Was the serpent in the wilderness a foreshadowing of Jesus?

> The Lord sent fiery serpents among the people and they bit the people, so that many people of Israel died. So the people came to Moses and said, “We have sinned, because we have spoken against the Lord and you; intercede with the Lord, that He may remove the serpents from us.” And Moses interceded for the people. Then the Lord said to Moses, “Make a fiery serpent, and set it on a standard; and it shall come about, that everyone who is bitten, when he looks at it, he will live.” **And Moses made a bronze serpent and set it on the standard; and it came about, that if a serpent bit any man, when he looked to the bronze serpent, he lived.** **(Numbers 21:6-9)** Someone recently told me that this was symbolic, and that the serpent is a symbol for sin, and that this was foreshadowing Jesus becoming sin for us and being lifted up and crucified so that we would live. My question is, how do we know that this is the right interpretation, and not just an interesting idea that someone had?