In this lesson, students use a 10 x 10 grid to solve various types of percent problems. The grid model offers a means of visualizing the given information as well as suggesting different approaches to solving problems. Students begin with representing simple percents on the grid and then move to percents less than 1 and greater than 100. Solutions to the three standard kinds of percent problems are illustrated, as well as problems involving percent increase and percent decrease. A reproducible grid sheet is provided and several Internet extensions are included. This lesson plan was adapted from an article that appeared in the April 1994 issue of Mathematics Teaching in the Middle School. (author/sw)

Students estimate the size of a large population by applying the concepts of ratio and proportion through the capture-recapture statistical procedure. Students are introduced to a problem involving an environmental issue: Scientists have determined that the number of fish in Chesapeake Bay has decreased. Assuming this is true, scientists must have counted the number of fish and noted the change. How did they count the fish? Groups are formed to explore a wide range of possible strategies. Students are introduced to the capture-recapture method which involves capturing fish, tagging them, returning them and recapturing another sample. In groups, students are given containers (the bay) and an unknown number of fish-shaped cheese crackers to use in simulating the capture-recapture method. Students net the fish-shaped cheese crackers and substitute fish-shaped pretzels to simulate tagged fish. Groups then take samples and record the number of tagged fish and the total number of fish. After several samples are taken, results from each group are recorded. Students apply their knowledge of proportion to arrive at an estimate of the total fish population. 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 Something Fishy 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)

In this lesson, students experience an application of proportion that scientists use to solve real-life problems. Students estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the total number of items in a sample is the same as the ratio of tagged items to the total population. An activity sheet, discussion questions, suggestions for assessment, a lesson extension, and prompts for teacher reflection are included. (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 at the PBS TeacherSource website. The video player necessary to view the video clips can be downloaded for free from the site. (author/sw)

Students must estimate a percentage of boxes sold. 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 12. (author/sw)

Students must use estimation skills to identify an unreasonable estimate. 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 25. (author/sw)

Students use proportional reasoning to estimate the number of acres a farmer will plant in soybeans. This multiple-choice question is a sample item used in the 2008 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: 2008 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 7. (author/sw)

Students must determine when a decreasing sale price on a piano reaches a certain value. This short-answer question is a sample item used in the 2006 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, a complete solution of the problem, and a scoring rubric. 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: 2006 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 26. (author/sw)

Students are asked to use given data to write a convincing argument. This short-answer 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, a complete solution of the problem, and a scoring rubric. 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 36. (author/sw)