Final answer:
Sidney's mother used inductive reasoning to predict Sidney's dance performance order at the recital after observing the sequence of previous dances.
Step-by-step explanation:
Sidney's mother, while waiting at Sidney's dance recital, has used inductive reasoning to determine when Sidney will perform.
After six dance numbers have been performed, she prepares to take pictures, expecting Sidney to be next because the program listed Sidney's dance as the seventh.
This type of reasoning involves observing a pattern or sequence and making a generalization or prediction about what will come next based on the observed order.