This lesson is a data analysis lab in which students gather mass and volume data for two mystery liquids--oil and water--and then use the data to explore linear functions. Connections to science are an important part of this algebra lesson, which deals with density. Active learning and communication are also essential aspects of the lesson. Students work in groups to collect, verify, and display the data. They then discuss the physical meaning of the slopes and y-intercepts of the various lines they have created from their scatterplots. 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 lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Mystery Liquids 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 week-long unit, students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. The unit provides students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities. One important outcome for this unit is helping students develop an appreciation for the power and limitations of mathematical modeling. They should realize that the two most basic expectations of models are (1) the ability to account for or represent known phenomena and (2) the ability to predict future results. The unit also illustrates the critical importance of mathematics in space science. Several Internet and teaching extensions are included. This unit was adapted from Modeling Orbital Debris Problems in Mission Mathematics, Linking Aerospace and the NCTM Standards, 9-12, a NASA/NCTM project, NCTM 1997. The user can easily forgive some typos in view of the detailed notes to the teacher and the highly informative and challenging student activity sheets. (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)

This four-lesson unit uses iteration and recursion to model and analyze a changing fish population. Graphs, equations, tables, spreadsheets, and calculators are used to investigate the effect of varying parameters on the long-term population of fish in a trout pond. Step-by-step instructions, activity sheets, questions for reflection, and suggestions for assessment are included. (author/sw)

Students must identify the slope of a line segment shown on a coordinate graph. 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 43. (author/sw)

Students must compute the distance between two points on a coordinate plane. This multiple-choice question is a sample item used in the 2007 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: 2007 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 30. (author/sw)

Students must find the slope of the line connecting two points in the coordinate plane. 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 25. (author/sw)