Students must estimate a number by interpreting a bar graph and using proportional reasoning. This multiple-choice question is a sample item used in the 2006 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, and discussion of incorrect responses. 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: 2006 Ohio Grade 7 Achievement Test for Mathematics, Annotated Item 4. (author/sw)

Students must select a statement that supports a given claim. This multiple-choice question is a sample item used in the 2005 Ohio Grade 7 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 7 Achievement Test for Mathematics, Annotated Item 27. (author/sw)

Students learn about sampling bias by working in three groups to survey separately students, parents, and teachers about the amount of homework students ought to have. They report and compare the responses from each of the three groups to see how the results differ. They then look at how item bias can influence responses by collecting data from different members of a single group using differently worded questions. Activity sheets, discussion questions, ideas for assessment and extensions, and Internet links are included. (sw)

Students first estimate the number of drops of water that will fit on the head of a penny. The teacher engages the class in a discussion on how to organize and display data in a stem and leaf plot. Using a Post-it, each student records the units digit of their guess and places it in the appropriate position on the stem and leaf plot. To check the range of guesses, each student experiments by actually placing as many drops of water on the head of a penny as possible. The units digits of the actual numbers are also recorded on Post-its and displayed on the same stem and leaf plot, thus creating a back-to-back stem and leaf plot. Students work in groups to analyze the data, paying particular attention to its range and to the extent that different variables may have had in contributing to the disparities. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, additional resources, and a discussion of mathematical content. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Wet Heads lesson and then access the appropriate video clips at the PBS TeacherSource website. The video player necessary to view the video clips can be downloaded for free from the site. (author/sw)

This third lesson in a multi-level, multi-lesson site engages students in analyzing information presented in four circle graphs depicting the population of three states relative to the rest of the country in 1800, 1850, 1900, and 1950. Students are asked to interpret and draw logical inferences from the graphs individually and collectively. Activity sheets, discussion questions, extensions of the lesson, and Internet links are included. This resource is based on an article that appeared in the October 1991 issue of Arithmetic Teacher. (author/sw)

This site provides hot links to other graphing sites that show both valid and misleading graphs of data. Unfortunately, 3 of the links that look most interesting, according to their titles, are dead, but 12 others are working and provide some good examples of misleading graphs. (sw)

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. 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)