FOXBOROUGH — The days after Christmas are reserved for showing off your new toys, so it wasn’t a big surprise that visitors to the Patriots’ locker room Tuesday were greeted by Julian Edelman zipping around on a remote-controlled skateboard.

As it turns out, Edelman was showing off Alan Branch’s new toy. Turns out the big man was on the big man’s nice list.

He’s also been on coach Bill Belichick’s favorite list this season. The coach clearly has been pleased by the production of Branch, the 10-year veteran who is enjoying perhaps his finest season as a pro.

“Branch has been by far our most consistent defensive tackle,’’ the coach said when the topic of the defensive line was broached on a conference call. “The other guys can shoot to get up to his level.’’

The 6-foot-6-inch, 325-pounder is playing 60 percent of the snaps this season – a 20 percent bump from last season – and has a career-high 47 tackles.

He’s literally a big reason the Patriots’ defense is ranked third in the NFL against the run, allowing just 89.5 yards per game.

“I’m playing the same ball. Teams just happen to be rolling [runners] out in my direction, I guess,’’ said Branch. “I’m able to make more plays and do well. Compliments to the scheme and everything. It’s allowing me to play pretty good.’’

Branch, who has started all 15 games this season, said he and his interior linemen have been “doing pretty well’’ as the first line of defense against opponents.

“We’re out there trying to build a wall, trying to knock guys back but, you know, there’s always a couple plays in the game where we’re not doing our job as well as we can,’’ said Branch. “So, it’s our job to make sure we try and lessen those plays and try to go out there and play some good ball.’’

Branch had a new partner against the Jets, as rookie defensive tackle Vincent Valentine started his first game and played a season-high 41 snaps in the blowout win.

The 6-3, 320-pounder normally has been the first player off the bench in a rotation with Branch and second-year man Malcom Brown.

Against the Jets, Valentine got the nod over Brown, who had started 13 of the previous 14 games. Brown didn’t enter until the fourth quarter after being demoted, reportedly for being late to a team meeting, according to ESPN.com.

Valentine acquitted himself quite well against the Jets, using his strength and size to occupy blockers and let the linebackers fill lanes and make tackles.

“Well, I think Vince is improving. He’s still got a ways to go,’’ Belichick said. “There are a lot of things he is working on, he’s gotten better at, but it’s a different game in there [as opposed to college]. Especially for us where we play guys like him in different spots. Sometimes he’s on the center, sometimes he’s in the gap, sometimes he’s on the guard, sometimes he’s in three-technique. He’s making progress. He’s coming along.’’

As for Brown, whose signature play this season was his safety against the Ravens, Belichick said, “Malcom’s had some good moments. We’re just looking really for more consistency there.’’

Turnovers popping up

After registering four takeaways against the Jets, the Patriots have soared up the NFL rankings and now are tied for third at plus-10.

What’s carried them is a six-game surge — all wins. Entering play against the 49ers Nov. 20, New England was at plus-1, with nine takeaways and eight turnovers.

The Patriots now have 21 takeaways and 11 giveaways.

“Turnovers are contagious, that’s what they say,’’ Branch said after Saturday’s 41-3 shellacking of the Jets.

“We’ve talked about it throughout the year, just getting these turnovers and how much it will help us, and we’re seeing the benefits of it,’’ said safety Devin McCourty.

“We’re keeping points off the board, which is the most important thing for us.’’

Familiarity breeds . . .

The Patriots have lost three straight in Miami and Branch said there’s no secret why the Dolphins are such a tough opponent. “They know us,’’ he said. “They know our personnel and they know the coaching staff. They go out there and play hard.’’ . . . Defensive end Chris Long’s foundation will host 100 military members and their families to a holiday steak dinner at Morton’s in Boston Wednesday night. “This dinner is a small token of my appreciation for the service and sacrifice military members have made to our country,’’ Long said.