Demonstrate the mechanics of the partial quotients algorithm.
The partial quotients algorithm for whole-number division is commonly taught in current elementary school curricula (especially Everyday Mathematics), while many adults are unfamiliar with it. This packet is intended to be an overview to the mechanics and thinking processes underlying the algorithm.
The partial quotients algorithm is an algorithm for dividing one whole number by another. Some important features of the algorithm are these:
In this packet, I will solve three problems:
This video demonstrates how to use the partial quotients algorithm with a one-digit divisor.
This video demonstrates a harder problem-division by a two-digit divisor. In this case, we have fewer memorized facts to rely on.
This video demonstrates how to handle a remainder in the partial quotients algorithm.
After you learn the basic mechanics of the partial quotients algorithm, you can practice it to get more efficient. This will mean coming up with strategies for finding partial quotients beyond 2, 10 and 100 (for example, if you know 100 groups of A, then 50 groups of A will be half of that total, and 25 groups of A will be half again). In contrast to the standard algorithm, it seems plausible that practice with the partial quotients algorithm could improve your mental math skills.
Then you can learn to use the partal quotients algorithm to find decimal quotients (instead of using remainders or fractions). This will be the subject of another packet.
Finally, you can use the algorithm to find quotients of polynomials. Again, this will be the subject of another Sophia packet.