FOXBOROUGH — The Patriots’ playbook is much smaller than the large cardboard box that sat on the floor near Leonard Hankerson’s locker on Tuesday afternoon. Despite the disparity in size, they hold equal importance in Hankerson’s hectic world these days.

The smaller item contains the information Hankerson needs to learn about the Patriots’ offense, with late-night cram sessions and additional meetings assisting with the wide receiver’s transition after being claimed off waivers from Atlanta just a week ago. After only two practices, Hankerson knew enough to dress for Sunday’s 33-16 win over Tennessee, when he was on the field for 10 snaps. He did not have any passes thrown his way.

The cardboard box? Inside were Christmas presents, shipped from Georgia, where Hankerson had been living while playing for the Falcons. Hankerson and his wife, Marketria, have three children — ages 9, 7, and 3 — and are expecting their fourth child, a second daughter, in late February. The family — all five of them (plus one) — is sharing a hotel room nearby.

Call it an adventure, one they’ve taken before.

“You always got to have family around with you to be more comfortable in a new situation,’’ Hankerson said. “I’ve been in the NFL for five years now. You’ve got to be a professional about it. You’ve got to know how to take care of home, you’ve got to take care of work.’’

Does that mean Hankerson has been light on sleep lately?

“Definitely. You get no sleep if you want to play at a high level and help the team out. Rest is limited,’’ he said.

Especially when there’s an opportunity to play, and Hankerson appears to have it. With Julian Edelman not expected to play in Sunday’s road game against the New York Jets, and Danny Amendola’s availability unclear after he suffered a knee injury against the Titans, the only other true receivers on the active roster are Hankerson, Brandon LaFell, and Keshawn Martin. The more comfortable Hankerson feels in the Patriots’ offense, the more he’ll play.

That’s partly due to necessity, but also because of Hankerson’s skill level. He appeared in eight games with the Falcons this season, after spending his first four years with Washington. In those eight games, Hankerson caught 26 passes for 327 yards and three touchdowns. Included was the second 100-yard receiving game of Hankerson’s career — a Week 4 win over Houston in which he had six catches, 103 yards, and a touchdown. He averaged 48 snaps per game with the Falcons before leaving an Oct. 25 game with Tennessee because of a hamstring injury.

After playing in one more game with Atlanta, a 24-21 loss against the Colts on Nov. 22, Hankerson was placed on the injured reserve list — which almost always ends a player’s season. But Hankerson was adamant that he was healthy enough to still contribute. So he passed a physical, and was waived by the Falcons, giving any other team a chance to claim him. The Patriots did.

“Things happen, whether it was on my end or the Falcons end, things happen,’’ Hankerson said. “People come, people go. That’s how it is.’’

He’s here now, studying the playbook and trying to find a role in the offense. In Sunday’s win, there were multiple plays where Hankerson was being told at the line of scrimmage exactly where to line up by some of his teammates. Perhaps that’s to be expected, days after joining the team.

Bill Belichick certainly gave him a pass.

“It was a little bit of a scramble, probably hard to evaluate a player off of that game with hardly any practice at all,’’ Belichick said. “Hopefully with a few extra days here over the weekend, we can get a little more done this week and move it forward. I thought he went in there and did the best he could, but it’s a tough situation.’’

After the team’s first practice in preparation for the Jets — the Patriots worked out in the fieldhouse on Tuesday — Hankerson said he’s already feeling more at home.

“I’m finally getting stuff down, figuring out where everything is. I’m getting there. Trying to cram into a couple days; usually the playbook, you learn it in OTAs and minicamp. Me, I’ve got to learn it quick. I’ve been here since Wednesday night, so it’s only been a couple days,’’ Hankerson said. “You can’t play as fast as you want to. You can’t run out to the huddle, run out to your spot, and look at the defense, because you don’t know what to do. Today I did much better. I had a little bit more time over the weekend, yesterday. It’s coming along.’’

It would be at just the right time for the Patriots, especially if they are without Edelman and Amendola for either or both of the two remaining regular-season games. The Patriots have clinched a first-round playoff bye, but have yet to earn homefield advantage throughout the postseason. That would come with a win over the Jets.

Hankerson figures to be out there, probably for more than the 10 snaps he received in his Patriots debut. There are a few more practices before then, giving him more chances to get familiar and comfortable with a new offense.

Back home, there also will be Christmas to celebrate, and three excited children opening presents. By playing in a game for the Patriots so soon after his arrival, Hankerson received his own present.

“I had no clue what was going to happen. Being in the National Football League, no matter who you are, you’ve got to prepare like you’re the starter,’’ Hankerson said. “I studied the plays a whole lot, figured out at least some parts of the offense, met with the coaches, stayed up late after hours with the playbook. But I just prepared like I was.’’

Michael Whitmer can be reached at mwhitmer@globe.com. Follow him on Twitter @GlobeWhitmer.