| More than likely, when you learned how to | | | | left addition excludes vocabulary related to |
| add, you started on the right and moved to | | | | place value. Left to right addition, on the |
| the left. If you were adding whole numbers, | | | | other hand, promotes an understanding of |
| you added the ones, "carried" if necessary, | | | | place value as each digit is given its |
| and repeated for the tens, hundreds and so | | | | correct value. In the example, the one in the |
| on. This works well on paper, and it is the | | | | thousands place is one thousand, the two in |
| most efficient paper and pencil method; | | | | the hundreds place is two hundred, and so |
| however, adding in the other direction has | | | | on.Left to right addition is well-suited to |
| several desirable advantages: the left to | | | | mental addition since the sum is cumulative |
| right method promotes a better understanding | | | | with no steps in between; in other words, |
| of place value, it can be done mentally with | | | | there is nothing for the student to keep in |
| much greater ease, and it does not require | | | | mind except for the cumulative sum. In right |
| that numbers be lined up in a column. | | | | to left addition, several numbers must be |
| Students can learn left to right addition, so | | | | remembered as the student proceeds. To |
| they have another method to choose from when | | | | illustrate this, consider the simple example, |
| presented with addition problems.Left to | | | | 64 + 88. In left to right addition, the sum |
| right addition involves adding the largest | | | | is simple to find: 60, 140, 144, 152. Only |
| place values first. As you move from left to | | | | one number had to be remembered at any point. |
| right, you keep a cumulative total, so it is | | | | In right to left addition, 4 + 8 is 12, so |
| simply a number of smaller addition problems. | | | | there are already two numbers to remember: |
| To give you an idea of how it works and what | | | | the two in the ones place and the regrouped |
| it sounds like, consider the example, 677 + | | | | ten. The next step is to add 60 + 80 + 10 to |
| 938.Begin by adding the left most place | | | | get 150. At this point, the two must be |
| values. In the example this is 600 plus 900 | | | | recalled and added to the 150 to get 152. |
| equals 1500. Add the values in the next | | | | Although this sounds simple, it becomes more |
| place, one at a time, to the previous sum, | | | | complicated with more digits.Right to left |
| and keep track of the new sum each time. In | | | | addition does not require numbers to be lined |
| the example, 1500 + 70 is 1570, 1570 + 30 is | | | | up in a column, but it is often taught that |
| 1600. For students who are more proficient at | | | | way because the method tends to ignore place |
| this algorithm, they don't necessarily think | | | | value and relies on a student's ability to |
| "plus 70" or "add 30." Their thought process, | | | | line up the place values to compensate. Many |
| if said out loud might sound like, "600, | | | | errors that students make in right to left |
| 1500, 1570, 1600, . . ." Continue adding the | | | | addition occur because they don't have a |
| values in each subsequent place until | | | | strong knowledge of place value, and they |
| finished. The final steps in the example are | | | | forget or don't realize that like place |
| 1600 + 7 is 1607, 1607 plus 8 is 1615. The | | | | values need to be lined up. They might, for |
| sum is 1615.As you can imagine, students need | | | | instance, add a digit in the tens place to a |
| to be proficient at single digit addition and | | | | digit in the hundreds place. Another scenario |
| have an understanding of place value before | | | | is a sloppy recording of numbers where a |
| attempting left to right addition. When they | | | | digit is mistakenly added to the wrong |
| are first learning it, they might try | | | | column.In left to right addition, the |
| repeating sums as they go along (e.g. 1500, | | | | emphasis is on finding a certain place value |
| 1570, 1570, 1570, 1600, . . .) to help them | | | | in each number rather than relying on the |
| retain the newest sums. They might also cross | | | | place values being aligned. Students, of |
| out digits as they are adding. There is no | | | | course, need to be able to recognize place |
| rule about having to add in this way | | | | value before they can be successful at this |
| mentally. Students could write down the sums | | | | method. For instance, they should be able to |
| as they proceed.Left to right addition | | | | recognize that the ones in the numbers: 514, |
| promotes a better understanding of place | | | | 1499, and 321 are in the tens, thousands, and |
| value than right to left addition. In right | | | | ones places respectively. If they can't, |
| to left addition, single digits are carried | | | | further teaching on place value is required |
| or regrouped with little emphasis placed on | | | | before addition can be taught |
| what the value of those carried digits are. | | | | effectively.Although left to right addition |
| In the example, 1246 + 586, students add 6 + | | | | has several advantages, it isn't suggested |
| 6 to get 12; they write down the 2 and carry | | | | that you scrap everything else. Learning a |
| the 1 when they should be carrying the ten. | | | | wide variety of addition methods allows you |
| In the next step, they add 8 + 4 + 1 to get | | | | latitude in problem solving situations. By |
| 13; they write down the 3 and carry the 1 | | | | teaching students this method, you give them |
| when they should be adding 80 + 40 + 10, | | | | another option when they are tackling |
| writing the 3 in the tens place (i.e. 30) and | | | | addition questions. |
| carrying the hundred. Essentially, right to | | | | |