Use the principles of expanded notation to explain borrowing, also known as regrouping, to your third grader. Write 56 as 50 + 6 and 37 as 30 + 7 for your math problem 56 – 37. Next, regroup your minuend, the larger number, to read (40 + 16) – (30 + 7). Your third-grader should find it easier to subtract the subtrahend to find the difference of 10 + 9. Convert the expanded difference to standard notation to get and answer of 19. Once your third grader understands the regrouping concept using the expanded form, computing problems becomes easier and takes less time to complete. Further practice reinforces the concept.
Some students use manipulatives to see a problem. Use connecting blocks, pennies, buttons or any handy item for this. Use different items for each place value, such as jelly beans for ones, chocolate drops for tens, and gummies for hundreds place values. Use the place value item for each number before you start the regrouping process, so 452 would be four gummies in the first column, five chocolate drops in column two and two jelly beans in the last column. Have one or two snack bags with 10 chocolate drops and the same number of bags with 10 jelly beans so you can easily regroup when necessary. Demonstrate the 10 chocolate drops equals one gummy and 10 jelly beans equals one chocolate drop. If the problem is 452-368, trade one gummy for 10 chocolate drops and one chocolate drop for 10 jelly beans. Have the student complete the problem using the regrouped manipulatives to reach a difference of 84. Continue through the rest of the subtraction problems and award a portion of the manipulatives for all correct answers.
Have your third grader practice reading and translating word problems into information she can understand. For example, “If Larry has eight chickens and he gives two each to Mary and Mike, how many does he have left?” She could write the problem in various ways, including eight minus two equals six minus two equals four or two plus two equal four given away and eight minus four equals four remaining. She could use manipulatives to work out the problem, beginning with eight and reducing it by two twice.
Adding the difference and the subtrahend together will give you the minuend. After the student completes the subtraction problems, rewrite the problems as addition problems and have the student check his work. Mark subtraction problems completed incorrectly and have the third grader recompute the answers.