Addition Algorithm

Contributor: Erika Wargo. Lesson ID: 12389

Large addition problems can add up to a struggle unless you know the secret. Algorithm to the rescue! Learn the steps to making addition simple. We've added an interactive quiz and video for sum help!


Arithmetic, Whole Numbers and Operations

learning style
personality style
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

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You are at your first ball game, and you are overwhelmed by the size of the ball park! The stadium has 15,500 seats in the lower level, and 10,250 seats in the upper level. How many total seats are in the stadium?

Addition is combining two or more groups into one group.

The answer to an addition problem is called the "sum." The standard algorithm for addition is a common way to solve addition problems. An algorithm is a set of steps that are used to complete a task. In this lesson, the steps are used to perform addition. The standard algorithm for addition has three steps:

  1. Line up the digits in each number vertically by place value, starting with the ones place.
  2. Add the common place values together, starting with the ones place and moving to the left.
  3. Regroup, if necessary.

It is also helpful to use grid paper to help you line up the digits in each number.

Example 1 

269 + 452

Step 1 Line up the digits by place value. The 9 and 2 are in the ones place, so they are stacked on top of each other. The other numbers are also stacked on top of each other according to place value.

Step 2 Add the common place values together. Notice how 9 + 2 = 11, so regrouping was necessary. Since 11 is greater than one ten, write down the 1 and regroup 1 in the tens place. When adding the tens place, 1 + 6 + 5 = 12, so regroup again. The 12 in the tens place represents 12 tens, so 10 tens becomes a hundred. When adding the hundreds place, 1 + 2 + 4 = 7, so 7 is written in the hundreds place. The solution is 721.

    hundreds tens ones
    1   1    
    2 6 9
  + 4 5 2
    7 2 1


Example 2 

345,600 + 451 + 5,000 =

In this example, there are three numbers to add together. The order of the numbers doesn’t matter, but the digits need to be lined up by place value. The first problem shows the numbers written in the same order as they were in the original problem. The second problem shows the numbers stacked with the greater number on the top and the smaller number on the bottom. Both ways will result in the same solution if the addition is done correctly:

    1   1               1   1        
  3 4 5 6 0 0     3 4 5 6 0 0
        4 5 1         5 0 0 0
+     5 0 0 0   +       4 5 1
_________________________________________   ___________________________________________
  3 5 1, 0 5 1     3 5 1, 0 5 1

Example 3

At the beginning of the lesson, you were asked the following question:

The stadium has 15,500 seats in the lower level and 10,250 seats in the upper level. How many total seats are in the stadium?

Using the standard algorithm, line up the digits and add, starting with the ones place:

    1 5, 5 0 0
  + 1 0, 2 5 0
    2 5, 7 5 0


There are 25,750 seats in the stadium.

Before you practice adding on your own, watch a few more examples in a video about multi-digit addition. Listen for the answers to these questions and write the answers on a piece of paper, if necessary:

  • How do you line up or stack numbers when writing an addition problem vertically?
  • In which place value spot do you start adding?

After you watch Math Antics - Multi-Digit Addition, discuss them with a parent or teacher:

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In the Got It? section, you will practice adding numbers as you play a game and complete interactive practice.

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