The Talmud in various places references children of that period learning a "verse" on a specific day.
In Gittin 56a of Talmud Bavli:
א"ל לינוקא פסוק לי פסוקיך אמר ליה (יחזקאל כה, יד) ונתתי את נקמתי באדום ביד עמי ישראל וגו' אמר קודשא בריך הוא בעי לחרובי ביתיה ובעי לכפורי ידיה בההוא גברא ערק ואזל ואיגייר ונפק מיניה ר"מ
Nero then conducted another test: He said to a child: Tell me the verse that you learned today. He said to him as follows: “And I will lay My vengeance upon Edom by the hand of My people Israel” (Ezekiel 25:14). Nero said: The Holy One, Blessed be He, wishes to destroy His Temple, and He wishes to wipe his hands with that man, i.e., with me. The Romans are associated with Edom, the descendants of Esau. If I continue on this mission, I will eventually be punished for having served as God’s agent to bring about the destruction. So he fled and became a convert, and ultimately Rabbi Meir descended from him.
In Chagigah 15a of Talmud Bavli it says:
תקפיה עייליה לבי מדרשא א"ל לינוקא פסוק לי פסוקך אמר לו (ישעיהו מח, כב) אין שלום אמר ה' לרשעים עייליה לבי כנישתא אחריתי א"ל לינוקא פסוק לי פסוקך אמר לו (ירמיהו ב, כב)
Nevertheless, Rabbi Meir took hold of him and brought him to the study hall. Aḥer said to a child, by way of divination: Recite your verse that you studied today to me. He recited the following verse to him: “There is no peace, said the Lord, concerning the wicked” (Isaiah 48:22). He brought him to another study hall. Aḥer said to a child: Recite your verse to me. He recited to him: “For though you wash with niter, and take for you much soap, yet your iniquity is marked before Me” (Jeremiah 2:22).
Similarly in Taanit 9a of Talmud Bavli:
אשכחיה ר' יוחנן לינוקא דריש לקיש אמר ליה אימא לי פסוקיך א"ל עשר תעשר א"ל ומאי עשר תעשר א"ל עשר בשביל שתתעשר אמר ליה מנא לך א"ל זיל נסי
Rabbi Yoḥanan found the young son of Reish Lakish. He said to the boy: Recite to me your verse, i.e., the verse you studied today in school. The boy said to him: “A tithe shall you tithe.” The boy further said to Rabbi Yoḥanan: But what is the meaning of this phrase: “A tithe shall you tithe”? Rabbi Yoḥanan said to him: The verse means: Take a tithe so that you will become wealthy. The boy said to Rabbi Yoḥanan: From where do you derive that this is so? Rabbi Yoḥanan said to him: Go and test it.
All of this suggests that the children of this time studied a specific verse in depth each day. Do we have additional information as to whether the children of this time studied actually one verse a day and that is it? Or perhaps they studied a range of subjects and halacha but also focused on a specific verse as well and delved into that verse in depth? I assume the latter (as how else could any student learn all of Jewish law and tanakah!) but I'm curious as to what sources we have on this practice.
Also, do we have information that is sourced on how the learning by students of the specific verse each day was done back then?