This lesson provides students with the description of an authentic situation (buying DVDs) and data points that fit that situation. Students graph the line that contains those points; determine its y-intercept, slope, and equation; and interpret the slope and y-intercept in the context of the problem. Finally, students extrapolate to determine a functional value that is outside the domain they have graphed. Questions for students, suggestions for assessment, extensions of the lesson, and questions for teacher reflection are included. (author/sw)

This lesson uses an airline ticket counter as a context for teaching students about queueing theory and average waiting time. Activity sheets take students step by step through the basic problem. A 38-page background manual for the teacher explains in clear and comprehensive detail the mathematical ideas behind queueing theory and the numerous real-life applications people encounter every day. Blackline masters and Internet extensions are included. (sw)

Students investigate the pattern determined by the areas of squares inscribed in squares formed by joining the midpoints of the sides of the previous square. The sequence generated is a simple geometric sequence. One special feature of this lesson is the use of the TI-92, which is used to generate the data. Students find both the explicit and recursive forms for the sequence. At the algebra I level, students do not necessarily need the formal notation, but are very capable of exploring the pattern, plotting the model, and describing how to generate the sequence. 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 Squares Inside Squares 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)

This lesson focuses on connections between the factors of quadratic polynomials of the form x² + bx + c, algebra tile representations of the factorization, and roots of the quadratic function. Students use algebra tiles to identify binomial factors and then use the graphing calculator to verify the result. In addition, students identify the x-intercepts and y-intercepts of each quadratic function and explore relationships between the graph of x² + bx + c and its factored form (x + m)(x + n). An activity sheet and related assessment items are included. Though the suggested time period for the lesson is one class period, ORC reviewers thought the ideas were rich enough to require more than a single day. (author/sw)

Students will investigate the input/output model for building function tables. Then they will connect tables, graphs, function rules, and equations in one variable. Finally, they will work backwards to determine function rules for given data sets or graphs. Four multi-page activity sheets, discussion questions, a lesson extension, and suggestions for assessment are included. (author/sw)