Organizing IdeaNumber — Number sense is developed through understanding the ways numbers describe the world.
Guiding QuestionHow can the symmetry of the number line contribute to a sense of number?
Learning OutcomeStudents analyze positive and negative numbers.
This lesson covers: opposites on the number line; the additive inverse (a number and its opposite always sum to zero); the symmetry of the number line around zero; zero as its own opposite.
Click or drag on the number line to place a number
Opposites on the Number Line
Every number has an opposite — a partner that sits the same distance from zero but
on the other side of the line. The numbers 5 and −5 are opposites.
Same distance, different direction.
The number line is perfectly symmetric around zero. Fold it at zero and every positive
number lands exactly on its negative partner. That symmetry is what gives the number line its balance.
Mathematicians call this the additive inverse. Any number added to its additive inverse
equals zero: 5 + (−5) = 0, −3 + 3 = 0.
Where you see this
Temperature. Yellowknife regularly reaches −38 °C in January — 38 degrees
below zero. A midsummer afternoon at +38 °C is exactly as far above zero.
Same distance, opposite side.
−38 + 38 = 0
Elevation. Sea level is zero. Banff sits at about +1400 m; a deep ocean trench
at −1400 m is equally far below. Equal distance, opposite direction.
+1400 + (−1400) = 0
Opposites
Two numbers are opposites if they are the same distance from zero but on opposite sides of the number line.
The opposite of 7 is −7. The opposite of −4 is 4.
Additive Inverse
The formal name for a number’s opposite. A number plus its additive inverse always equals zero.
8 + (−8) = 0 −2.5 + 2.5 = 0
Zero
Zero is neither positive nor negative. It is its own opposite — the only number where folding the line at zero puts it back on itself.