be quite tedious and confusing, they make a chart to examine patterns and then graph Harry's and Tortisha's progress. Finally, students analyze the problem to arrive at algebraic representations for both Harry's and Tortisha's rates. This information is entered into the graphing calculator which generates both a chart and graph of the situation. So, the question still remains, "Who will win the race?" Students discover that either Tortisha or Harry could win the race, or it could be a draw. It all depends on the length of the race. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, and additional resources. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Great Race lesson and then access the appropriate video clips. (author/sw/js)

This NCTM E-Example features a software simulation that illustrates one or two runners racing on a track. The resource, designed to introduce the teacher to the use of the simulation, includes a discussion about the mathematics that can be developed when using the simulation with students. With the simulation, students can control the speeds and starting points of the runners, watch the race, and examine a graph of the time-versus-distance relationship. Working with this simulation can help students in the upper elementary and middle grades understand ideas related to functions. See a related two-lesson unit, Understanding Distance, Speed, and Time Relationships. (author/sw/js)

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. You must start the ball at a corner and use only 45-degree angles. An extension 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. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)

Students develop their skills in collecting and recording data using the real-world situation of bouncing a tennis ball. They use the data collected to formulate the relationship between the dependent and independent variables in their experiment. Use of a graphing calculator is illustrated but not required, and Internet extensions are provided. This resource was adapted from Navigating Through Algebra in Grades 6-8 published by NCTM in 2001. (author/sw)

Given that 38% of the 1200 students enrolled in a school participate in sports, students are asked to determine the number of students participating in sports. They have the option of using a calculator. This multiple-choice question is a sample test item used in grades 8 and 12 in the 2003 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring key, and discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 2003-8M7, No. 14. (sw)

Students must interpret a pictograph in which each icon represents four students. They have the option of using a calculator. This multiple-choice question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring key, and discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 1990-12M9, No. 6. (sw)

Students turn a bar graph into a circle graph. They begin by conducting a survey to determine their classmates' favorite sport, soft drink, music, and color. Working in small groups, the students construct bar graphs to illustrate the survey results in each category, coloring each bar in the bar graph a different color. They cut out the bars of the bar graphs and tape them together, end to end, to make one long multicolored strip for each of the categories. They then form each long strip into a circle and mark along the circle the points at which the strip changes color. Connecting these points to the center of the circle, they have a circle graph that corresponds to the original bar graph. In a separate activity, students estimate the fractional part of the class that prefers each item in a category by repeatedly folding the long strip in half and comparing each colored segment to 1/2, 1/4, 1/8, 3/8, and so on. Guiding questions, summary questions, assessment tasks, lesson extensions, a survey sheet, and three activity sheets are included. (sw)

How many times does a basketball bounce before its rebound is less than two feet high? This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 2870.11)(author/sw)

Can you reason from information about the team's average weight to determine the weight of one particular player? This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 2452.14)(author/sw)

This unit is centered around the analysis of the statistical data contained on professional baseball trading cards. These cards are first used to familiarize students with some of the basic terminology associated with the game. Next, students are directed to the actual statistical data included on the card and how to utilize these data to determine the overall rating of past performance. Additionally, students work with decimals and ratios to obtain key statistical data. In addition to the lesson plan, the site includes ideas for teacher discussion and additional resources. This lesson is accompanied by video clips illustrating lesson procedures. The user should first locate the Fantasy Baseball, Part I lesson and then access the appropriate video clips. (author/sw/js)

Student pairs act as co-managers of a baseball team. Each pair receives a pack of baseball cards. They compute and analyze the key statistical data of the given players, make decisions on who they want to keep and who they want to trade, arrange their lineups, and play simulated games. Students use the key statistical data to construct individual player spinners, determine the line up, and play a simulated baseball game. The ultimate goal is to be the manager of the winning team of the Fantasy Baseball World Series. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, and additional resources. This lesson is accompanied by video clips illustrating lesson procedures. The user should first locate the Fantasy Baseball, Part II lesson and then access the appropriate video clips. The video player necessary to view the video clips can be downloaded for free from the site. (author/sw)

This lesson capitalizes on students' interest in sports to integrate instruction on fractions, decimals, percents, rounding, Cartesian coordinates, probability, and statistics. Students create their own game board using baseball card statistics and then play a simulated baseball game. The game board worksheet, suggested enhancements, and Internet extensions are included. This lesson is based on an article that appeared in the May 1996 issue of Mathematics Teaching in the Middle School. (author/sw)

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. Students formulate questions that can be asked about this situation. A discussion of the underlying mathematical ideas is 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. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)

This two-lesson unit explores the meaning of constant rate of change with an interactive simulation of one or two runners racing along a track. Students can control the speeds and starting points of the runners, watch the races, and examine a graph of the time-versus-distance relationship. Activities like these can help students in the upper elementary and middle grades understand ideas about functions, constant rates, and change over time. Activity sheets and discussion questions are included. Go to ORC#1444 for a resource designed to introduce the teacher to the use of the simulation. (author/sw/js)

Students construct charts to examine number patterns and use these patterns to generate a graph. The story of Tortisha and Harry is presented to the class: Harry is so sure that he can run faster than Tortisha, that he will give her a 2 mile head start in a race. Harry runs at the rate of 3/4 mile in 6 minutes and Tortisha runs at the rate of 1/2 mile in 5 minutes. Will Harry ever catch Tortisha? Students first map the progress of Tortisha and Harry using the Dream Track worksheet. Finding this to be quite tedious and confusing, they make a chart to examine patterns and then graph Harry's and Tortisha's progress. Finally, students analyze the problem to arrive at algebraic representations for both Harry's and Tortisha's rates. This information is entered into the graphing calculator which generates both a chart and graph of the situation. So, the question still remains, "Who will win the race?" Students discover that either Tortisha or Harry could win the race, or it could be a draw. It all depends on the length of the race. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, and additional resources. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Great Race lesson and then access the appropriate video clips. (author/sw/js)

This NCTM E-Example features a software simulation that illustrates one or two runners racing on a track. The resource, designed to introduce the teacher to the use of the simulation, includes a discussion about the mathematics that can be developed when using the simulation with students. With the simulation, students can control the speeds and starting points of the runners, watch the race, and examine a graph of the time-versus-distance relationship. Working with this simulation can help students in the upper elementary and middle grades understand ideas related to functions. See a related two-lesson unit, Understanding Distance, Speed, and Time Relationships. (author/sw/js)

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. You must start the ball at a corner and use only 45-degree angles. An extension 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. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)

Students develop their skills in collecting and recording data using the real-world situation of bouncing a tennis ball. They use the data collected to formulate the relationship between the dependent and independent variables in their experiment. Use of a graphing calculator is illustrated but not required, and Internet extensions are provided. This resource was adapted from Navigating Through Algebra in Grades 6-8 published by NCTM in 2001. (author/sw)

How many matches must be played to determine a tennis tournament champion? This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 1180.65)(author/sw)

This three-part activity illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. The activity is adapted from High School Mathematics at Work, a publication from the National Research Council. In the first part, Modeling the Situation, an interactive environment is used to show the parameters involved and the range of results that can be obtained with different dosages of medicine. In the second part, Long-Term Effect, the interactive environment is used to investigate how changing parameter values affects the stabilization level of medicine in the body. In the third part, Graphing the Situation, an interactive graphical analysis provides a visual interpretation of the results. Through multiple representations of a common concept, better insight into, and a deeper understanding of, the problem situation can be achieved. (author/sw)

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. They also explore how these kinds of models apply to testing for medical conditions. 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. (author/sw)

Given that 38% of the 1200 students enrolled in a school participate in sports, students are asked to determine the number of students participating in sports. They have the option of using a calculator. This multiple-choice question is a sample test item used in grades 8 and 12 in the 2003 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring key, and discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 2003-8M7, No. 14. (sw)

Students must interpret a pictograph in which each icon represents four students. They have the option of using a calculator. This multiple-choice question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring key, and discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 1990-12M9, No. 6. (sw)

Students turn a bar graph into a circle graph. They begin by conducting a survey to determine their classmates' favorite sport, soft drink, music, and color. Working in small groups, the students construct bar graphs to illustrate the survey results in each category, coloring each bar in the bar graph a different color. They cut out the bars of the bar graphs and tape them together, end to end, to make one long multicolored strip for each of the categories. They then form each long strip into a circle and mark along the circle the points at which the strip changes color. Connecting these points to the center of the circle, they have a circle graph that corresponds to the original bar graph. In a separate activity, students estimate the fractional part of the class that prefers each item in a category by repeatedly folding the long strip in half and comparing each colored segment to 1/2, 1/4, 1/8, 3/8, and so on. Guiding questions, summary questions, assessment tasks, lesson extensions, a survey sheet, and three activity sheets are included. (sw)

Students must critique a method of sampling to determine the most popular sport in a city. They have the option of using a calculator and must explain their answer. This constructed-response question is a sample test item used in grades 8 and 12 in the 2003 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring guide, sample student responses, and a discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 2003-8M7, No. 15. (sw)

Troy is building a pool that is proportional to an Olympic-size pool. Given the width of Troy's pool, students must find the scale factor and the length. This short-answer question is a sample item used in the 2007 Ohio Grade 7 Achievement Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the OAT item (PDF), with access to performance data, complexity level of the item, a complete solution of the problem, and a scoring rubric. The Ohio Department of Education Instructional Management System website allows visitors to search for test items by subject and grade band and build a printable database of questions using the Add to Your Backpack function. ODE Reference Information: 2007 Ohio Grade 7 Achievement Test for Mathematics, Annotated Item 31. (author/sw)

Students use quadratic functions to describe the relationship of the height of a football thrown in a parabolic path to its distance from the goal line. Working with graphing calculators, students collect and organize data, make a scatterplot, fit a curve to the appropriate parent function, and interpret the results. Discussion questions, an activity sheet, an extension of the problem, and suggestions for assessment are included. (author/sw)

How many times does a basketball bounce before its rebound is less than two feet high? This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 2870.11)(author/sw)

Can you reason from information about the team's average weight to determine the weight of one particular player? This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 2452.14)(author/sw)

When does a soccer player running down the sideline have the best chance of making a goal? This lesson uses the Power of Points Theorem to answer this question. The Power of Points theorem is often taught as three separate theorems: the Chord-Chord Power Theorem, the Secant-Secant Power Theorem, and the Tangent-Secant Power Theorem. Using a dynamic geometry applet, students discover that these three theorems are all applications of the Power of Points Theorem. They also use their discoveries to solve several related problems. Activity sheets, applets, overheads, discussion questions, lesson extensions, suggestions for assessment, and issues for teacher reflection are included. (author/sw)

How many matches must be played to determine a tennis tournament champion? This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 1180.65)(author/sw)

Figure out the worst tennis player from the given clues. This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 1230.36)(author/sw)

Given 5 pieces of information, sort out 4 athletes and identify the golfer. This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 1230.33)(author/sw)

This three-part activity illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. The activity is adapted from High School Mathematics at Work, a publication from the National Research Council. In the first part, Modeling the Situation, an interactive environment is used to show the parameters involved and the range of results that can be obtained with different dosages of medicine. In the second part, Long-Term Effect, the interactive environment is used to investigate how changing parameter values affects the stabilization level of medicine in the body. In the third part, Graphing the Situation, an interactive graphical analysis provides a visual interpretation of the results. Through multiple representations of a common concept, better insight into, and a deeper understanding of, the problem situation can be achieved. (author/sw)

In this problem, an injured athlete is afraid she will have too much anti-inflammatory drug in her system at any one time. Students are given the amount of anti-inflammatory drug the athlete takes, how often she takes it, and how long it takes the body to metabolize 60% of the drug. Their goal is to help the injured athlete understand what is going on in her system. To solve the problem, students will develop recursive relationships and work in several different mathematical systems, using equations, tables, and graphs. The problem can be solved by hand (although this is quite tedious), or using the list function on a graphing calculator, or using the software Fathom™. Through this investigation, students use mathematical modeling to gain a better understanding of a medical situation. They discover that they can make predictions about the amount of a drug in one’s system, depending upon how much and how often the drug is administered. 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. (author/sw)

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. They also explore how these kinds of models apply to testing for medical conditions. 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. (author/sw)

Students must critique a method of sampling to determine the most popular sport in a city. They have the option of using a calculator and must explain their answer. This constructed-response question is a sample test item used in grades 8 and 12 in the 2003 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring guide, sample student responses, and a discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 2003-8M7, No. 15. (sw)