This is called tower addition and I use it after introducing combining like terms. I pass out one sheet (one-third of the page) to each student and have them put their name on the back and keep it upside down. I set a timer for about 3 minutes and students work individually to complete their tower. In order to fill in a box, they need to add the two boxes below it. They continue this until the top box is completed.
I do not have my students race because my slower students will give up. Once all students are done, I call out ONLY the top box. All students who get it correct will fold their paper in half and put it into a bucket, then I will draw a winner.
The most important part is to make sure students who did not get the final correct answer can find their mistake. I put my answer key on the document camera and each student finds their own mistake. My students love doing this and don't realize how many problems they are doing in a short amount of time...and no one is off-task!
*Make sure you do an example on the board so all students understand the process*
I also have tower multiplication for exponents!