Winning Ways with Integers
6th - 9th, Homeschool
Integers are a common tripping point with students who are moving into advanced mathematics. They often understand the concepts we are teaching but make errors with signed numbers that prevent them from being successful. This handout is a collection of 30 years of the best practices I have found for teaching integer calculations. You’ll find five strategies that appeal to all types of learners: mathematical, linguistic, and visual and kinesthetic.
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to see state-specific standards (only available in the US).
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.