Magic Elevator - Games for Developing Integer Sense

Here are two of the games I play to give the students practice with integers in the first weeks of school. 

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. 

After some example sums, we play a game to get a feel for it.  I give pairs of students a vertical number line, a token for each student, and a deck of cards with the face cards removed.  Black cards are positive, red cards are negative.  They draw two cards at a time, and pretend those were the buttons pushed in their magic elevator.  The first student to get to +20 wins, then they play first to -20.  Drawing two cards at once seems to get them thinking in sums; some students process each card separately, some combine them then move the token.

The next day I introduce one more button, [-], which instructs the elevator to move in the opposite direction of what is normally expected.  When we play the game that day, we use mini white boards, and after the students draw their two cards, they write them with a subtraction sign in between, but they get to choose which order.  The student above could write -8 - -5, or -5 - -8, and write the answer, and then move the result on her elevator.  The whiteboard was a new idea this year, and I loved how it allowed me to check on what had been happening at tables while I was talking with other groups.

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. 

Each turn, the student can move only one of the tokens to make a new numbers.  You can ask students to use only addition, only subtraction, or give them the choice.  Again, this year I asked them to write their problems on a whiteboard so that their partners could check the work, and I could check on the progress of the game.