Long Division Strategies Part 2
A few days ago, I posted about how I progress through the CRA (concrete, representational, abstract) model for introducing division. From the very basic use of splitting base 10 blocks into groups, all the way to a method very similar to the standard algorithm (that still builds conceptual understanding without just memorizing steps). You can find part 1 here in case you missed it!…did I mention there’s a freebie???
These next two strategies are both partial product strategies. This confused me soooo much when I first started teaching division. I love it now, because it gives students the chance to use facts they are familiar with to solve division problems! This biggest complaint many teachers have when teaching division is that students don’t know their multiplication facts…they don’t have to known all their facts for partial product strategies! Students can depend on knowing their friendly facts like 2s, 5s, and 10s for these strategies.
The area model connects nicely to the rectangular place value boxes being used in the strategies above. The difference is, the number of groups you are able to make doesn’t always have to be the largest groups possible. Students can use familiar facts and simply subtract from the total until the entire area of the rectangle is made up.
This was an new one for me my third year teaching, but definitely one of my faves… I think I’ve claimed all of these strategies as my favorite at this point. Oops! Similar to the area model, students can use friendly numbers to form groups until they reach the whole dividend. Below is a picture of this strategy, but you can also view this video to see it in action!
Again, these strategies pair nicely side by side and allow for some great conversations and questioning to happen.
You might be thinking…man, that’s a lot of different strategies to teach and wayyy too many for students to keep track of, BUT students do not have to be masters of all of these strategies. I do think that they need to be exposed to different strategies and be able to explain why the strategies work, but they do not have to completely master all of them. The goal would be that they would pick a couple that work for them and be able to show understanding in a variety of ways. With that being said…
The bonus strategy! I just learned about this not too long ago! I haven’t ever taught this method, but I know I have a few kiddos who would have loved it. It doesn’t necessarily fit in nicely with the other strategies, but would definitely be a good one for students to add to their arsenal of strategies. I would equate this method to lattice method with multiplication. Nice to know and fun for students but not totally necessary to succeed. And so I bring you…
Line Dot Division
In this strategy, students really need to have a pretty solid grip on skip counting or they can even list out the multiples of the number they are dividing by next to the problem. Basically, students will skip count by the number they are dividing by until they reach the digit inside the division box. Each time they say a multiple, they draw a line. If they can’t say the next multiple without going over you will draw dot until you reach the inside number…it makes more sense in the picture below.
Any dots drawn, carry over to the next digit. So in the picture above, there was one dot under the digit 7, so the 1 would carry over to the digit 8 to make 18. The student repeats the process of skip counting and drawing lines, then dots until they reach the inside number. Carry over the number of dots to the next digit. And continue this process for the rest of the problem.
If there are no dots, nothing gets carried to the next digit.
Students will then count the number of lines under each digit and write that in the quotient. Any dots left at the end of the problem will be the remainder.
Have you taught these strategies with your students??? Which is your favorite? Don’t forget to check out part 1 for a division freebie!