Old Testament Question

I was recently asked, Why do we need to read or study the Old Testament? The first thought that came to my mind was 2 Timothy 3:16-17 "All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work." Ok, but how does that help us make sense of what we are reading and does this old stuff doesn't apply to my life today? I have recently started to explore the Old Testament more since I'm taking OT 1 in school and it is amazing that so much of the Old Testament helps us to understand the New Testament. Last night I was teaching JR High Youth on the sacrificial system of the OT and we were looking at all the different type and styles of sacrifices. But the offerings weren't there to save the people they were there for the obedience of the people. The sacrifices didn't cleanse the offender but covered them in the blood of the animal to hide their transgressions. That is why they continually needed to offer up sacrifices. We looked at how the heart was impure and the sacrifices became thoughtless and detestable to God. Later we discussed the greatest sacrifice of all time. Jesus dying on the cross for us, and how Jesus' blood doesn't cover us but cleanses us. May God bless all of my readers.