on (one's) best behavior
Being very polite or exercising exceptionally good manners. Primarily heard in US. Now, you kids must be on your best behavior for your Auntie this weekend! Good morning, class. I hope everyone was on their best behavior for the substitute teacher yesterday.
on one's best behavior
being as polite as possible. When we went out, the children were on their best behavior. I try to be on my best behavior all the time.
on one's best behavior
Also, on one's good behavior. Very polite, as in Mother told the children to be on their best behavior during Grandma's visit, or The whole staff were on their good behavior while the client inspected the premises. [Late 1600s]