During the insurance contract, the insurance company shall bear the insurance liability for the following items:
(1) The staff of the insured suffers from work-related accidents or occupational diseases within 24 hours of each working day (including commuting);
(2) The faculty and staff of the insured suffered accidental injuries due to work during their business trip in People's Republic of China (PRC);
(3) Accidents suffered by the staff of the insured in activities organized by the insured;
(4) Other faculty accidents that should be borne by the insured according to law.
Therefore, if the teacher goes out on Sunday for reasons other than business or work and encounters a traffic accident, the insurance company will not bear the responsibility and will not compensate.
Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.