Soda cans are often packaged in rectangular arrays, but more efficient arrangements that require less packaging material are possible. In this lesson, students investigate various designs for packaging soda cans and use geometry to analyze their designs. An activity sheet, discussion questions, a lesson extension, and suggestions for assessment are included. (author/sw)

Students determine the dimensions of a can that has minimum surface area for a given volume. Reviewers liked the systematic approach described in the lesson and noted that this activity leads naturally into the minimum of a function. An activity sheet and extensions of the lesson are included. (sw)

This lesson is a data analysis lab in which students analyze mass and volume data for two mystery liquids, oil and water, and use the data to explore linear functions. Students relate slope and y-intercept to a real-world context. This lesson was developed for a teacher workshop conducted by Project STEP at the University of Cincinnati. The workshop session was designed to give teachers an introduction to graphing calculators. This lesson uses graphing calculators in an activity that integrates high school mathematics and science. (author/sw)

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 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 must find the sum of the measures of the exterior angles of a triangle. 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 38. (author/sw)

Students must identify the measure of one interior angle of a regular pentagon. 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 42. (author/sw)

Students must find the measure of an interior angle of a regular hexagon. 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 34. (author/sw)

Students must determine how many gallons of paint are needed to paint a fence, and they must show their work. This short-answer 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, 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 8 Achievement Test for Mathematics, Annotated Item 16. (author/sw)