Partial Quotients Too?!

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?

Long Division: Should it be Long Gone?

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.

Sharp came out with a scientific calculator in 1978. It had a square root button. No more algorithm.

Long Division – Scaffolded Handout

Many teachers shared that long division is one of the hardest math topics to teach. A major factor is likely related to a lack of mastery of multiplication facts. I have posted about some strategies related to multiplication. Here is a handout my initial attempt at scaffolding long division (WORD, PDF).

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).

Long Division for Students who Struggle

Long division

Making the concept of long division accessible:

  1. Start with simpler problem
  2. Use base ten blocks (and later with drawings as seen in the photo) and have students model each step of the long division with the base ten blocks.
  3. Do this for each step.
  4. Follow with more complicated problems

See link  to document with full explanation.