So…I wouldn’t exactly say this went viral, but last year The Teaching Channel came and filmed the work I did with my students around integer addition. Since then, on and off, I have gotten emails asking to hear more about how I teach integer operations. What I have decided over my 14 years of teaching, is that with integers, I prefer to use just one model: a number line.
The 6th and 7th grade teachers at my school use multiple models, like plus and minus tiles and colored discs. But as an 8th grade teacher, who cannot afford to spend a whole lot of time reteaching integer operations (but nor can I ignore the fact that you really can’t learn algebra without it), I find that sticking with a single model works best for me and my students.
This year, for the first time, I used only generic number lines. By that I mean a number line where zero is the only number written on it and it extends in both directions. We started with temperature and used a vertical number line, looking at temperatures rising and falling from am to pm and finding the change (absolute value). We looked at elevation gain and loss and also at sea birds and dolphins which dive under and jump out of the water. Oh year, and we talked about my alma mater, Dartmouth, where the stacks in the library extended many floors underground and how I had an office down there, but the Peruvian literature that I needed for my research was way up on the 6th floor. So my students got their integer fingers wet through real world scenarios.
BUT, from day one of these scenarios, we only used generic number lines. I really discouraged them from making tick marks for each integer (remember…8th grade here).
I got a brilliant idea from a blog (which I suspect was from Everybody is a Genius, but looking back, I’m not totally sure it originated there), of using plastic sleeves as white boards. You make a sheet (in this case, a generic number line), slip it into the sleeve, hand out white board markers, and shazam, you have a personalized white board for the lesson you’re teaching that day. So, my students all used these to think about questions such as if the temperature was -10 degrees in the am and the afternoon temperature was 25 degrees in the pm, how much did it rise.
So, we actually didn’t start with questions like -3 + 5. We started with generic number lines and counting by 5s and 10s on much larger numbers.
Which brings me to my revisions of the “Hey Baby, What’s your Sign” lesson featured in my video. This year, I decided to use the stickers to mark the ‘jumps’ which happened when you add two integers. It looked like this:
Same idea as last year…make a jump from zero for the first addend. Look at the second addend and decide which way you’re going to move. Then ask yourself (in your sexiest possible voice), “Hey Baby, What’s your Sign?” to determine where your second jump will land. THEN, use the orange sticker to note the sign of the sum, and only then, add the sticker for the second addend.
After students finished this worksheet they had a choice of 2 differentiated ones. One of which had more practice of single and small double digit addends. Or, they could choose the extra challenge one which had all double and triple digit numbers.
A few kids were really stubborn and didn’t want to use the stickers. I quickly learned that 100% of the complainers were already quite proficient in integer addition of big numbers. Of the kids who needed the time to think through these problems, none of them complained about the stickers slowing the pace of their work.
So, really, there’s just one major change from last year: at no time did we use number lines where integers from -10 through +10 (or something similar) were written on the number line, nor did I encourage kids who were confused to do that. I tried to be patient, and really help them think about each addend as one single jump and work towards ‘seeing’ when you’d add the 2 absolute values together and what you’d find the difference. By no means do we have 100% mastery after just a single block period. But I don’t plan to introduce any new models, nor encourage those who are confused to draw each tick mark. I want to continue to be patient with this generic number line model.
We ran out of time today, but I had wanted to do a number talk about this problem:
I am curious how kids approach it…left to right? Or are there some (hopefully) who will see that the opposites cancel and you’re left with 2. I want to move them to looking beyond 2 addends, but starting to group integers into friendly sums.