Students must find the measure of the third angle of a triangle, given the measures of the other two angles. This multiple-choice 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, 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 7 Achievement Test for Mathematics, Annotated Item 18. (author/sw)

Students use the Pythagorean Theorem to find a distance. 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 23. (author/sw)

Students must find the length of a diagonal of a rectangle. This multiple-choice 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, 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 7 Achievement Test for Mathematics, Annotated Item 2. (author/sw)

Students must find the height of a tree using similar right triangles. This multiple-choice 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, 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 7 Achievement Test for Mathematics, Annotated Item 43. (author/sw)

Students use proportional reasoning to find the length of a shadow. This multiple-choice 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, 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: 2007 Ohio Grade 7 Achievement Test for Mathematics, Annotated Item 9. (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)

This activity shows how cutting geometric shapes and rearranging the pieces leads to some standard area formulas and to the Pythagorean Theorem. Complete proofs are 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)

Though written in the format of a lesson, this resource is more valuable as a source of information on two different ideas -- equity in mathematics and applications of the Pythagorean Theorem. In the first part of the lesson, students share thoughts about careers and gender roles. Then they read an article that discusses the long history of discrimination against women in mathematics and science. In the second part of the lesson they work in groups to apply and prove the Pythagorean Theorem in several real-world contexts. Discussion questions, suggestions for homework and assessment, lesson extensions, and interdisciplinary connections are included. (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)

This site features well over a dozen activities, any one of which could easily constitute a full lesson. Students identify, construct, and sketch cubes and other prisms and identify parallel and perpendicular lines and planes. They analyze nets, including those classified as pentominoes. They identify, construct, and sketch 2-dimensional representations of 3-dimensional objects and build 3-dimensional objects from 2-dimensional representations. They study patterns of oblong, square, triangular, and other figurate numbers and use geometric models to investigate and prove relationships among these special kinds of numbers. They look for patterns in (a) structures made of cubes, (b) points on a line versus number of segments, (c) sides of a polygon versus number of diagonals, and (d) tile patterns versus the number of vertices and sticks. They analyze the kinds of figures that can and cannot be constructed on a geoboard. They use grid paper to identify Pythagorean triples and then work through several applications of the Pythagorean Theorem. They prove some basic theorems in number theory using geometric models. Activity sheets and extensions are included, but not all answers are provided. These activities are adapted from Geometry in the Middle Grades, a publication in the NCTM Addenda Series. (sw)