Reasoning
Number - Which Deal Makes Sense?
Teacher Guide
This task requires learners to:
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interpret proportional statements
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compare equivalent and non-equivalent discounts
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justify conclusions using mathematical reasoning
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challenge misleading claims
This is not a speed-calculation task. If learners calculate without explaining why the discounts are equivalent or different, they have missed the point.
Key mathematical ideas
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Equivalence of fractions and percentages
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Guaranteed vs possible outcomes
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Interpreting “up to” in a mathematical context
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Relationship between structure (Buy 2 Get 1) and percentage discount
Progression Continua
Element
Reasoning
f
The learner
Uses number sense to identify unreasonable and reasonable answers.
g
The learner
Uses estimation when solving problems involving operations with whole numbers, decimals and percentages to help judge reasonableness of a solution.
h
The learner
Justifies the selection and use of operations in a variety of contexts.
i
The learner
Analyses, evaluates and justifies answers to problems involving estimation and/or calculation.
What learners can typically do in this task
f
The learner
Recognises that “up to 35% off” does not guarantee the greatest saving.
g
The learner
Estimates likely savings before calculating to judge whether claims are reasonable.
h
The learner
Justifies whether an offer is equivalent using percentage, fraction or total-cost calculations.
i
The learner
Evaluates misleading claims and defends conclusions even when prices change.
A learner may show different levels across different parts of the task. Judge using best overall evidence, not a single statement.
Teacher Scaffolding Questions Examples Prompts
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“What does ‘up to’ guarantee and what does it not?”
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“Is this discount always the same, or only in this case?”
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“How could you convince someone who believes the biggest percentage is always best?”
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“Can two different-looking offers give the same saving?”
