Students must match a portion of a circle graph with data in a table. This multiple-choice question is a sample item used in the 2005 Ohio Graduation Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the OGT test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. The test item is also available in Microsoft® Word. 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: 2005 OGT for Mathematics, Annotated Item 22. (author/sw)

Students are asked to interpret data shown in a box-and-whiskers plot. This multiple-choice question is a sample item used in the 2004 Ohio Graduation Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the OGT test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. The test item is also available in Microsoft® Word. 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: 2004 OGT for Mathematics, Annotated Item 2. (author/sw)

Students must determine the interval of greatest increase on a scatterplot. This multiple-choice question is a sample item used in the 2004 Ohio Graduation Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the OGT test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. The test item is also available in Microsoft® Word. 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: 2004 OGT for Mathematics, Annotated Item 34. (author/sw)

Students are asked to construct a circle graph using percentage data in a table. They have the option of using a calculator. This constructed-response question is a sample test item used in grade 8 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 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: 1990-8M9, No. 16. (sw)

Students are asked to interpret a bar graph and determine the approximate number of votes a candidate received. This multiple-choice question is a sample item used in the 2008 Ohio Graduation Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the OGT test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. This OGT item is also available in Microsoft® Word. 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: 2008 OGT for Mathematics, Annotated Item 18. (author/sw)

Students are asked to interpret the smallest value displayed on a stem-and-leaf plot. This multiple-choice question is a sample test item used in grade 8 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: 2003-8M10, No. 8. (sw)

Students must interpret box-and-whiskers plots to find a difference of medians. This multiple-choice question is a sample item used in the 2005 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. This OAT item is also available in Microsoft® Word. 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: 2005 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 34. (author/sw)

Students must read a temperature versus time graph and find the difference in temperatures at two different times. This multiple-choice question is a sample test item used in grade 12 in the 1996 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: 1996-12M13, No. 1. (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 write their interpretation of a bicycle trip based on a line graph of the speed over an 80-minute period of time. This constructed-response question is a sample test item used in grade 8 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: 2003-8M10, No. 19. (sw)

Students are asked to estimate the number of radios represented by a 37° sector of a circle. 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 1992 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: 1992-8M12, No. 4. (sw)

Students are asked to solve a multi-step problem involving average hourly wages using data in a table. They have the option of using a calculator. This constructed-response question is a sample test item used in grade 12 in the 1996 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: 1996-12M12, No. 2. (sw)

Students are asked to determine the average of data given in a frequency bar graph. They have the option of using a calculator. This constructed-response question is a sample test item used in grade 12 in the 1992 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: 1992-12M7, No. 12. (sw)

Students are asked to explain why a pictograph is misleading. This constructed-response question is a sample test item used in grade 8 in the 1992 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: 1992-8M15, No. 17. (sw)

This lesson is most meaningful to students in states like Ohio, where turnpike tolls are proportional to distance. Students use a toll ticket or a state website like The Ohio Turnpike to collect data on distance traveled versus the toll collected, and they create a scatterplot using spreadsheet software or a graphing calculator. They find the line of best fit and discuss the interpretation. Activity sheets, discussion questions, suggestions for assessment, lesson extensions, and questions for teacher reflection are included. (sw)

In this lesson, students model linear data collected in a variety of settings that range from car repair to sports to medicine. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the line of best fit. Activity sheets and guiding questions are provided for four applied data contexts. (author/sw)

Students are asked to find the average birth month. Analysis of the data and examination of just what “average” means in the case of months leads to the mode being selected as the best way to find an "average" with categorical data. Students create appropriate graphs to illustrate what the mode is. Next, students are asked if this information is representative of the entire population, and why or why not. Questions about sampling arise in this portion of the lesson. Finally, students are asked to create a method to determine the average day of the week for birthdays. Students explore a question that engages them even as it leads to deeper understanding of basic statistical concepts. 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 investigate the average earnings of a movie in a given week using data they collect from web or print resources. In this investigation, students use the measures of center and different graphical displays of the data to make an argument that each of the measures of center may be appropriate, providing an explanation for their choice of mean, median, or mode. They identify outliers and create box plots (both modified and non-modified), histograms, and stem-and-leaf plots. Students also analyze spread and distribution of the data as part of their investigation. To conclude the exploration, students prepare a poster and give a report to the class. As students analyze actual data about a topic that engages them, they apply mathematics to a real-world situation and can see the value of the statistical concepts they are studying. Evaluation rubrics are included. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)

Using simulated data, students determine the probability that a customer calling to order a shirt gets a busy signal. They then estimate the amount of money the company might lose when customers get a busy signal. Activity sheets take students step by step through the basic problem. A second activity considers the situation if the company installs a second phone line. A 31-page background manual for the teacher explains the mathematical ideas behind the lesson and the numerous real-life applications of these ideas. Blackline masters and Internet extensions are included. (sw)

This site offers graphical images that portray data accumulated from a range of sources (historical events, spread of disease, distribution of resources, etc.). The purpose of the collection is to give examples of the "best and worst of statistical graphics." The author contrasts the differences between the best and worst by showing how some images communicate data clearly and truthfully, while others misrepresent, lie, or totally fail to "say something." Among the images are Florence Nightengale's coxcomb graphic of deaths among soldiers and a cartogram showing the 2004 U.S. election results, an unusual map of the country in which the size of each red or blue state corresponds to its population rather than its land area. Teachers looking for examples of innovative representations of data or examples of misrepresentation will find this resource helpful. (author/th)