Correct.

Why the Law then? It was added because of transgressions, having been ordained through angels by the agency of a mediator, until the seed should come to whom the promise had been made.  Galatians 3:19 (NAS)  

This covenant, referred to as the Law of Moses (which includes the Ten Commandments) was given because the Jews (the children of Israel) transgressed or sinned against God.

What Happened at the Time the Law was given by God to Moses?

"Then he (Moses) took the book of the covenant and read it in the hearing of the people; and they said, "All that the LORD has spoken we will do, and we will be obedient!" So Moses took the blood and sprinkled it on the people, and said, "Behold the blood of the covenant, which the LORD has made with you in accordance with all these words."  Exodus 24:7-8 (NAS)

After Moses received additional laws and commands from God, God told Moses:

"Write down these words, for in accordance with these words I have made a covenant with you and with Israel." So he was there with the LORD forty days and forty nights; he did not eat bread or drink water. And he wrote on the tablets the words of the covenant, the Ten Commandments." Exodus 34:27-28 (NAS)

The Law of Moses was also enacted with blood:

As the covenant that God made with Abraham involved the sacrifice of animals, the covenant or law between God and the children of Israel (the Law of Moses) also involved the sacrifice of animals:

"And he sent young men of the sons of Israel, and they offered burnt offerings and sacrificed young bulls as peace offerings to the LORD. And Moses took half of the blood and put it in basins, and the other half of the blood he sprinkled on the altar. Then he took the book of the covenant and read it in the hearing of the people; and they said, "All that the LORD has spoken we will do, and we will be obedient!" So Moses took the blood and sprinkled it on the people, and said, "Behold the blood of the covenant, which the LORD has made with you in accordance with all these words." Exodus 24:5-8 (NAS)

What was the sign of the covenant with Moses and the children of Israel?

"And the LORD spoke to Moses, saying, "But as for you, speak to the sons of Israel, saying, 'You shall surely observe My sabbaths; for this is a sign between Me and you throughout your generations, that you may know that I am the LORD who sanctifies you. 'Therefore you are to observe the sabbath, for it is holy to you. Everyone who profanes it shall surely be put to death; for whoever does any work on it, that person shall be cut off from among his people. 'For six days work may be done, but on the seventh day there is a sabbath of complete rest, holy to the LORD; whoever does any work on the sabbath day shall surely be put to death. 'So the sons of Israel shall observe the sabbath, to celebrate the sabbath throughout their generations as a perpetual covenant.' "It is a sign between Me and the sons of Israel forever; for in six days the LORD made heaven and earth, but on the seventh day He ceased from labor, and was refreshed." Exodus 31:12-17  (NAS)

*Hebrews 9:22 says "And according to the Law, almost all things are cleansed with blood, and without shedding of blood there is no forgiveness." (NAS)

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