Is it necessary to give tetanus vaccine to prepubescent kids with injuries even though they have received three shots of tetanus toxoid as toddlers?

Tetanus: Nope. Not at all. If they are up to date and on schedule with their childhood vaccinations no booster or extra tetanus vaccinations are needed.

Incomplete series: Depending on the formulation used, the cdc recommended tetanus vaccine series includes 5 doses between 6 weeks and 6 years of age. For those not receiving tetanus as toddlers, 3 doses at appropriate intervals is accepted. A dose of tdap, is recommended for 11-12 yo to provide a booster for the pertussis as well as the tetanus, and dosing with td every 10 years thereafter.