There is a difference of opinion on what is essential to teach in math. Partial Quotients algorithm (and the Standard Algorithm for division) are topics I believe are worth discussing regarding the need to master these beyond a single digit divisor.
In response to the post on the value of teaching Long Division by muli-digit divisor, there were several responses that cited the value of Partial Quotients. I like that approach much more but the same question still arises. Are students grasping the concept or do they not see the forest among the trees? What is the cost-benefit analysis for this? What do they gain, besides practicing skills?
I have seen many students struggle with long division (especially the Standard Algorithm but also the Partial Quotients Algorithm). Similarly, I have seen many teachers lament this lack of proficiency. I suggest that it is prudent to conduct a cost-benefit analysis for learning these algorithms for division beyond 1-digit divisors.
If students understand the concept of division and perhaps can do long division with 1 divisor, what is the purpose of teaching long division with a multiple digit divisor (or the partial quotients algorithm).
For a long time square roots were computed using a lengthy algorithm, similar in nature to long division. We don’t teach that any more.
There are 4 versions: with and without arrows and with or without all squares. I am interested in feedback and would revise as needed. (Update, if you accessed the files before 8:30AM EST on Dec 4 you will see that I changed the wording in the left columns.)
I did not attempt to include using “R” to identify the remainder as my focus is on the steps.
The handout has a full page of each type. (partial pages shown).