Final answer:
Lyra uses the associative property of addition in mental arithmetic to solve 642+229 by breaking it down and calculating interim sums on a number line, ending up with a total of 871.
Step-by-step explanation:
Lyra's strategy for solving the addition problem 642+229 by breaking it down into 642+200+30-1 is a mental arithmetic technique that utilizes the associative property of addition. The missing numbers on Lyra's number line would represent the interim sums during each step of the calculation. For example, starting with 642, adding 200 to get 842, then adding 30 to achieve 872, and finally subtracting 1 to arrive at the final total, 871. This method allows for easier mental calculations by simplifying the numbers involved.