There is a rabbinical obligation on every father to educate his children to fulfill mitzvot even before they reach the age of Bar Mitzvah/Bat Mitzvah. The age at which this obligation begins varies according to the Mitzvah. Below are the details of this Mitzvah.
Who is obligated in Chinuch?
- While the majority of the Poskim hold that Chinuch only applies to the father, some say it also applies to the mother. 
- Regarding a child's obligation to pray, see the Obligation_to_pray#Children page.
- Some say that children from the age of 6 should say Birkat Hamazon. 
- While there is a prohibition in saying G-d's Name (Ado-nai), when it is isn't warranted, the prohibition is waived when being used in the process of Chinuch. Therefore, it is permitted(obligatory, rather) to say the full Bracha, with Shem and Malchut, in order to teach a child how and when to say what Brachot. 
- A life devoted to HaShem is the most pleasurable and fulfilling one. Therefore, the Chinuch stage must be pleasing and joyful for children. The proper attitude and approach for children to learn is through "Darchei No'am" (pleasant ways). 
- A parent and/or teacher should generally be careful not to be excessively forceful. There are several cases where Talmudic personalities praised their behavior of not being "makpid"(strict) in their home over their wives and children even though they lived a life filled with mitzvot.
- Sefer Chinuch Yisrael (p. 59) writes that Chinuch is a rabbinical Mitzvah, and quotes the Chaye Adam (66:1) who writes that this is a Mitzvah Midivrei Kabbalah (institution of the Nevi'im).
- Sefer Chinuch Yisrael (p. 61). See further in the Magen Avraham 343, S"A HaRav 343, Mishna Brurah 616:5, Aruch HaShulchan 343, and Pri Megadim E"A 225:5.
- Rabbi Mansour on dailyhalacha.com writes that parents should ensure that children from the age of 6 say Birkat HaMazon.
- The Gemara (Brachot 53b) says that one doesn’t say amen after the Bracha of a katan when he is just saying a Bracha as he is being taught the Brachot. The Rambam (Brachot 1:15) codifies as halacha. The Kesef Mishna there writes that it’s clearly implied that the teacher is permitted to say the Brachot with hashem’s name to teach the children how to say the Brachot and when the children repeat the Bracha after him, since the Bracha is only for Chinuch, one doesn’t answer amen. Shulchan Aruch 215:3 rules that if a child is saying a Bracha as he is learning from his teacher one doesn’t answer amen, but if a child says a Bracha in order to exempt himself from some obligation (meaning saying a Bracha when he is obligated to say it), then one should answer amen.
- Mishna Brurah 215:14 writes that it is permitted for the teacher to say the Brachot with hashem’s name to teach the children how to say the Brachot. Although saying a Bracha for Chinuch is permitted, saying a Bracha as one is learning such as an adult who finds the text of a Bracha in the gemara as he is learning should not say the Bracha with hashem’s name as one is reading the gemara. However, Yalkut Yosef 215:15 writes that in order to teach a child how to say Brachot one may say them with Hashem’s name, however, once the child knows how to make a Bracha and he just needs help in saying the Bracha one should say it without ashem’s name.
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- Gitin 7a,