Comparing negatives: right is greater
Use the same order on a number line below zero.
Begin with the activity ↓Which is greater, −5 or −2?
The number to the right is greater. Since −2 is right of −5, −2>−5.
Compare temperatures of −5°C and −2°C. −2°C is warmer because it is not as far below zero.
From −5, take three steps right to −2. Values increase to the right, so −2 is greater. Negative numbers do not reverse this direction.
It is tempting to say “5 exceeds 2, so −5 is greater.” But 5 and 2 describe different positions from −5 and −2. Keep the signs and place both points.
The statement −5<−2 says −5 is smaller. The same fact can be written −2>−5. The open side of the comparison sign faces the greater number. Read both statements aloud.
Every negative number is left of zero and every positive number is right of zero. Thus −1 is less than 0, which is less than 1. For two identical positions use =.
Order and distance from zero are different. −5 is smaller than −2 but farther from zero. The next story explores why greater and farther mean different things.
Listen one paragraph at a time
Hold on to this distinction
Move right from −5 to reach −2, so −5<−2. This differs from asking which is farther from zero.
Change it and check
Change both positions. Say which dot is to the right and read the comparison. Try equal positions too.
Order uses the convention that values increase to the right on a horizontal line. Read it separately from distance.
Try with paper and objects
Place −4, −1 and 0 on equally spaced ticks, then explain their increasing left-to-right order.
Check and explain another example
Check your idea 1
Check your idea 2
Apply it in a new setting
Write an answer yourself
Return to the explanationCompare with a solution
-1 · number only
−1 is to the right, so it is greater.
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
Continue, or pause here
Distinguish opposite numbers from their distances from zero.