Hi Sarah,
Unfortunately there is not an out of the box way to automatically include additional tickets (free or paid) with a ticket purchase, but I would recommend taking a look at some of the extensions that WooCommerce offers. Since tickets are essentially WooCommerce simple products, you should be able to use these extensions with tickets.
Alternatively, you could look into some other third-party plugins (many of which are free)…I did a quick search and found this one. You may also look into a plugin that extends the default WooCommerce coupon functionality to allow users to get the additional tickets for free when purchasing the sponsorship – I did another quick search and found this one (but please note that I have not tested these out).
I’m sorry I don’t have a more straightforward solution here, but I hope this helps! Please let me know if you have any questions.
Thanks,
Jennifer