The Battle of the Integers (Army Men kick inergers chips arses)
Start the video: The opening sequence is enough time to hand out bags of army men. I hand them out one ziploc bag per pair, and worksheet/notes per student.
Then I press pause when "Integer addition" shows up on the screen. This is the easy part. We talk about what happens in war. In integer war they always kill each other off in pairs (zero pairs to be specific). Kids catch on to this pretty quick. So we can begin with our first example. This is our basic addition example. Have students start with three positive army men, then add three more. Easy peasy! I play the video for a few seconds to let those three positive guys come in. Now we have six, so ask the students what if the 4 red guys came to the battle scene? The students recreate the battle scene, write down there answer, and then view it on the video! (This involves pausing and playing, and you really have to know where to stop it).
Then students work out their own examples, they can use the army men, and they plot their actions on a number line. I have tried to make the work sheet one that slowly removes steps (I think I saw Jason Buell do this, and I love it). By the end students get a pretty good grasp of integer addition. It is just practice (I pick integer addition war, or a pre-alg with pizazz that I snagged from Dan Meyer).
Where battle starts getting tough... (AKA Subtraction, and its difficulties...)
I start by asking the students to make a battle situation that will result in a zero, but uses ten men (in total). Students work through it, and with a little bit of help and guiding questions, they get 5 red and 5 blue. I then introduce them to the idea of retreat. Subtraction is like retreating, so I tell them,"from this battle, retreat (or subtract) +3 guys. What do we have left?"
Students show me and tell me, "Negative 3! You have -3 left!" I get them to write this down (I am working on a worksheet still, but for now blank paper will do). So I decided to pull out my infinite cloner from my Smart notebook, and get them to show me on the board.
- Reset to zero
- For the first number of the equation, add those army men (start with zero, go to positive, then go to negative).
- Subtract the number (in battle terms, tell which side should retreat, start with positive, work to negative).
- Fight the battle, see what remains.
Go through the combinations, and keep asking students, "Do you notice patterns?" Follow along on the smartboard. Here is an example of what it looks like on a Smartboard.