Temperature and Integer Word Problems with Movement on the Number Line

🔑 Key Concepts

  • Integer word problems often describe movement up and down on a number line.
  • A rise or increase usually means add a positive value.
  • A drop or decrease usually means add a negative value or subtract.
  • Thermometers, elevation, and depth are natural examples of signed numbers.
  • Distance asks how far apart two positions are, regardless of direction.

✏️ Worked Examples — Integer Movement in Real Life

🧠 Math Vocabulary

  • Rise: Movement upward, usually represented by a positive number.
  • Drop: Movement downward, usually represented by a negative number.
  • Increase: A positive change.
  • Decrease: A negative change.
  • Above Sea Level: A position greater than zero, so it is positive.
  • Below Sea Level: A position less than zero, so it is negative.
  • Altitude: Height above a reference point, often sea level.
  • Depth: Distance below a reference point.
  • Distance: How far apart two positions are, regardless of direction.
  • Integer: A positive number, a negative number, or zero.

💡 Main Idea

Integer word problems often describe movement back and forth on a number line. A thermometer is a great example because temperatures can rise above zero or drop below zero. The same idea applies to elevation, sea level, and depth. Students should first identify the direction of the movement, decide whether each change is positive or negative, and then write an integer expression to model the situation.

📚 What You Should Already Know

You should already know what positive numbers, negative numbers, and zero represent on a number line. You should also know how to add and subtract integers.

🚀 What Comes Next

Next, students can apply these same ideas to more complex integer word problems involving temperature changes over several days, gains and losses, elevation changes, and finding total distance traveled between two signed positions.

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