Math Mammoth Integers

77 pages
(includes answers)

Sample pages (PDF)
Contents
Coordinate Grid Practice
Addition and Subtraction on the Number Line 1
Dividing Integers

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Math Mammoth Integers is a worktext that covers all the important integer topics for middle school (grades 6-8). The instructions are written directly to the student, so using the book requires very little teacher involvement.

Integers are introduced using the number line to relate them to the concepts of temperature, elevation, and money. We also study the ideas of absolute value (an integer’s distance from zero) and the opposite of a number.

Next, students learn to locate points in all four quadrants of the coordinate plane, and how the coordinates of a figure change when it is reflected across the x or y-axis. Students also move points according to given instructions and find distances between points with the same first coordinate or the same second coordinate.

Adding and subtracting integers is presented through two main models: (1) movements along the number line and (2) positive and negative counters. With the help of these models, students should not only learn the shortcuts, or “rules,” for adding and subtracting integers, but also understand why these shortcuts work.

The lesson Subtraction of Integers focuses on this important principle: Any subtraction can be converted into an addition of the number with the opposite sign. For example, 2 − 5 can be written as the sum 2 + (−5). In fact, this is the way mathematicians define subtraction as an operation.

This principle allows us to calculate not only subtractions such as 5 − (−7) but also problems that contain both addition and subtraction. These mixed problems become simple sums after the subtractions have been converted into additions. Converting subtractions into additions or vice versa is also important when simplifying expressions. For example, 5 + (−x) can be simplified to 5 − x.

Next, we study the distance between two integers. While you can find this by calculating the difference of two numbers x and y, there is a more general formula that works even if you don't know which of x or y is the greater number: the distance between x and y is | x − y | (the absolute value of their difference). Students learn to use this formula to find distances between integers, and practice the concept in several real-life situations.

The lesson Multiplying Integers 1 focuses on giving several different justifications for the shortcut “a negative times a negative makes a positive.” In the next lesson, students practice multiplying several integers and finding the value of expressions involving several operations using the order of operations.

In the lesson Dividing Integers we solve division problems with integer quotients. This lesson leads naturally into the last topic of the book: negative fractions.

Being able to calculate with negative numbers is actually a foundational skill for algebra: they are encountered universally when working with equations, graphing, and functions.

You can find matching videos for the topics in this book at
https://www.mathmammoth.com/videos/integers/integer_lessons 

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.

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Homeschool Math For All Ages — review of Integers book by Jeniffer from Thou Shalt Not Whine blog