Beyond Jordan - Or, by the side of Jordan. Matthew begins here to give an account of Christ's journey (the only one he mentions) to Jerusalem, a little before the passover, at which he was crucified. See Mark 10:1; Luke 9:51.

Jesus came from Galilee (which lay to the north of Judea) into the coasts of Judea; and from thence, in his way to Jerusalem, he went through Jericho, (Matthew 20:17, Matthew 20:29), which lay at the distance of sixty furlongs, or seven miles and a half from Jordan, to the western side of it. See Joseph. War, book iv. chap. 8. sect. 3. It seems, therefore, most probable, that the course of Christ's journey led him by the side of the river Jordan, not beyond it. That the Greek word περαν, especially with a genitive case as here, has sometimes this signification, see on John 6:22 (note); see also Bp. Pearce.

that when.

Mark 10:1 And he arose from there, and comes into the coasts of Judaea by the farther side of Jordan: and the people resort to him again; and...

John 10:40 And went away again beyond Jordan into the place where John at first baptized; and there he stayed.

he departed. This was our Lord's final departure from Galilee, previous to his crucifixion; but he appears to have taken in a large compass in his journey, and passed through the districts east of Jordan. Some learned men, however, are of opinion, that instead of 'beyond Jordan,' we should render, 'by the side of Jordan,' as [peran,] especially with a genitive, sometimes signifies.

On the Words of the Gospel, Matt. xix. 28, "Come unto Me, all Ye that Labour and are Heavy Laden," Etc.
1. We heard in the Gospel that the Lord, rejoicing greatly in Spirit, said unto God the Father, "I confess to Thee, O Father, Lord of heaven and earth, because Thou hast hid these things from the wise and prudent, and hast revealed them unto babes. Even so, Father: for so it seemed good in Thy sight. All things are delivered unto Me of My Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal Him." [2306] I have …
Saint Augustine—sermons on selected lessons of the new testament

On the Journey to Jerusalem - Departure from Ephraim by Way of Samaria and Galilee - Healing of Ten Lepers - Prophetic Discourse of the Coming
The brief time of rest and quiet converse with His disciples in the retirement of Ephraim was past, and the Saviour of men prepared for His last journey to Jerusalem. All the three Synoptic Gospels mark this, although with varying details. [4875] From the mention of Galilee by St. Matthew, and by St. Luke of Samaria and Galilee - or more correctly, between (along the frontiers of) Samaria and Galilee,' we may conjecture that, on leaving Ephraim, Christ made a very brief detour along the northern …
Alfred Edersheim—The Life and Times of Jesus the Messiah

The Last Incidents in Peræa - the Young Ruler who Went Away Sorrowful - to Leave all for Christ - Prophecy of his Passion - The
As we near the goal, the wondrous story seems to grow in tenderness and pathos. It is as if all the loving condescension of the Master were to be crowded into these days; all the pressing need also, and the human weaknesses of His disciples. And with equal compassion does He look upon the difficulties of them who truly seek to come to Him, and on those which, springing from without, or even from self and sin, beset them who have already come. Let us try reverently to follow His steps, and learn of …
Alfred Edersheim—The Life and Times of Jesus the Messiah