Integers
Lessons in this chapter
About Integers
Integers extend the number line to the left of zero, which is the first genuine extension of what counts as a number since kindergarten.
Understand Integers introduces negative numbers through contexts where they already make sense: temperature below zero, debt, floors below ground. Having a real referent matters, because a negative quantity is hard to picture in the abstract.
Identify Opposites and Absolute Values of Integers names two things kids tend to merge. The opposite of a number is the same distance from zero on the other side, so the opposite of −7 is 7. The absolute value is the distance itself, so both 7 and −7 have an absolute value of 7.
Compare and Order Integers is where whole-number intuition actively misleads. −8 is less than −3, even though 8 is greater than 3, because −8 sits further left. The number line settles every one of these questions and is worth reaching for every time.
This chapter is also where the minus sign starts doing two jobs, marking a negative number and indicating subtraction, and keeping those readings apart is most of what makes 7th grade integer arithmetic go smoothly.
All three lessons in Integers open as 6th grade math worksheets inside the page. Understand Integers and Compare and Order Integers give practice questions worked one at a time and marked as you go, which matters here because ordering negative numbers tends to look secure until the next question. They are free to try, with no login needed for your first 3.
Frequently asked questions
Understand Integers introduces negative numbers as the other half of the number line, with the meanings they already carry in temperature, elevation and money. The second lesson separates the two ideas that get confused most often, the opposite of a number and its absolute value, one being the number on the other side of zero and the other being the distance from zero. Compare and Order Integers then works through the reversal that catches almost everyone, that -8 is less than -3 because it sits further left. The chapter sits in the Common Core domain The Number System (6.NS).
A whole number together with its negative, so ... −3, −2, −1, 0, 1, 2, 3 ... Fractions and decimals are not integers.
Because it is further left on the number line. Whole-number intuition says 8 is bigger than 3, but with negatives the order reverses.
The distance a number is from zero, regardless of direction. Both 7 and −7 have an absolute value of 7, so it is never negative.
The number the same distance from zero on the other side. The opposite of −7 is 7, and the opposite of 7 is −7.
The opposite is a number on the other side of zero; the absolute value is the distance itself. The opposite of −7 is 7, and its absolute value is also 7, which is why they get confused.