Addition with chips
I spend a few days on integer addition. One integer addition strategy that many teachers use with students is the two-sided chips manipulatives. When I started teaching, this was my go-to activity for integer operations. Then I discovered the Interactive Integers iPad app which I've blogged about previously. Unfortunately our tech people were re-imaging all of the iPads so they were not available to use, so I had to fall back on the 2-sided chips. I knew from previous experience with my OCR classes that my LLD class would have a hard time remembering which color is positive and which is negative so I wrote + and - on each side with a Sharpie.
I begin by demonstrating on the SmartBoard using an infinite cloner for the chips so I could drag out as many as needed, just like the app. We discuss what a "zero pair" is and first related it to money - "If I had $1 (+1), but owed my friend $1 (-1), how much money would I have left? Right, $0!" I repeated this a few times with different amounts. Then I go around the room asking each student what their favorite number is. For example, if they tell me 7, I say "so positive 7 and negative 7 equals...?" and wait for them to answer 0! I repeat this with each student.
Now it's their turn - I write an integer addition problem on the SmartBoard and have them also write it on their individual whiteboards. Then I give them chips and ask them to just set up or model the problem before attempting to take away "zero pairs". I'm a real stickler for having them set up their chips neatly and lining up the chips under the correct number that they've written on their whiteboards. Once I know they can model the problems correctly, then I have them start the "game". "Can you make a move (take away a zero pair)?" Once they do that I ask again, "can you still make a move or is your turn over?" They like thinking of this as a game. Once you cannot make any more moves, count up your chips for your final answer.
Addition with a number line
Then we move to the number line method. I explain to them that most students end up liking this method better. It's one that you can use anywhere, even on the PARCC test because as long as you have scrap paper you can always draw your own number line. I even show them that if there's any coordinate plane somewhere on the test, you can use the x-axis as a number line. All of my students' desks have these stick-on number lines from Nasco:
On the SmartBoard, I have this template set up with the "start" and "move" boxes and the number line:
I give them communicators with the same number line and plenty of empty space at the top for them to write in the problem. (Note to self: as I'm writing this, I realized that I should create a new template for them with the "start" and "move" at the top instead of just empty space.) I have them draw a dot at the "start" number, then use the "move" number to move that amount of times in the correct direction (I remind them that - is left and + is right, just like the all the negative numbers on the number line are to the left and all the positive numbers on the number line are to the right). Most students pick up on this strategy very quickly.
One way I provide practice for integer addition and subtraction is to play a friendly game of bingo! Students love the friendly competition and don't mind doing the work if it's fun. I use BingoBaker.com to create my online bingo games. I blogged about Bingo! a few years ago - check it out!
Multiplication and Division
On to the easy part! I explain the really easy-peasy rules for multiplication and division and tell them that they can only use the calculator (basic 4-function calculators, no negative button!) for the fact part but must use the rules to determine the sign of their answer. I emphasize that for addition and subtraction, they should use the number line (none of them this year liked the chip method better) and not the calculator, but for multiplication and division, they can't use the number line and should either do the fact in their heads or use the calculator. Still I saw some students try to use the number line for multiplication and division, or try to use the calculator for addition and subtraction, but not too many!
On Wednesday, we did centers for a review. This is my favorite day!! The centers are:
They have about 10 minutes at each center. Partners worked together on the cubes and puzzle, and independently on the app.
When they were working on the study guide Thursday and taking the quiz on Friday, I left the rules on the board for them to reference.
Now that this unit is over, I will allow my students to use the scientific calculators so they can use the negative button to do the calculations. Integers are such as big part of the 8th grade curriculum so I want them to be aware that they are not the same as positive numbers, but then again, I'm realistic and know that if they must continue to do these operations without the aid of a calculator, even if they correctly learn the procedures for solving equations for example, they will get an incorrect answer if the integer operations are done incorrectly. (Not to mention that use of a calculator is in every one of their IEPs.)