Annotating our Dividing Experiences
For a very long time, I have found the long division algorithm problematic. Yes, it works. Yes, it is efficient. However, it is an algorithm that complicates division for students who are ‘learning’ about division for the first time in school (because we all have experiences dividing things prior to formal education). What we are asking students to do is learn to annotate their dividing experiences, by making groups, short division, long division, the list goes on.
The long division (and short division) algorithm requires students to divide as a secondary step to memorizing where to put numbers, and which numbers to attend to. Even the language we use to describe the division algorithm can be problematic: Let’s say we’re thinking about the question “what is 500 divided by 5?”. The phrase ‘how many times does 5 go into 500?’ is specific to the long division algorithm & it makes me wonder how this language impacts s/s understanding of what division is. Indeed we could even say that asking how many times 5 goes into 500 is less useful and less manageable than the question ‘If I have 500 dollars and I want to share it with 5 people, how much money will each person get?’
To that end, when I ‘introduce’ division to students, here is how I begin teaching them to annotate their thinking:
The beauty of this annotative format is that it values estimation. If a student guesses too many the first time around, they will figure it out on their own fairly quickly and have an opportunity to make a more accurate estimate.