Students must identify a graph that represents a linear relationship. 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 42. (author/sw)

Given four equations of functions, students must identify which one is linear. 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 44. (author/sw)

Given four equations of functions, students must identify which one is nonlinear. This multiple-choice 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, 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: 2006 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 3. (author/sw)

Students must identify a table of values that represents a linear function. 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 10. (author/sw)

In this lesson, students focus on China's population growth. They graph data on graph paper using a graphing calculator or spreadsheet software. Students predict future population numbers and decide if the population growth is linear or exponential. Students analyze the data they collect and write equations that match their graph. Resources include Web sites with current and archived population data, government sites (ORC notes that a couple of these general information links are broken, but their inaccessibility does not affect the lesson in a critical way), and mathematical sites with interactive graphs comparing linear and exponential functions. Extensions are made to other linear and exponential growth situations that exist in the real world. The site includes a complete lesson plan for teachers and detailed instructions for students. (author/sw)

This lesson introduces students to the many factors that play a role in creating a forest-fire danger index. Students work with the Angstrom and Nesterov Indexes. To complete the activities, students should be comfortable with linear, quadratic and exponential functions. Summation notation is also used with the Nesterov index. Graphing calculators are required for some of the activities, but not all activities have to be included in the lesson. The site provides activity sheets, Internet extensions, and considerable background for the teacher on fire danger indices. This lesson originally appeared in the October 1999 issue of Mathematics Teacher. (author/sw)

This lesson emphasizes patterns, discovery, and vocabulary by focusing on the basic connections between graphs, tables, and symbolic representations for lines, parabolas, inverse models, and exponential functions. Students investigate various patterns and models using the graphing calculator. This lesson is designed for first-year algebra students and is an ideal follow-up to a unit on lines. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. The 39-page pdf file includes several pages of nice applications of the models presented. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Getting Out of Line 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/pk)

In this lesson, students design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Using the data they gather in a table, students graph and write an equation for a line of best fit. They then use their derived equation to make predictions about the amount of water that would be wasted from one leak over a long period of time or the amount wasted by several leaks during a specific period of time. 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 Drip, Drop, Drip, Drop 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/sk)

Students learn about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers with different bases. The lesson begins with a review of direct variation and contrasts the properties of direct variation with those of inverse variation.  A supporting article on oil spills, as well as suggestions for assessment, are included. (author/sw)