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Math Mammoth Integers

Math Mammoth Integers workbook cover
87 pages
(includes answers)

Sample pages (PDF)
Addition of Integers: Counters and More
Dividing Integers
Coordinate Grid Practice

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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 explains the shortcut for subtracting a negative integer using three different viewpoints (counters, number line movements, and as a distance or difference). The lesson also includes this important principle: Any subtraction can be converted into an addition (of the number with the opposite sign) and vice versa.

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

In the lesson Graphing, students plot points on the coordinate grid according to a given equation in two variables (such as y = x + 2), this time also using negative numbers. They see the patterns in the coordinates of the points and the pattern in the points drawn in the grid, and also work through some real-life problems.

Next, we study the distance between two integers. This can be found by taking the absolute value of their difference: the distance between x and y is | xy |. Students learn to use this formula to find distances between integers, and they also compare the result the formula gives to the answer they get by logical thinking.

Multiplication and division of integers is explained, first of all using counters, and then relying on the properties of multiplication and division. The lesson Multiplying Integers not only teaches the mechanics of how to multiply integers but also gives both intuitive understanding and formal justification for the shortcut, “a negative times a negative makes a positive.” This formal justification using the distributive property introduces and illustrates the type of careful and precise reasoning that mathematicians use in proofs.

Then, the lesson on the division of integers leads naturally into the topic of negative fractions. The final topic is a review of the order of operations: we perform several operations at a time with integers.

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.

I have also created a set of free video lessons to match this book.


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

Dear Maria,

I appreciate your approach when you explain a topic. From time to time you approach a topic differently than I do (e.g. long division, integers) and your explanation teaches me something new and gives my children a different perspective. I taught upper elementary math for 10 years in the classroom and now for 3 years at home with my own kids and I love learning a new strategy. And, now that my son is working independently through your books, for example Integers, I love that he is working with your explanations and is exposed to more than just "mom's" way to work it out. These multiple problem solving strategies in his bag of tricks help him succeed no matter what he is working on. Thank you!


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How and where to order

You can buy Math Mammoth books at:

  • Here at MathMammoth.com website — simply use the "Add to cart" buttons you see on the product pages.
  • Rainbow Resource carries printed copies for the Light Blue series books, plus several CDs (Light Blue and Blue series).
  • Homeschool Buyers Club offers download versions of the Light Blue series, plus the Blue series bundle.
  • Homeschool Planet sells the digital versions of the main curriculum and lesson plans to go with them.
  • K5 Learning offers download versions of the Blue series.
  • TPT sells the Light Blue Series downloads, plus topical units.
  • Lulu sells printed copies for most of the Math Mammoth materials (various series).

By purchasing any of the books, permission IS granted for the teacher (or parent) to reproduce this material to be used with his/her students in a teaching situation; not for commercial resale. However, you are not permitted to share the material with another teacher.

In other words, you are permitted to make copies for the students/children you are teaching, but not for other teachers' usage.

Math Mammoth books are PDF files. I recommend you use Adobe Reader to view them, including if you use a Mac. You can try other PDF viewers, but they may at times either omit or mess up some of the images.

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