Name zero and the positive direction
If sea level is zero, a diver below it has a negative elevation. In a bank balance, a positive value means credit and a negative value means debt. Establish the meaning before choosing operations.
Integers in the real world
Turn a situation into a signed model, then check that the answer makes sense.
Understand it
Make the idea make sense.
Translate the change, not just a keyword
A rise usually adds a positive change, while a fall adds a negative change. Read the whole situation. “How much colder?” asks for the size of a decrease, while “What is the signed change?” asks for ending minus starting.
Choose a model before calculating
For a diver at −30 m rising 8 m, write −30 + 8. For the change from 3 °C to −5 °C, write −5 − 3. The operation comes from the relationship between values.
Interpret the answer
A signed change of −8 °C describes an 8 °C decrease. A diver at −22 m is 22 m below sea level, not 22 m above it. Include units and check whether the direction is reasonable.
Words worth knowing
- Reference point
- The position or value represented by zero.
- Signed change
- Ending value minus starting value; positive for an increase and negative for a decrease.
- Distance
- Separation between two positions; always non-negative.
A starting value is not a change.
The starting temperature is a position. The hourly change is a signed rate. Predict when the temperature crosses zero, if it does.
Choose values and predict the result.
Khan Academy
Pause before the next calculation. Predict the sign and explain the model, then compare the reasoning.
See the thinking
One step at a time.
Predict each next step, then reveal the explanation.
A diver at −30 m rises 8 m.
- Sea level is zero; upward is positive.
- Model the rise: −30 + 8 = −22.
- The diver is now 22 m below sea level, at an elevation of −22 m.
The temperature changes from 3 °C to −5 °C.
- Use ending − starting for the signed change.
- −5 − 3 = −8.
- The signed change is −8 °C: a decrease of 8 °C.
An elevator goes from level −2 to level 5.
- Use the end minus the start: 5 − (−2).
- Rewrite and calculate: 5 + 2 = 7.
- The elevator travels upward by 7 floors.
Try together
A little support. Your thinking.
An elevator goes from level −3 to level 4. Find its upward change.
Nicely reasoned. Try a fresh question below, or revisit any step.
Your turn
Practice with purpose.
New questions, useful feedback and hints that build on your thinking.
Question 1 of 8Build confidence
Loading your practice…
Progress stays on this device.Hints help you learn. First-try answers and supported answers are recorded separately.
Connections
In the real world
All Class Notes →A hockey team earns 2 points for each win. A penalty adjustment removes 3 points. After 4 wins, its adjusted points are 4 × 2 − 3 = 5.