Addition is the combining of two or more numbers. In the early days of school, students are asked to add single digit numbers and are given objects such as buttons to aid them in the process. By the end of grade 2, students begin to add numbers that are not easily added with objects because the process is time consuming.
Traditional adding method of carrying is common, but new methods are available to assist students. Partial sums, place value, and column addition method are three strategies for students to learn addition. After students have been exposed to all three methods, they will chose the best method for themselves.
Partial Sums Method
Partial sums method has the student focus on one place value column at a time. This method allows the student to see how much the number is really worth. Before this method is introduced, the student needs to understand place value. It is best to allow students to work with base 10 blocks to illustrate numbers.
Adding with partial sums is a two step process. In the example 384 + 147 =
- Add each place value separately. Start always with the left side and work to the right side.
- Add hundreds (400) + add tens (120) + add ones(11) = add partial sums (531)
- Question can be written horizontal or vertical.
Column Addition Method
Column addition method has the student focus on regrouping, also known as carrying. Students must understand place value to be successful with this method, which is a two step process. In the example 384 + 147 =
- Write the equation vertically in wide columns separated by vertical lines. For this equation there would be 3 vertical lines, with a vertical line separating ones, tens, and hundreds.
- Add each column separately and place the numbers in the appropriate column.
- 384 + 147 = 4/12/11
- Next step is to regroup the ones, tens, and hundreds. Simply add the digit to the number to its left. At the end each column should only have one number. Start with regrouping in the ones and lastly the tens.
- 384 + 147 = 4/12/11 = 5/3/1 =531
Place Value Method
Place value method has the student focus on place value. Students will need a place value chart, hundred blocks, ten rods, and ones. Before beginning, students should be introduced to the different manipulatives. For example, 10 ones represent one rod, while 10 rods represent a hundred block. This is a three step process. In the example 384 + 147 =
- Do each addend separately and place the appropriate manipulatives in the the place value chart.
- 384= 3 hundred blocks placed in the hundred place value, 8 ten rods placed in the ten place value, and 4 ones placed in the ones place value.
- 147= 1 hundred block placed in the hundred place value, 4 ten rods placed in the ten place value and 7 ones in the one place value.
- aAdd the blocks, rods, and ones together beginning with the ones place value.
- For place value, only 9 or fewer are allowed in the place value columns. Example: Student counts the number of ones and removes multiples of 10 and trades them in for a rod equaling 10. Rod is then placed in the tens place value.
- 384+147= 4 hundred blocks, 12 rods, 11 ones
- 11 ones is too many, therefore 10 ones are traded in for 1 rod and the rod is placed in the tens place value.
- 384+147= 4 hundred blocks, 13 rods, 1 one
- 13 rods is too many, therefore 10 rods are traded in for 1 hundred block and it is placed in the hundreds place value.
- 384+147=5 hundred blocks, 3 rods, 1 one= 500+30+1=531
Teaching 3-digit addition is not always an easy concept for primary students to comprehend. The traditional method is easy for some students to master but other students need to be exposed to other strategies. Partial sums, column addition, and place value addition are good math strategies to teach the concept of addition.
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