Testing a numerical rule
A fictional classroom task supplies the complete pairs 4 to 9 and 6 to 13 and asks for the partner of 10 under the same simple intended rule. Four response values are 18,20,21 and 24. The worksheet asks learners to explain their operation, test it on both complete pairs and distinguish a plausible intended pattern from a universal mathematical uniqueness claim. A second exercise uses the equation 24/y+3=9 with y nonzero. A student adds five in the analogy because it fits the first pair; another selects a value for y without substituting it. No official age band, test form or normed difficulty is asserted. All quantities are pure classroom numbers without physical units, and the exercises are used to compare reasoning steps rather than to establish real assessment statistics.
1. Find and verify the intended analogy rule.
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The rule 2 n+1 gives 9 from 4 and 13 from 6, then gives 21 from 10. Adding five alone fails on 6. A finite set can admit other constructed rules, so this is the simple intended rule supported by both pairs and the given choices, not a claim of unrestricted uniqueness.
2. Solve the equation and check the permitted value.
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Subtract 3 to obtain 24/y=6, hence y=4. It is nonzero as required, and substitution gives 24/4+3=9. The check tests the original division equation rather than only a later algebraic rearrangement.