The story handed down in the Palestinian Targum may be supplemented by details preserved elsewhere in the Jewish interpretative tradition. The targumic version merely implies that Isaac is an adult participant and not a boy as in Genesis 22:12. In midrashic sources, we are told that he is 37 years old. This figure is derived from a Jewish legend reporting the sudden death of the 127-year-old Sarah (Genesis 23:1) when she is mendaciously told by Satan that Abraham has killed their son. Sarah was 90 when she bore Isaac: hence the figure 37. Without explaining the difference, the first-century CE Jewish historian Flavius Josephus makes Isaac 25 years old. 

According to Pseudo-Jonathan, a shining cloud and a pillar of smoke lead Abraham to the chosen mountaintop. Pirke de-Rabbi Eliezer, a midrashic composition dating from the ninth century CE, also mentions a pillar of fire resembling the one that directed the Jews in the wilderness in the Book of Exodus. Similarly, the cloud appears in the representation of the Binding of Isaac in Jewish art, on a fresco in the third-century CE synagogue of Dura Europos in Syria, and on the mosaic floor of the fifth-century Galilean Bet Alpha synagogue. 

In another ancient Midrash, Rabbi Akiva (martyred by the Romans in 135 CE) appended to Deuteronomy 6:5, "You shall love the Lord, your God, with all your heart, with all your soul and with all your might" the words, "In the same way as Isaac who bound himself on the altar." 

This type of Scripture exegesis did not originate with Akiva. First-century CE Jewish sources are already aware of it. Flavius Josephus (37 - c. 100 CE) in his Jewish Antiquities recounts that Isaac, informed by his father about God's demand, joyfully runs to the altar. Another first-century CE writer, Pseudo-Philo, the author of the Book of Biblical Antiquities, emphasises that Isaac explicitly agrees to become a sacrificial victim and that God's election of the Jewish people is the reward for the shedding of Isaac's blood. There is no reference to the shedding of blood in the Bible. Finally, in the Fourth Book of the Maccabees (mid-first century CE), Isaac is the proto-martyr, who with fearless courage stares at the threatening knife. 

Since the main theme of the Fourth Book of the Maccabees is Jewish martyrdom under Antiochus Epiphanes in the early second century BCE, and the death of martyrs is viewed as expiation for all the sins of Israel, Isaac's action is presented as atonement offered for the Jewish people and seen as a source of merit earning their future salvation.

Why did God subject Abraham to a trial in the first instance, wondered the Jewish Bible commentators. From the Book of Jubilees (second century BCE), through Pseudo-Philo and the rabbis, we are told that both Satan and the angels envied Abraham and Isaac.