In this 5-lesson unit, students take a pretend scuba-diving trip to Belize. They explore various real-world applications of time and distance measurement, make estimations and calculations, and use online resources to plan the trip. In the first lesson, students view several websites and determine what mathematical ideas and concepts are involved in scuba diving. In the second lesson, students use various resources to choose travel dates, compare temperatures, estimate and calculate distances to Belize City, and determine the length of their flight. The third lesson focuses on time zones and the effects of traveling across time zones. In the fourth lesson, students pretend to travel to the island of Ambergris Caye off the coast of Belize; they complete the measurements needed for their scuba diving gear and solve elapsed time problems. In the final lesson, students complete linear conversions, find elapsed time, calculate a percentage, and analyze data from a chart. ORC reviewers especially liked this lesson as a context for integrating mathematics, science, reading, and social studies. Videos, Internet resources, activity sheets, questions for students, suggestions for assessment, lesson extensions, and prompts for teacher reflection are included. (author/sw)

In this lesson, students explore how variations in the shape, color, and other characteristics of solar collectors affect the energy absorbed. Students make rectangular prisms that have the same volume but different linear dimensions. After measuring the volume of several boxes with unit cubes, they develop the formula for the volume of a rectangular prism. They consider several other factors besides shape in experimenting to see what kind of solar collector is most efficient. This lesson is a nice integration of mathematics and science. (author/sw)

Making a scale model of the solar system is not a novel idea, but this site restricts its consideration to the Earth, Moon, and Mars and explains in more detail than most. Using balloons for the planetary bodies makes the actual construction simple. A student activity sheet and several links to Internet resources are included. (sw)

Exploring the relationship between two variables prepares the student for the study of functions, which in turn provides the basis for much of the study of algebra. Students work in pairs to measure their arm span and height and record them on a class chart. The class works together to create a scattergram to display the data. Class discussion focuses on interpreting the scattergram, followed by using graphing calculators to plot the scattergram. Finally, students examine the graph of y = x and its relationship to the scattergram. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, additional resources, a discussion of mathematical content, related research findings, and technology connections. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Reaching New Heights 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 multiple-day activity, students measure the time it takes balls made of different materials to roll down inclines of varying lengths and heights, then make inferences about the relationship among the variables involved. Teachers are encouraged to act as facilitators while students decide which variables are important and can be measured, how best to collect the data, and how to interpret the results. Student input is elicited at all stages of the activity. Diagrams of the experimental apparatus, sample data tables, and suggestions for questions to guide students' thinking are included. Internet extensions are also provided. This lesson plan is adapted from an article that appeared in the November-December 1995 issue of Mathematics Teaching in the Middle School. (author/sw)

Students are asked to determine the actual dimensions of a kitchen from a scale drawing. This short-answer 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, 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 7 Achievement Test for Mathematics, Annotated Item 6. (author/sw)

Troy is building a pool that is proportional to an Olympic-size pool. Given the width of Troy's pool, students must find the scale factor and the length. This short-answer question is a sample item used in the 2007 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, a complete solution of the problem, and a scoring rubric. 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 7 Achievement Test for Mathematics, Annotated Item 31. (author/sw)

Given a scale model of a building and the scale factor, students must find the height of the building. This multiple-choice question is a sample item used in the 2008 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: 2008 Ohio Grade 7 Achievement Test for Mathematics, Annotated Item 43. (author/sw)

Students find the area of a natural feature, such as a lake or forest, using a map and the scale of the map. A discussion of the underlying mathematical ideas is included. 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)