From Horizontal to Vertical Addition: The Second Grade Shift

Until recent years, I had never really considered how major the shift is in second grade, as students move from horizontal to vertical addition.

But being in this math-only world of coaching and intervention has really opened my eyes.

I remember when I was working with a second grade math group on addition with expanded form.

We set up the equation using vertical addition and represented our addends with place value disks:

We then wrote out the addends in expanded form and set up the rest of the equation:

I remember briefly noting the equal sign as I wrote it under the expanded addends, then we moved on to find the sum.

Later in the week, my students were working independently on addition with expanded form and I noticed all kinds of interesting setups:

And then I realized I had seen something similar recently from third graders working on partial sums (a story for another time).

It hit me that my students didn’t truly understand the equal sign in these vertical addition equations.

They knew there was a line somewhere in the equation, so they made sure to include it. Or even sprinkle it in a couple of times, thinking it was used to separate the addends (great thinking, organization-wise!)

But they only saw it as a line, not as an equal sign.

The more I thought about it, the more I realized how we had moved from horizontal equations only in Kindergarten and first grade to a BIG jump in algorithms in second grade, without really explaining the how and why.

Moving from Horizontal to Vertical Addition

These days, I take the time to explain a bit more about vertical addition… how the equal sign is represented as a single line, along with its placement in the equation.

Since addition with expanded form is one of the first algorithms we use vertical addition with, I embed this into my introductory lessons:

I’m also more mindful of supporting this transition to vertical addition in my students’ independent work.

I’ve started using built-in scaffolds in our practice problems, gradually releasing as students gain fluency with adding the numbers, until they are confident in setting up and solving the algorithm with ease:

Taking the time to explain the equal sign in a vertical equation has truly helped with this transition to the more complex algorithms that begin in second grade.

These days, I make sure to share this information with my students in second, third, and fourth grade. This ensures there are no misunderstandings as they learn new vertical addition strategies.

Would you like to try this with your students? These addition with expanded form resources are my go-to starting point when introducing vertical addition: