Integer Word Problems - Altitude

🔑 Key Concepts

  • Integer word problems often describe changes in height, depth, temperature, or money.
  • Words like increase, rise, and gain usually represent positive integers.
  • Words like decrease, drop, loss, and below usually represent negative integers.
  • Sea level is often used as zero in real-world integer problems.
  • Read carefully so you can determine whether a number should be positive or negative before solving.

✏️ Worked Examples — Integer Word Problems

🧠 Math Vocabulary

  • Integer: A whole number that can be positive, negative, or zero.
  • Increase: A change upward, which is usually represented by a positive integer.
  • Decrease: A change downward, which is usually represented by a negative integer.
  • Above Sea Level: A position higher than zero, so it is represented by a positive value.
  • Below Sea Level: A position lower than zero, so it is represented by a negative value.
  • Gain: An increase in amount or value.
  • Loss: A decrease in amount or value.
  • Altitude: Height above a reference point, often sea level.
  • Depth: Distance below a reference point, often sea level.
  • Absolute Value: The distance a number is from zero on a number line.

💡 Main Idea

Integer word problems become much easier when you first identify the meaning of the situation. In real-world contexts, values above a reference point are usually positive, and values below a reference point are usually negative. Words such as increase, rise, and gain suggest positive movement, while words such as decrease, drop, and loss suggest negative movement. Once you assign the correct signs, you can write an integer expression and solve the problem step-by-step.

📚 What You Should Already Know

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

🚀 What Comes Next

Next, students will apply these same ideas to temperature changes, money gains and losses, elevations, and other real-world situations involving signed numbers. These skills also prepare students to solve multi-step integer problems and to interpret rational number situations later on.

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