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MathidiaMathematics Academy
Proof and mathematical reasoning
Lesson 70 of 75
Review

Extended reasoning chains

Objective. Communicate complete multi-topic solutions with explicit justification.

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

Learn: the key idea

Extended reasoning chains require communicating a complete solution across several connected topics, showing each stage's working and explicitly justifying why each step is valid before moving to the next. Plan the overall route through the problem first, identify which pieces of information unlock each subsequent stage, then write the solution so a reader can follow the logic without guessing missing steps. Explicit justification means stating the rule or reason used, not just the calculation performed. For example, a problem might need a circle theorem to find an angle, then trigonometry using that angle, then a final percentage comparison. Marks are awarded for the reasoning shown, not only the final value.

Worked example

A problem requires finding angle x using the alternate segment theorem, then using x in a right-angled triangle to find a length. If x = 35°, and the hypotenuse is 10 cm, find the opposite side to x.

Diagram of a triangle
  1. 1Identify the right triangle with angle x = 35° and hypotenuse 10 cm
  2. 2Use sin(x) = opposite ÷ hypotenuse
  3. 3Opposite = 10 × sin(35°)
  4. 4Opposite ≈ 5.74 cm

Answer: ≈5.74 cm

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Common mistake. Students often jump straight to a final answer across a multi-topic problem without showing the intermediate linking steps, losing method marks even when the final numerical answer happens to be correct.

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