The Power of Partial Sums (Especially for Upper Elementary!)

Partial sums is an addition algorithm often taught in the younger grades as students learn to use place value strategies to add two-digit and three-digit numbers.

But partial sums is one powerful strategy that can be a fantastic support for upper-elementary students as well!

Especially when it comes to those 4th and 5th grade standards.

Students stuck on addition with the standard algorithm? Partial sums is the perfect solution!

Before we continue, I must confess: standard algorithms are NOT my favorite strategies. They are often confusing for students (especially those not yet confident in math) and require more memorization than true place value understanding.

However, they are efficient for solving problems in the upper grades…and they must be taught as part of our math standards. But that doesn’t mean we can’t use all the delightful place value based strategies along the way!

Introduce Partial Sums

As soon as I find students are struggling with the standard algorithm, I move to the the partial sums method.

If you are new to this algorithm, I have another post featuring how to introduce it here: The Partial Sums Algorithm (a Step-by-Step Teaching Guide)

I always launch this algorithm with two-digit numbers (no regrouping just yet!) and place value disks to make the concept concrete:

(I have a post with a free resource on introducing place value disks to your class here if you would like: Introducing Place Value Disks with 4 Guiding Questions)

This helps students to truly see the tens and ones as we add the numbers, making it easier to set up the algorithm.

Start with the Ones Place

As I mention in my other post on introducing partial sums, there are many variations on setting up the algorithm. And there really is no one correct way to do so…it’s a matter of adding each part, then combining the partial sums.

I always begin with the ones place, then move to the tens, and hundreds:

I like this sequence to become a habit early on, as it will be easier for my students once they reach the standard algorithm.

Scaffold the Steps

Over the years, I’ve learned to provide scaffolds to build student confidence and understanding with the partial sums algorithm (and all algorithms!).

I use visual scaffolds with these gray bars to help line up our digits by place value:

And gradually release the scaffolds when my students become comfortable with the concept:

I also like to scaffold the problems themselves. We begin with two-digit addition without regrouping, then move to regrouping in a leveled series of practice problems:

As students become more fluent working with the algorithm, we move to three-digit numbers…and release all the scaffolds:

My ultimate goal is for students to work fluently and add the partial sums below the equation (no need to record the addends on the side once they are comfortable with the algorithm).

Connect the Algorithms

Now that students are able to solve with ease, we make the connection to the standard algorithm.

I set up two of the same addition problems, solving one with partial sums and the other with the standard algorithm:

Then I ask my students one of my favorite questions in math (and one I ask about 1,000 times a week!)…

What do you notice?

(I have a free set of more open-ended questions like this here: 5 Tangible Ways to Support Productive Struggle in Elementary Math)

I guide my students to identify how we are regrouping numbers in both algorithms…and how the standard algorithm is more of a shortcut as it combines the partial sums in one row as we work:

It can also be helpful to highlight or shade how the numbers are regrouped in both algorithms:

Get Started Now!

Would you like to try this with your students? No need to plan a single problem in the process…I have all the partial sums you will need in this set of practice sheets.

Everything has been scaffolded and leveled for you, so you won’t have to spend one moment planning things out:

Is this something you would try with your upper-elementary students? I would love to hear your thoughts!