Jot down
Definition 1 of 1
Pro Tip 1/3Speed Matters
Jot down emphasizes quick writing, often without much concern for neatness. 
She jotted down the address on a napkin.
Pro Tip 2/3Temporary Note
The phrase often implies the information is temporary and may be transferred to a more permanent place later. 
Jot down your ideas here, we'll organize them into a report later.
Pro Tip 3/3Informality
Use 'jot down' in casual situations; it's less formal than 'document' or 'record'. 
Just jot down your thoughts during the brainstorm.