Represent Opposite Directions with Signed Numbers
Use the supplied zero reference and direction convention.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: With sea level defined as zero, a model location 6 meters below it is −6 m.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Positive and negative numbers can represent directions on opposite sides of a chosen zero reference. Opposites are equally distant from zero on different sides. The zero reference must be stated: below sea level, below a temperature benchmark, or left of an origin are different contexts. Zero is its own opposite.
Use the supplied zero reference and direction convention. Write the signed location, then identify its opposite by changing sign. Check that both locations have equal distance from zero and lie on opposite sides unless both are zero.
State what zero represents in the model. A negative sign gives direction; it does not mean the amount is absent. Draw equally spaced points on both sides of a labeled zero.
- Draw equally spaced points on both sides of a labeled zero.
- Work through the supplied example and label what each number or attribute represents.
- Use the supplied zero reference and direction convention.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
With sea level defined as zero, a model location 6 meters below it is −6 m. Its opposite location is +6 m above sea level. Both are six meters from the reference. Negative does not mean no distance; the sign gives direction relative to zero. State what zero represents in the model. A negative sign gives direction; it does not mean the amount is absent. Draw equally spaced points on both sides of a labeled zero.
Check your reasoning
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Helpful tips
- State what zero represents in the model.
- A negative sign gives direction; it does not mean the amount is absent.
See the answer and explanation
3
The opposite is equally far from zero on the other side.
Take it further
Write the opposite of 0 and of 2.5. Expected: 0 and −2.5.
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