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Interpret integers in real-world contexts

Integers represent quantities relative to a reference point: positive values indicate one direction or condition, negative values the opposite, and zero indicates the reference state. In contexts such as temperature, elevation, money, and changes in quantity, learners interpret an integer’s sign and magnitude, distinguish a value from its opposite, and locate it on a number line; the focus is on integer values rather than fractions, irrational numbers, or more advanced real-number modeling.

Detailed Explanation: Interpret integers in real-world contexts

An integer describes a quantity compared with a reference point.

  • A positive integer means a quantity in one direction or condition.
  • A negative integer means the opposite direction or condition.
  • Zero means the quantity is exactly at the reference point.
  • The absolute value tells how far the quantity is from the reference point.

Example: A diver is 88 meters below sea level. What integer represents the diver’s elevation?

Step 1: Identify the reference point.
Sea level is the reference point, so it is represented by 00 meters.

Step 2: Decide the direction.
The diver is below sea level. Below the reference point is represented by a negative number.

Step 3: Use the magnitude.
The diver is 88 meters from sea level, so the magnitude is 88.

Therefore, the diver’s elevation is

−8 meters.-8\text{ meters}.

The integer −8-8 means 8 meters below sea level. Its opposite, +8+8, would mean 8 meters above sea level.

On a number line, −8-8 is 8 units to the left of 00:

⋯ −10−9−8−7⋯0⋯\cdots\ -10\quad -9\quad \boxed{-8}\quad -7\quad \cdots\quad 0\quad \cdots

Learn by doing: Interpret integers in real-world contexts

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    Number Line - Positive Integers, Select Dot - From Ticks

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