Update 2021: Pretty much the same activity however I've added a three hint quiz making activity to follow up the write and race. This can be done in groups, pairs or on their own. Finally if there is time I've included a basic quiz game template that can be used with 'A bunch of Quiz Questions' you can find those elsewhere on this site. You can it to fill time if the other parts finish quickly.
UPDATE: for the 'something to love' style of infinitive I've added a short powerpoint quiz to use as a warm up. It is based on 'something to do at school'. After a student answers a quiz they pick one of the caps and you click on it to give the team points. Because there are three caps three teams can have a chance to answer rather than just the fastest. Then click on the question to see an answer and then on the picture to go to the next slide.
Make groups or pairs in a very small class.
Give them the first question or situation and they work together to think of their answer. Then the first student in the group comes to a teacher with their answer. If the answer is okay the teacher gives them the second question. They return to their group, share the question and then the second student brings that answer to the teacher.
You can reward points or stickers for completing a target number of questions.
You can make it a game on the board such as horse race or almost mario.