This guide to Understanding Integers begins with an 11-page tutorial on integers and their operations in clear, student-friendly terms. This resource can be used to teach, reteach or reinforce basic integer concepts. Beginning with a brief, concise description and introduction to integers, each operation is described visually using white and black chips to represent positive and negative numbers. Multiple examples for each operation using these visual illustrations are provided for each operation enabling students to connect integer operations to previously learned, elementary math skills.
For example, subtraction of integers is introduced as “taking away” the amount to be subtracted, the language used at the elementary level to describe the operation. Students can build on their prior knowledge of subtraction as they begin to explore subtraction of integers. The visual “taking away” of either positive or negative chips will help students to discover that subtracting is actually “adding the opposite.” As students see the answer visually using the chips, they begin to envision the process, building understanding of the operation. Some students need few examples before they adopt the concept while other students will still need to picture the operation with chips in order to master the process. Using this method, students do not need to memorize a rule or learn a jingle which often provides only temporary success. They are making connections between what they have already learned about operations with natural and whole numbers and what they must master with integers. Operations with integers are building blocks in successive math courses and are essential for students to be proficient in algebra.
In addition, this product includes 10 worksheets, beginning with 2 worksheets on Addition of Integers, each consisting of 30 exercises. The initial exercises can be completed using chips because the numbers are small. The exercises increase in difficulty level so that by the end of the second worksheet, students should be able to envision the correct answer without relying on the chips. For some students, additional worksheets may be required to cement this skill. This product also provides an answer key in the same format as the worksheet for students to easily check their work as well as a list of the correct answers for teachers who choose to read the answers more quickly.
The contents of this guide are:
► 11 pages of instruction as described above
► 11 pages of worksheets:
► 11 pages of answer keys identical to the original worksheets with step-by-step solutions included for more difficult exercises
► 3 pages of quick reference answer keys to the worksheets
This guide has been written so that students of all ages can understand basic integer concepts. These clear, concise examples of integers and their operations will aid middle school students as they begin to study integers. The worksheets can be used to assess and/or refresh high school students’ skills with integers. This tutorial is essential for high school students who struggle with integers and yet must master algebra in order to pass standardized tests.
Students can access this resource for quick reference in any math class, and teachers can reproduce this guide for individual student use. This resource is a companion to our Gaining Math Momentum Warm Ups. Please check out our newest resources: Quick Reference Guide to Fractions, Quick Reference Guide to Decimals, and Quick Reference Guide to Percents.