Math Mammoth Integers worktext covers all important integer (signed numbers) topics for middle school (grades 5-8), with instructions written directly to the student.
The first topic in the book is integers themselves, presented on a number line (negative and positive numbers) and tied in with temperature. Next we move on to modeling additions and subtractions as movements on a number line. Another model used in the book for addition is that of counters or chips. One lesson explains the shortcut for subtracting a negative integer using three different viewpoints (difference, counters, and number line movements).
Multiplication and division of integers is explained using counters, first of all, and then relying on the properties of multiplication and division. We use multiplication and division in the context of enlarging or shrinking geometric figures in the coordinate grid.
