As a young Jew what would Jesus have been taught about heaven and hell?

To understand their view, you would need to understand what Sheol is to them. In The Hebrew Old Testament, or the Judaism view, Sheol (שְׁאוֹל) is described as the permanent place of the dead, known as the common grave for man (mankind), in addition, it is associated with an individual’s burial place or grave (Judges 16:31; Genesis 35:20) or a burial tomb (Job 21:32). So, regarding death, physically, an end of life, which seems to be the case regarding figures such as Abraham, Moses, and Miriam. Sheol is also called a dark and or deep pit, an abyss, or a land of forgetfulness when a human die and is buried. Moreover, Ecclesiastes and Job, insist that all the dead go down to Sheol, whether good or evil, rich or poor, slave or free man (Job 3:11-19). Later on in Ecclesiastes, death is spoken of as a cease of consciousness.

Now in the Bible, it says in Ecclesiastes 9:5 and Psalm 146:4 that those who are alive are conscious that a time will come that they will die, however, those in death, they’re the opposite, conscious of nothing at all, and their thoughts have perished with them, so in short, when we die, we cease to exist, we cannot think, we cannot act and or take action, we cannot feel, we cannot act upon goals and or anything else, essentially, when a light blub stops working, in this sense. The Bible even goes on to say that from dust we came and to dust we return in Genesis 3:19, hence Adam’s case, Genesis 2:7, in addition, Ecclesiastes 3:19, 20, not only refers to humans, but animals as well.

Despite this, death is not necessarily the end of everything. We already know that in the Bible, death is compared to sleep (Psalm 13:3; John 11:11-14; Acts 7:60). A person who is fast asleep is unaware of what is happening in their surroundings. Likewise, the dead are not conscious of anything as mentioned. But we do have the hope of the Resurrection that Jesus talks about. In the Bible, it teaches that God can awaken the dead as if from sleep and give them life again (Job 14:13-15). For those whom God resurrects, death is not the end of everything.

Well it depends on who was attempting to teach Jesus at the time. The Pharisees heavily influenced by Greek philosophy, would likely have concurred with Josephus,himself a Pharisee, who wrote:

"Now as to Hades, wherein the souls of the righteous and unrighteous are detained, it is necessary to speak of it. Hades is a place in the world not regularly finished; a subterraneous region...allotted as a place of custody for souls, in which angels are appointed as guardians to them, who distribute to them temporary punishments, agreeable to everyone's behavior and manners... while the just shall obtain an incorruptible and never-fading kingdom. These are now indeed confined in Hades, but not in the same place wherein the unjust are confined. For there is one decent into this region...the just are guided to the right hand and are led with hymns, sung by the angels appointed over that place, unto a region of light, in which the just have dwelt from the beginning of the world; not constrained by necessity, but ever enjoying the prospect of good things they see, and rejoice in the expectation of those new enjoyments which will be peculiar to every one of them, and esteeming those things beyond what we have here; with whom there is no place of toil, no burning heat, no piercing cold, nor any briers there; but the countenance of the Fathers and of the just, which they see always smiles upon them, while they wait for that rest and eternal new life in heaven, which is to succeed this region. This place we call The Bosom of Abraham.

But as to the unjust, they are dragged by force to the left hand by the angels allotted for punishment, no longer going with a good-will, but as prisoners driven by violence... they are struck with a fearful expectation of a future judgment, and in effect punished thereby: and not only so, but where they see the place of the fathers and of the just, even hereby are they punished; for a chaos deep and large is fixed between them; insomuch that a just man that hath compassion upon them cannot be admitted, nor can one that is unjust, if he were bold enough to attempt it, pass over it."

The Works of Flavius Josephus, William Whiston, A.M., Translator. Hartford Conn. The S.S. Scranton Co., 1900, pp. 901-902