Also known as decomposing or separating, breaking apart involves dissecting numbers into more easily added parts. In fourth grade, students learn how to add large numbers -- into the millions. An example of breaking apart at this level would be 1,000,379 + 2,001,505. When breaking apart, the student would add 1,000,000 plus 2,000,000, then 379 + 1,505. A final addition of all would reach the grand total. The separating strategy helps students approach the problem in smaller parts.
A slight variation of breaking apart both numbers in a math equation is to break down only the second number. Students can also break down numbers in any order they find easiest. For example, when adding 10,004 and 98, a student might add 10,004 + 96 + 2, knowing that a 6 is needed to make a round number (10,004 + 96 = 10,100 + 2 = 10,102). Adults often separate numbers in this way automatically, and it's a useful strategy for fourth-graders as well.
Another strategy fourth-graders can use when combining numbers is to round numbers up to more easily added numbers. So, for instance, a student given the problem 30,545 + 23,791 could add 9 to the last number for 23,800, and then add 23,800 to the first number more easily. The key is to remember the amount of adjustment so it can be subtracted later. In this case, the student would subtract 9 from the subtotal to reach the final number.
Transformation is a more complex version of the compensation strategy. It involves taking from some numbers and adding to others in order to make more easily added sums. It basically involves more addition and subtraction within the equation. For example, for 345 + 882, the student might subtract 45 from 345 and add the 45 to 882, making it 300 + 927. Try this strategy out with a child who is a more mathematically advanced.