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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 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

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