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MathidiaMathematics Academy
Number, accuracy and bounds
Lesson 3 of 75
Standard practice

Calculations with bounds

Objective. Find bounds for sums, products and quotients.

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

Learn: the key idea

Calculations with bounds develops a connected mathematical idea rather than an isolated trick. Control accuracy, error intervals and numerical reasoning. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

A length is 7 cm to the nearest cm. State the upper bound.

7
Illustrated card showing 7
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is 7.5 cm.

Answer: 7.5 cm

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. A common error in calculations with bounds is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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