This learning unit helps students explore the golden ratio and golden rectangles and to find the golden ratio in regular pentagons and in the Fibonacci sequence. Students use Geometer's Sketchpad® to rotate, translate, and dilate various figures to solve problems. Activity sheets and complete solutions are included. An extension of the lesson using a spreadsheet is also suggested. (author/sw)

On a sunny day, students measure their height and the length of their shadow and use proportional reasoning to find the heights of various tall objects by measuring the lengths of the shadows of the objects. A recording sheet, questions for students, assessment options, and ideas for teacher reflection are included. (author/sw)

In this lesson, students view a picture or video of the Statue of Liberty and are asked how long the arm would be if the nose measures 4 feet 6 inches. Given chart paper, string, and rulers, students work in groups to develop their own strategies for finding the solution. They measure the length of their own nose and the length of their arm and form a ratio. Using proportions, students compute the length of the statue's arm. Group results are displayed and compared. The actual length of the Statue of Liberty's arm (about 42 feet) is located in the almanac and compared to the lengths determined by the students. 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 How Many Noses Are in Your Arm 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 compute appropriate distances in different scale models of the solar system and universe using a variety of units, scale factors, and scientific notation. In so doing, students learn to write and solve equations that relate real distance measurements to scaled representations of the distances. They also appreciate how scientific notation makes calculations involving large numbers easier to manage. Discussion questions, extensions, readings, an evaluation rubric, and a video are provided with the lesson. Two student worksheets are included in the pdf file. (author/sw)

Students are asked to use a map scale to estimate distance between cities. 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 29. (author/sw)

Students must evaluate a given expression to convert a Fahrenheit temperature to Celsius. 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 5. (author/sw)

Students can use an indirect measurement technique to solve a rate problem. 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 24. (author/sw)

Students must estimate the number of miles in 61 kilometers. 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 18. (author/sw)

Students can use proportional reasoning to see how long it will take to raise the temperature of a cup of water from 22°C to 100°C. 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 44. (author/sw)