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The Prophet (peace and blessings be upon him) would come in to his family and ask, “Do you have anything to eat?” If they said no, he would say, “Then I am fasting.” Thus, he would form the intention to observe a voluntary fast during the day. Sometimes he would intend to observe a voluntary fast, then subsequently break it. ‘Ā’ishah reported both practices: the first is recorded in Sahīh Muslim (1), and the second in al-Nasā’ī’s book (2).

As for the hadith reported from ‘Ā’ishah in the Sunan collections (3):

“Hafsah and I were fasting when we were offered some food that we desired, so we ate some of it. The Messenger of Allah (peace and blessings be upon him) then came, and Hafsah forestalled me in speaking to him—she was her father’s daughter—and said, ‘O Messenger of Allah, we were fasting when we were offered some food that we desired, so we ate some of it.’ He said, ‘Both of you should fast another day to make up for it.’”

This is a defective hadith. Al-Tirmidhī said (4): Mālik ibn Anas, Ma‘mar, ‘Abd Allāh (5) ibn ‘Umar, Ziyād ibn Sa‘d, and several other masters of hadith narrated it from al-Zuhrī, from ‘Ā’ishah, with an interrupted chain. They did not include “from ‘Urwah” in it. This version is more authentic.