The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers. The Factor Game is a two-person game in which players find factors of numbers on a game board. To play, one person selects a number and colors it. The second person colors all the proper factors of the first person's number. The roles are switched and the play continues until there are no numbers remaining with uncircled factors. Each person adds up the numbers s/he has colored. The winner is the person with the largest total. The purpose of this investigation is twofold: to help students determine whether a given number has many or only a few factors and to show how this property of numbers is useful for problem solving by developing a winning game strategy. A link to a Factor Game applet is provided, but use of the applet is not essential to the lesson. (author/sw)

Students see real-life applications of rational functions and the Pythagorean Theorem, as they investigate the essential concepts of how lenses work to magnify vision, and then build simple telescopes to demonstrate their understanding. Discussion questions, suggestions for assessment, additional activities, interdisciplinary connections, and Internet extensions are included in the lesson plan. (author/sw)

Students use a carpenter's square and protractor to measure the sides and angles of several right triangles. To confirm their measurements, they then compute the size of selected sides and angles using (a) the Pythagorean Theorem and (b) trigonometric ratios. Finally, they apply what they have learned about right triangles to compute how big an elevator shaft must be to accommodate a rotating car at an amusement park. Solutions to the problems are provided and extensions of the activity are suggested. (sw)

Students are asked to solve a problem involving squares and square roots. 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 18. (author/sw)

Students must identify which of four integers is a perfect square. 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 27. (author/sw)

Students must approximate the square root of 183. 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 28. (author/sw)

Students must estimate the length of a side of a square whose area is 369 square inches. 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 41. (author/sw)