Manipulatives are the best way to demonstrate the mathematical concepts of “regrouping” which is really what you are doing in adding and subtracting rather than carrying and borrowing. Regrouping is more accurately based on place value, so children can more readily master these math skills.Regrouping means that if you add a column and get a sum that is greater than 9, you must regroup due to place value.
Manipulatives such as place value rods are excellent ways to demonstrate to the child that you cannot have more than 9 in a column. If the sum in a column is ten or more, you only write down the number in the ones place. Ten “ones” equal ten.
In our system of arithmetic,based on tens, a sum of more than ten moves you to the left as you move across a math problem requiring regrouping.A bundle of ten ones or units equals one ten. Ten tens equals one hundred, etc.
You can purchase or borrow Base Ten blocks or Cuisenaire rods to practice this skill. It is also good for sharing in pairs or small groups. You can even use inexpensive household items such as paper clips, dried beans or macaroni, or any easily handled item. Adding involves trading in ten items for another different item, representing 10. Use four columns,moving from right to left:ones, tens, hundreds, thousands. Using poker chips, “beans” or other item, place them in the ones column. Show how you must move them to the next column when you have ten or more. The student can see how many items are remaining in each column.
Another effective technique is using pennies, dimes, and one dollar bills for the ones, tens, and hundreds place. Ten pennies get traded in for a dime and ten dimes get turned in for a one dollar bill. This use of manipulatives uses visual and tactile senses as well as thought processing.
In the absence of these manipulatives, you can also create your own from cardboard. Graph paper with large squares works well. The “ones” is a single square. A rod or column of ten is the “tens” place and a 10 X 10 block is “hundreds”. The graph paper, colored, if you like, can be glued to a cardboard backing of equal size.
Regrouping is a trading skill. Ten “ones” is traded in for a “tens”. Moving on to the next column from right to left, if you have ten or more rods (a line of ten), you then trade 10 in for a block, 20 in for two blocks, etc.
Using these manipulatives helps the student understand place value and that is the key concept in teaching regrouping, formerly taught as “carrying” and “borrowing.”