To continue:
The material which is specific to the Gospel of Matthew is called Special Matthew (M material). You have, for example, the Matthean birth narratives (1-2; we’ll classify this as M material here because while Matthew and Luke do agree in the basics, namely that Jesus was born in Bethlehem and that His parents were named Mary and Joseph, the two Gospels give two different accounts), a good deal of Matthew-only parables such as the Parable of the Weeds (13:24-30, 36-43), the Hidden Treasure and the Pearl of Great Price (13:44-46), the Dragnet (13:47-50), the Unmerciful Servant (18:23-25), the Laborers in the Vineyard (20:1-16), the Two Sons (21:28-32), the Ten Virgins (25:1-13, but cf. Luke 12:35-36), and the Sheep and the Goats (25:31-46), Judas’ death (27:3-10), and the soldiers guarding the tomb of Jesus (27:62-66, 28:11-15).
It could also be considered that a part of the Sermon on the Mount, especially the first half of chapter 6, constitutes M material. However, it should also be kept in mind that it is often difficult to distinguish between what is called M material and what might be regarded as simply fuller versions of Triple Tradition pericopes. You have, for instance, Matthew 3:14-15, where Jesus comes to ask baptism from John.
Then Jesus came from Galilee to the Jordan to John, to be baptized by him. John would have prevented him, saying, “I need to be baptized by you, and do you come to me?” But Jesus answered him, “Let it be so now, for thus it is fitting for us to fulfill all righteousness.” Then he consented. And when Jesus was baptized, immediately he went up from the water, and behold, the heavens were opened to him…
On the one hand, these are two whole verses’ worth of what would be Special Matthew. On the other hand, though, these verses only make sense in the narrative context provided by Triple Tradition material (verses which have parallels with Mark and Luke). Much of the special material is in this fashion - unique to Matthew yet sandwiched in a Triple Tradition context. Other examples include Peter trying to walk on water (14:28-31), “Thou art Peter and upon this rock…” (16:17-19), the infirm and the children in the Temple (21:14-16), the dream of Pilate’s wife (27:19), and the earthquake and other supernatural events at the death of Jesus (27:51b-53). All in all, one would notice that like Double Tradition, Special Matthew is rich in sayings material, especially parables. It also has narrative, though one would notice that M Material has a more greater emphasis towards the supernatural and (for lack of a better term) ‘fantastic’: i.e. the coin in the fish’s mouth and the resurrection of the saints.
This feature is another element which needs to be considered when trying to solve the Synoptic Problem. The question that arise is: has Matthew ‘added’ these materials to an already existing account in Mark (or Luke, or both of the two), or did Mark (or Luke, or both) excise them away?
Moving on: material specific to Luke is called Special Luke or L Material. Some of the most prominent representatives of this are the Lukan birth narratives (1-2), the boy Jesus in the Temple (2:41-52), the raising of the widow of Nain’s son (7:11-17), the Samaritan villages (9:51-56), the return of the seventy-two disciples (10:17-20), the Good Samaritan (10:29-37), Mary and Martha (10:38-42), the friend at midnight (11:5-8), the rich fool (12:13-21), the murder of the Galileans (13:1-5), the fig tree (13:6-9), the fig tree (13:6-9), the healing of the bent woman (13:10-17) and the man with dropsy (14:1-6), the invitation to feasts and dinners (14:7-14), the lost coin (15:8-10), the Prodigal Son (15:11-32), the rich man and Lazarus (16:19-31),the servant of all work (17:7-10), the healing of ten lepers (17:11-19), the Unjust Judge (18:1-8), the Pharisee and the Publican (18:9-14), Zacchaeus the tax collector (19:1-10), the two swords (23:6-12), the trial before Herod Antipas (23:6-12), and the road to Emmaus (24:13-35).
L shares one of the complications of M material: sometimes, though less often than in Matthew, it appears in a Triple Tradition context, for example the women of Jerusalem (23:27-32) and the conversation with the two crucified criminals (23:40-43). In addition, L has another complication shared hardly at all by Special Matthew. It is sometimes difficult to judge whether one should ascribe a piece to L or whether one should call it a different version of Triple Tradition material. Examples of this include Luke’s version of the rejection in Nazareth (4:16-30; cf. Matthew 13:53-58; Mark 6:1-6a), the calling of the first disciples (5:1-11; cf. Matthew 4:18-22; Mark 1:16-20, also cf. John 21:1-11), and the anointing of Jesus (7:36-50; cf. Matthew 26:6-13; Mark 14:3-9, also cf. John 12:1-8). In each case the incident is placed differently from its (partial) parallel in Matthew and Mark and in each case the account is a much fuller one. In both the pericopes about the calling of the disciples and the anointing one can also see a few parallels with the Gospel of John.
Out of all materials we’ve discussed, L Material is the most famous. Here you will find some of the most-loved parables - the Good Samaritan, the Prodigal Son, the Rich Man and Lazarus to name three. In addition, one can find in the non-parable materials some of the most three-dimensional, human touches in the Gospels.