Students can better understand the algorithm for dividing fractions if they analyze division through a sequence of problems starting with division of whole numbers, followed by division of a whole number by a unit fraction, division of a whole number by a non-unit fraction, and finally division of a fraction by a fraction. A lengthy list of guiding questions, summary questions, an assessment task, a lesson extension, and a set of carefully sequenced activity sheets are included. (sw)

In this lesson, multiplication of integers is presented in a format that encourages understanding, not simply rote memorization of rules. Using the rewinding of a videotape to represent negative time, students convince themselves that a negative rate times a negative time yields a positive distance. A student worksheet and Internet extensions are included. This lesson is adapted from an article that appeared in the November 1993 issue of Arithmetic Teacher. (author/sw)

Students strengthen their percentage and fraction skills by comparing the nutritional values of similar food products. They individually calculate their own daily intake of various nutrients and compare their diets to recommended daily percentages. Older students might create a dietary spreadsheet to track their daily intake of various nutrients. Discussion questions, additional activities, suggestions for assessment, and Internet extensions are included with the lesson plan. (author/sw)

Students must find the divisor in an integer division problem. 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 12. (author/sw)

Students must identify the result of dividing two negative integers. 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 40. (author/sw)

Students must identify a statement that is always true about the sum of a positive integer and a negative integer. This multiple-choice question is a sample item used in the 2006 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: 2006 Ohio Grade 7 Achievement Test for Mathematics, Annotated Item 43. (author/sw)

Students must describe the result of subtracting a negative number from a positive number. 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 7. (author/sw)

Students can use this applet to practice addition and subtraction of integers (signed numbers) at five different levels of difficulty. (sw)

Students must identify the proportion that represents a problem situation involving percentage. 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 28. (author/sw)

Students are asked to give examples of subtracting a negative number from a positive number and explain the results. 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 41. (author/sw)

This site comprises six lesson activities including the definition of a fraction, equivalent fractions, addition of fractions, and multiplication of fractions. Students may respond online to get immediate feedback, or they can work the examples on grid paper. Explanations are too brief for a first introduction to fractions but are engaging and appropriate for a review, tutorial, or extra practice. (sw)