1) Magic Elevator - There is the hot air balloon model (presented here by NRICH), but I feel like the model gets a little detailed, keeping track of sandbags and air puffs, adding and subtracting. A colleague of mine uses a magic elevator, which still utilizes a natural model of up and down movement, but simplifies the reasoning behind the direction changes somewhat. I built the story off of The Phantom Tollbooth, which our students read in 6th grade, by telling them about the elevators found in the buildings in Digitopolis.
I tell them the elevators can take them as far as they want to go up or down, and the buttons in the elevator look a lot like ours, except there are an infinite number of them.
And when you push the buttons, instead of going to that floor, they move from wherever they are that distance up or down. We do some practice, and the students seem to pick up the idea quickly.
A third variant we played on the third day was allow students to choose addition or subtraction. Again they were asked to write the problem and answer on the whiteboard, and I reminded the students to check each other. This time the goal was to end the game after 5 rounds as close to 0 (or any other number) as they could.
2) Integer Bingo - This comes from Nimble With Numbers. Integers are arranged in a 6x6 grid, with 2,4,5,6,-2,-3,-4,-5 arranged along the bottom. Students place two tokens on two of the numbers on the bottom row to make a number, then they claim that number on the board.