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: absolute value as the distance a number sits from zero; why |x| = |−x| for any number x; relating absolute value to position on the number line for positive and negative integers, decimals, and fractions.
Click or drag to place a number and see its distance from zero
What is Absolute Value?
The absolute value of a number is its distance from zero on the number line.
Distance is never negative — it doesn’t matter which direction you travel.
So the absolute value of both +5 and −5 is 5.
We write absolute value with vertical bars: |−5| = 5, |5| = 5.
The bars mean “take the distance, ignore the sign.”
Every positive number and its negative partner share the same absolute value.
They are the same distance from zero — just on different sides.
This is the symmetry that makes the number line work.
Challenge: Order by Absolute Value
Click the numbers below in order from smallest absolute value to largest absolute value.
Think about distance from zero, not which number is biggest.