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Partial sums algorithm

Partial sums algorithm

Author: Christopher Danielson

To help the reader perform the steps of the partial sums algorithm, and to suggest some productive ways of thinking about addition in the process.

This packet consists of two videos demonstrating the partial sums algorithm, including its relationship to the standard US addition algorithm.

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There are many reasons to learn a new addition algorithm. Perhaps you are:

  • A teacher teaching an unfamiliar curriculum,
  • A parent of a child in an unfamiliar curriculum,
  • A student in one of my math courses,
  • A student who never quite understood why the standard algorithm works, or
  • A person who is simply interested in this sort of stuff.

This packet does not attempt to present the case that alternate algorithms are better than the standard algorithm. It is instead intended to demonstrate a particular algorithm-the partial sums addition algorithm-in sufficient detail that the reader will be able to do it on his/her own, and to demonstrate important features of the algorithm and its relationship to the standard algorithm.

The reader is also invited to perform an Internet search on "partial sums algorithm" for more demonstration, debate and information.

Working from left to right

This video demonstrates the process of working the algorithm from left to right.

The algorithm

This video demonstrates the partial sums algorithm, and compares it to the standard algorithm in US classrooms.


So the partial sums algorithm is different from the standard algorithm in several important respects:

  1. We pay attention to place value, thinking "eighty" instead of "eight" if there is an 8 in the tens place,
  2. There is no carrying involved-every time we get a sum, we write that sum exactly as a partial sum, and
  3. For large numbers, the algorithm may become unwieldy; adding two 7-digit numbers will require seven partial sums, taking up quite a bit of space.

It is worth considering what sorts of addition problems will result in special cases. For example, how do these problems work out (and what makes them possibly different from the cases in the videos?)

  • 238 + 662
  • 123,478 + 43,799