# Beginning Column Addition – Partial Sums Method

by on December 27, 2009

WHAT IS IT?

Column Addition is adding 2-digit numbers (or larger) to other numbers.  For example, 43 + 12:  This would be written vertically with one number on top, and the other on the bottom.  Column Addition can be solved using a few different methods.  In my last blog, I discussed using the Traditional Method.  Today, I will explain another method called the Partial Sums Method.  The Partial Sums Method of Addition requires the learner to think about the numbers in each column for what they are worth.  For example, the 4 in the example above is really worth 40, because it is ‘4’ in the Tens column.  The 1 in the example above is really worth 10, because it is ‘1’ in the tens column.  A “sum” in Addition means the answer.  This method is called Partial Sums because the student finds part of the sum, then another part of the sum, then adds the ‘parts” to find the final answer, or sum.

HOW DOES IT WORK?

Using the example 43 + 12, the student would go through the following steps:

43

+12

Step 1:  First look in the Tens column, and evaluate the numbers: 40 + 10 = 50.   Write ‘50’ below the equal sign:

43

+12

50

Step 2: Next, look at the Ones column and evaluate the numbers:  3 + 2 = 5.  Write ‘5’ under the 50, being sure to write the 5 in the Ones column:

43

+12

50

+ 5

You now have 2 partial sums (the 50 and the 5), and you are ready for the final step:

Step 3:  Add the partial sums, and write the answer (55) below the equal sign.

WHY DOES MY CHILD NEED TO KNOW TWO METHODS OF COLUMN ADDITION?

• Your child certainly does not NEED to know two methods of column addition.  Many schools will teach more than one method, as children learn in many different ways.  Most schools will eventually let the child decide which method to use, once he has shown that he can complete problems using both methods.
• Many children enjoy a challenge, and teaching them more than one method can expand their way of thinking.
• The Partial Sums Method of Addition is unfamiliar to many adults, and this makes it more frustrating to try to help your child at home.  But this method is not meant to aggravate the parent, nor is it simply another method of addition.  It is great for improving your child’s Mental Math abilities.  For example, when the child adds 43 + 12, he may later mentally add the “tens” (40 + 10), then add the “ones” (3 + 2) to get the answer in his head.

WHAT TO WATCH FOR:

• If your child is learning both the Traditional Method and the Partial Sums methods of Addition at school, you will want to watch that he doesn’t get the two methods mixed up with one another (i.e. he may want to start in the Tens column (like in the Partial Sums method), but then try to “carry the 1” into the Ones column (like in the Traditional Method) by accident.  This is a common error in children who are learning two methods simultaneously.  If you find that your child understands one method over another one, you may want to stick with one method so that he can be successful.

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