6.NS.C.5+C.6a 6th Grade The Number System

Positive & Negative Numbers in Context

Understand that positive and negative numbers describe quantities with opposite directions or values, and recognize opposite signs as locations on opposite sides of zero.

How to explain it

At this standard, students write signed numbers for real-world contexts, explain the meaning of 0, and identify opposites on a number line, including recognizing that −(−n) = n.

The anchor students hold onto: Opposite numbers are the same distance from 0 but on opposite sides. −(−n) = n.

Signed integers (6.NS.C.5+C.6a) lead to Rationals on Number Line & Coord Plane (6.NS.C.6c): fractions, decimals, and rational numbers on the number line and coordinate plane.

Worked examples

Example 1 Writing a Signed Number

Write: 40 feet below sea level.

Step 1Below sea level = negative direction

Step 240 feet below → −40

Step 30 = sea level (reference point)

Answer−40 feet

Example 2 Opposites and −(−n)

Opposite of −6? Simplify −(−6).

Step 1−6 is 6 units to the LEFT of 0

Step 2Its opposite is 6 units to the RIGHT of 0: +6

Step 3−(−6) = 6 (opposite of the opposite = original)

AnswerOpposite: +6; −(−6) = 6

Common mistakes

What students write A student writes the opposite of −8 as −8, reasoning that the negative sign stays when finding an opposite.

The fix Taking the opposite always changes the sign: the opposite of −8 is +8.

What students write A student simplifies −(−6) as −6, applying the multiplication rule that two negatives make a negative.

The fix −(−n) means taking the opposite, not multiplying. The opposite of −6 is +6, so −(−6) = 6.

Teacher tip

Head off the two predictable errors before they happen. First: Taking the opposite always changes the sign: the opposite of −8 is +8. Second: −(−n) means taking the opposite, not multiplying. The opposite of −6 is +6, so −(−6) = 6.