Using Alternative or Standard Algorithms

Alternate Algorithm: What is it?

The alternate algorithm (also called the partial sums Algorithm) has students add the numbers in place value chunks from left to right and line up the numbers the same as a standard algorithm.

Overview

This 'alternate algorithm' can be an important "bridge" for students who are splitting efficiently but may lack the confidence to regroup while using the 'standard algorithm'. When students use the alternate algorithm, they focus on each place value and write the number, in whole, down. They then continue to the next place value and write the whole number down underneath. The numbers are then added up to arrive at the final answer. 

Supporting Students Using 'Alternate Algorithm'

The alternate algorithm allows students to look at math as a process and allows students to understand where the partial sums are coming from. The alternate algorithm flows naturally from splitting and requires students to use the same thinking process, but has them line the numbers up vertically, similar to standard algorithm.  This algorithm develops from left to right, which is the most ‘natural’ way to add. To support students to shift toward representing this way, educators may need to explicitly make the connection between 'splitting' and the alternate algorithm. Modelling this representation can also be beneficial for students. 

Standard algorithms can be efficient but do not necessarily allow the students to see why they really work and understand if their answers are reasonable or not. Exposing students to the alternate algorithm will help build deeper understanding.

Where to Next?

Students who are using the standard or alternate algorithm should be encouraged to think strategically about the numbers being presented. There are situations that the algorithm may not be the most efficient strategy and students should be flexible when choosing the most appropriate strategy for every question. For example, when considering 399 + 198, using the algorithm to arrive at the answer may not be the most efficient way. Keep in mind this 'alternate' algorithm can be as efficient for students as the 'traditional' algorithm and involves identical mathematical thinking.