Friday, September 18, 2020
US flag

Vertical addition (m3.nbt.2) math practice

This test question, released by the Partnership for the Assessment of Readiness for College and Career (PARCC), is discussed here in the interest of helping third-grade students, their parents, and friends understand more clearly the knowledge and skills that third graders should have in math by the end of the school year (2018 #2).


five hundred twenty eight plus two hundred eighty eight equals question mark

Enter your answer in the box.

Correct Answer
For this problem, you have to type a number into a box that represents the sum of 528 and 288. The correct answer is 816.

  • If your answer is in the 700s, you forgot to “carry” the number “1” from the tens place.
  • If your answer has a “0” in the tens place, you forgot to carry the “1” from the ones place.

You should always start addition problems like this from the ones place, which for whole numbers is the number on the right. The ones place of the top number is 8, and the ones place of the bottom number is also 8. Adding these gives 8 + 8, which equals 16. As you know from place value, 16 is the same as 6 plus one 10. What that means in the addition problem is that underneath the ones place in the problem write down the “6” from your answer, which is “6,” and put the one 10 in the the tens place by writing a “1” there.

Next, add the three numbers in the tens column: the 2 from the top number, the 8 from the bottom number, and the 1 that you carried over from the ones column. 2 tens + 8 tens + 1 ten = 11 tens. 11 tens is the same as 1 ten plus 1 hundred, so you now write down the 1 ten in the tens place of your answer and carry the one hundred to the hundreds place.

Finally, add the three numbers in the hundreds column: 5 hundreds + 2 hundreds + 1 hundred equals 8 hundreds. When you write the “8” in the hundreds place of the problem, you see that the resulting answer is 816.

If You Don't Understand This Problem
When we write the number “528,” what does that mean. There’s a “5” in the hundreds place, so that’s 500. There’s a “2” in the tens place, so that’s 20. And there’s an “8” in the ones place, just that’s just 8. We can write this about the number:

528 = 500 + 20 + 8

Likewise, with the second number, it can be broken down by place value as well.

288 = 200 + 80 + 8

We can then add the two numbers piece by piece. 8 + 8 in the ones place is 16, or 6 plus one 10. Then we add the tens place: 80 + 20 + the 10 from the 16 in the ones column, and that makes 110, which is actually 11 tens, or 1 ten plus 1 hundred. For now, “carry” the 1 hundred to the hundreds place and add it up there.

That makes 500 + 200 + 100 in the hundreds place, which is 800. Our final answer is:

800 + 10 + 6 = 816

Learn More at Home
You can learn more with this type of question by practicing different “strategies” for performing the three-digit addition. Some of the different strategies include:

  • the traditional way, right to left
  • an approach using just place value
  • explaining that the answer is correct by subtracting one of the numbers from the sum

It would be best if students could explain what they’re doing (thinking out loud) as they solve the problems using each of these strategies.

Internet Resources
Here’s a lesson from the Khan Academy that can help you understand addition of three-digit numbers when carrying, or regrouping, is involved.

Information for Teachers

This problem tests students’ understanding of the Common Core mathematics standard 3.NBT.A.2, which says that by the end of third grade, you should have the ability to “fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.”

Note that “fluency” means much more than being able to add and subtract quickly. The National Council of Teachers of Mathematics defines procedural fluency as “the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another.”

In that sense, using only one strategy to add three-digit numbers falls short of a demonstration of fluency, and teachers and parents should encourage students to explain different approaches to finding the arithmetic answer to these problems.

For the first six months following the publication of this article, we encourage and welcome comments about extending this lesson or information about how you have taught this lesson in your classrooms. #LearnTogether #Voxitatis

Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

Recent posts

Students help in wake of Gulf Coast storms

Hurricane victims in the South got some much needed help from students at one Louisiana school. Laura and Sally have been very destructive.

Scientific American endorses a candidate

It's rare that a science journal would endorse a presidential candidate, but it has happened, due mainly to Pres. Trump's rejection of science.

Student news roundup, Maryland, Sept. 16

The pandemic reveals much more about us than our unpreparedness for virtual learning; Md. students look at healthcare and choices about schooling.

Smoke from Calif. paints the East Coast sun

The sunrise this morning in Baltimore and Chicago was cooled by smoke from the Calif. wildfires, which created a thick haze aloft.

Student news roundup, Illinois, Sept. 14

Special ed advocate in Evanston dies; Remembering 9/11; Business, fine arts, and cultural life during the pandemic.

No, the president can’t run for a 3rd term

The 22nd Amendment limits the number of times a president can be elected to two. But maybe Constitutions mean little to the current administration.

Worst Calif. wildfire season in decades

Wildfires in what could be one of Calif.'s worst autumns ever have destroyed structures, including schools, killed people, and mass evacuations.

Children will wait to impress others

Does it pay off to wait for a bigger reward, or should you just take a smaller reward quicker? The "marshmallow test" has some insights.

School opens virtually in most Md. districts

School is now in session across all of Maryland, and it's mostly online, despite calls to keep trying to get in-person instruction.

Student news roundup, Illinois, Sept. 8

The pandemic, performing arts, and politics generally led student news stories from the Prairie State this past week.

On Trump’s ‘losers’ and ‘suckers’ remark

It was hard to swallow when it was reported that the president said military personnel who had died in battle were suckers and losers.


Please enter your comment!
Please enter your name here

This site uses Akismet to reduce spam. Learn how your comment data is processed.