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MathidiaMathematics Academy
Integers and negative numbers
Lesson 10 of 75
Review

Negative-number problems

Objective. Solve multi-step temperature, height and financial problems.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Negative-number problems use directed numbers in context: temperatures, heights above and below sea level, bank balances and lift floors. Decide what the start value is, which way it changes, and whether you need a new value or a difference. A difference is always found by subtracting: from −4°C to 7°C the rise is 7 − (−4) = 11 degrees.

Worked example

A diver is at −12 m (below sea level) and swims up to −4 m. How far has she risen? Then she dives 9 m deeper. Where is she now?

12 … 4
Illustrated card showing 12 … 4
  1. 1Rise = higher position − lower position = −4 − (−12).
  2. 2−4 + 12 = 8, so she rises 8 m.
  3. 3Diving 9 m deeper means subtracting 9: −4 − 9.
  4. 4She is now at −13 m.

Answer: 8 m; −13 m

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Practice

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Common mistake. Pupils often subtract the digits when finding a difference across zero, saying −4 to 7 is 3 degrees. Count the distance from −4 up to 0, then 0 up to 7: 4 + 7 = 11.

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