Once these simple straightforward concepts are mastered children will be able to carry and borrow with ease.
Carrying Numbers while Adding
Carrying is a mathematical action you perform when adding two numerals (1, 2, 3, 4, 5, 6, 7, 8, 9, and 0) together in a mathematical problem. Numerals are commonly referred to as numbers (a series of numerals such as 12, 123, and 585). They will be addressed as such in these instructions. In performing these procedures with a child, you will need a place to sit, a surface to work on (such as a table), 31 popsicle sticks/pennies/like pieces of candy, etcetera, 2 pencils, at least 2-3 sheets of blank paper, patience, a willingness to teach, and the belief this process may be easier than you think.
Allow the child to get a visual image by counting out twenty-four of the items you've chosen to work with, and placing them in a column on the table. Then, have him/her count out seven items and align them below the twenty-four. Ask how much is twenty-four plus seven. The answer, thirty-one should be given.
Have the child write twenty-four plus seven in a columned math problem on a piece of paper. You do the same. The twenty-four should be above the seven. There should be a plus sign to the left of the seven, further out than the number two.
Draw a vertical line between the number two and the number four, down passed the seven, and across the horizontal line (that should be written below the minus sign and the seven). Have the child do the same. After the vertical line crosses the horizontal line, there should be enough space to separate the numbers that are going to be written below the horizontal line. Explain that the tens column is the column the number two is in; and that numbers four and seven are in the ones column.
Note: The purpose of the vertical line is to help the child grasp the concept that the numbers are lined up in columns. Make sure your and the child's numbers are lined up properly.
Tell the child that the numbers in the ones column must be added together before the numbers in the tens column are added together. Ask the child how much you get when you add four to seven. Once the correct answer, eleven, has been given, explain that you are going to "put down" one of the number ones below the seven just below the horizontal line in the ones column, but that you'll have to "carry" the other number over to the tens column because you cannot have two numbers next to each other in the ones column. Write a number one below the horizontal line. Place the other number one above the number two. Have the child do the same.
Tell the child that the number you carry will always be the numeral to the left of the added numbers. In this case, since the added numbers make eleven, you're carrying the same numeral you're going to keep. However, this will not always be the case.
Note: A zero may be placed to the left of the seven and just under the number two so the child can get a visual image that there are zero items in the tens place.
Now the carried number one must be added to the two. Ask how much is one plus two. After the correct answer, three, is given, you and the child write a number three below the horizontal line just below the number two.
The problem has been completed. The child can see the answer to the problem, thirty-one, is the same as the answer when he/she added their items together on the table.
Repeat this process until the child is comfortable the carrying concept.
Borrowing Numbers while Subtracting
Borrowing is a mathematical action you perform when subtracting high valued numerals from low valued numerals in a mathematical problem.
Allow the child to get a visual image by counting out 31 items (as in carrying above) by placing them in a column on the table. Have him/her count out twenty-four items and align them near the upper area, and align the remaining seven below. Ask which is more, twenty-four, or seven.
Ask how many items will be left in the column of twenty four if you take seven items away. Have child consider the problem and allow him/her to remove seven items from the column of twenty-four. After the child counts the remaining seventeen items in said column, tell him/her that is the number you should have after you subtract seven from twenty-four on paper.
Instruct the child to align four items horizontally on the table. Below the four items, instruct him/her to align seven items horizontally. Ask which column has more. After the correct answer, seven, is established, tell the child to take seven items away from the column of four. This action helps the child understand the concept that you cannot subtract more from less; and gives him/her a chance to think about how to solve the problem.
Write twenty-four minus seven in a columned math problem on a piece of paper. Have the child do the same. Explain that just like with the tangible items, you cannot take seven away from four and that you'll have to "borrow" from the "tens" column. Explain that the tens column is the column the number two is in on the paper; and that numerals four and seven are in the ones column. Then draw a vertical line as with "carrying" above.
Going back to the tangible items, have the child form two columns of ten items, and a column of four items to the right of the column of ten so that the combined columns symbolize twenty-four items in a problematic structure. There should be a space between the twenty-four items and the four items. The column of seven items should be below the column of four.
him/her "borrow" one of the columns of ten items by placing them closer
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