MISSION · Number sense
Negative Numbers on a Number Line
Use direction and distance to make negatives feel natural
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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The idea in one sentence
Negative numbers live to the left of zero; farther left always means smaller.
Use a real-world picture
Imagine temperature. A temperature of \(-2°\) is colder than \(3°\), so \(-2 < 3\). And \(-8°\) is colder than \(-2°\), so \(-8 < -2\).
That last comparison can feel backward. Remember: on the number line, the number farther right is greater.
Add by walking
Start on the first number. A positive number means walk right; a negative number means walk left.
For \(-3 + 5\):
- Start at \(-3\).
- Walk 5 spaces right.
- Land at \(2\).
So \(-3 + 5 = 2\).
Subtraction means add the opposite
Turn subtraction into addition by changing the second number to its opposite:
\[4 - (-3) = 4 + 3 = 7\]You can picture this as removing a debt of 3. Losing a debt leaves you with 3 more.
Common mix-ups
- Thinking \(-10\) is greater than \(-2\) because 10 is greater than 2. On the number line, \(-10\) is farther left.
- Automatically making every answer negative. The direction and distance decide the sign.
- Treating two negative signs as a magic rule. Say “subtracting a negative means adding its opposite.”
Check yourself
Which is greater: \(-6\) or \(-9\)? Then solve \(-6 + 4\).
\(-6\) is greater because it is farther right. \(-6 + 4 = -2\).
LEVEL 3 · REFLECT
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