The fall was part of God's plan?

So the latter day saints are saying that God planned for Adam and Eve to fall from grace and bringing sin into the world?

Yes, basically. The Book of Mormon, 2 Nephi chapter 2, explains this. The whole chapter is fantastic, and quite the sermon of one of the prophets to his sons, so I recommend reading the whole thing because it's hard to pull these verses out of context. Still, this is the best I can do and I think gets at the crux of your question:

22 And now, behold, if Adam had not transgressed he would not have fallen, but he would have remained in the garden of Eden. And all things which were created must have remained in the same state in which they were after they were created; and they must have remained forever, and had no end.

23 And they would have had no children; wherefore they would have remained in a state of innocence, having no joy, for they knew no misery; doing no good, for they knew no sin.

24 But behold, all things have been done in the wisdom of him who knoweth all things.

25 Adam fell that men might be; and men are, that they might have joy.

26 And the Messiah cometh in the fulness of time, that he may redeem the children of men from the fall. And because that they are redeemed from the fall they have become free forever, knowing good from evil; to act for themselves and not to be acted upon, save it be by the punishment of the law at the great and last day, according to the commandments which God hath given.

I'm going to add Alma 42 as well, and do my best to choose the most relevant excerpt (although the whole chapter is important for this topic):

11 And now remember, my son, if it were not for the plan of redemption, (laying it aside) as soon as they were dead their souls were miserable, being cut off from the presence of the Lord.

12 And now, there was no means to reclaim men from this fallen state, which man had brought upon himself because of his own disobedience;

13 Therefore, according to justice, the plan of redemption could not be brought about, only on conditions of repentance of men in this probationary state, yea, this preparatory state; for except it were for these conditions, mercy could not take effect except it should destroy the work of justice. Now the work of justice could not be destroyed; if so, God would cease to be God.

14 And thus we see that all mankind were fallen, and they were in the grasp of justice; yea, the justice of God, which consigned them forever to be cut off from his presence.

15 And now, the plan of mercy could not be brought about except an atonement should be made; therefore God himself atoneth for the sins of the world, to bring about the plan of mercy, to appease the demands of justice, that God might be a perfect, just God, and a merciful God also.

16 Now, repentance could not come unto men except there were a punishment, which also was eternal as the life of the soul should be, affixed opposite to the plan of happiness, which was as eternal also as the life of the soul.

17 Now, how could a man repent except he should sin? How could he sin if there was no law? How could there be a law save there was a punishment?

18 Now, there was a punishment affixed, and a just law given, which brought remorse of conscience unto man.

19 Now, if there was no law given—if a man murdered he should die—would he be afraid he would die if he should murder?

20 And also, if there was no law given against sin men would not be afraid to sin.

21 And if there was no law given, if men sinned what could justice do, or mercy either, for they would have no claim upon the creature?

22 But there is a law given, and a punishment affixed, and a repentance granted; which repentance, mercy claimeth; otherwise, justice claimeth the creature and executeth the law, and the law inflicteth the punishment; if not so, the works of justice would be destroyed, and God would cease to be God.

23 But God ceaseth not to be God, and mercy claimeth the penitent, and mercy cometh because of the atonement; and the atonement bringeth to pass the resurrection of the dead; and the resurrection of the dead bringeth back men into the presence of God; and thus they are restored into his presence, to be judged according to their works, according to the law and justice.

24 For behold, justice exerciseth all his demands, and also mercy claimeth all which is her own; and thus, none but the truly penitent are saved.

25 What, do ye suppose that mercy can rob justice? I say unto you, Nay; not one whit. If so, God would cease to be God.

26 And thus God bringeth about his great and eternal purposes, which were prepared from the foundation of the world. And thus cometh about the salvation and the redemption of men, and also their destruction and misery.

Sorry for the wall of text. But you asked a question where the answer is the whole Plan of Salvation, which has a lot of substance to it. These passages are saying that we were consigned to fall out of God's presence, to be tried and tempted, and learn from our own experience, and then to be able to prepare to meet God and become like Him, whereby we'd be redeemed from the fall and from our own sins through the Atonement of Jesus Christ, and to be brought back into His presence by the power of the resurrection. Without the Fall, none of that could have happened.

According to this theology, Jesus Christ was not a backup plan, He was always The Plan.