If this link does not help, let me explain something;
Facebook will not offer you an opportunity to put in your new phone number, without gaining access to the account. Lets go through some scenarios of why, sound good?
Facebook offers you the opportunity to enter in your new phone number, you enter it in, and it sends you a code to allow you to login and change your password. That is great! You are back in!
Now, Facebook offers me the same opportunity to enter in YOUR NEW NUMBER, which happens to be MINE (because I am gaining access into your account, because it is just that simple now)! Facebook sends me the code, I log in change your password, and VIOLA, the account is mine!
Please, I hope you understand why account management is very important. If you are going to place so much value on these networks for your daily living, you need to understand HOW TO MANAGE the accounts that are so important. Before your CHANGE PHONES because you need the latest and greatest, be certain you think about HOW TO MANAGE your accounts!