Reasoning
Measures - Who’s Right? Let’s Talk it Through
Teacher Guide
Even though shape and number are involved, the key learning focus is communicating mathematical reasoning about area.
This task is explicitly about:
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Talking mathematically
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Explaining and justifying ideas
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Using representations to support explanation
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Listening to and responding to others’ thinking
Mathematical Resolution (for teacher reference):
An open cube has 5 faces, not 6. Each face has an area of 16 cm², giving a total surface area of 80 cm².
Progression Continua
Element
Reasoning
f
The learner
Explains and justifies the necessity of selecting the same unit when comparing two things.
g
The learner
Assesses reasonableness of estimations and measurements with reference to previous measurements and personal benchmarks.
h
The learner
Explains and justifies the selection of a particular unit of measure used to measure and/or compare things.
i
The learner
Tests and evaluates the reasonableness of measurements and numerical calculations of measurements.
What children can typically do in this task
f
The learner
Recognises that each face must be counted once and that all faces are measured using the same unit (square centimetres).
g
The learner
(Not a primary focus of this task.)
h
The learner
Justifies why surface area is measured in square centimetres rather than linear units.
i
The learner
Evaluates both claims (96 cm² and 80 cm²) and explains why one is unreasonable.
Teacher Scaffolding Questions Examples Prompts
To support discussion
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What does open change?
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Which face is missing?
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To deepen explanation
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How could you show that clearly in a diagram?
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How would you convince someone who disagrees?
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To challenge
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What if two faces were missing?
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How would the surface area change if the edge was doubled?
