![]() ![]() Second, using the term “borrow” addresses a different issue. Instead of teaching a rule and then contradicting it later, manipulatives can be used to show the child that the subtrahend is smaller than the minuend, and therefore it wouldn’t make sense to end up with a negative difference. In this example, as soon as students learn about negative numbers, they will learn that subtracting a larger number from a smaller number is possible, and that the difference will be negative. In the education world, we call this a “rule that expires”, meaning that the rule applies to the particular concept taught, but will no longer apply when a new concept is introduced. First, it is completely false that a larger number cannot be subtracted from a smaller number. Many adults teach students that they “can’t” subtract a larger number from a smaller number, and therefore they must “borrow”. For example, in 34 – 19, many students would swap the digits 4 and 9 and solve 9 – 4 = 5 to satisfy the confusion caused by trying to take a larger number from a smaller number. All of a sudden, it isn’t as clean and simple as before, and many students choose to simply switch digits between the minuend and subtrahend. ![]() When students begin learning subtraction with regrouping, it can feel like a whole separate giant to tackle. Subtraction With Regrouping Misconceptions This is easy for most children to conceptualize since the difference is a positive number. Within each place, the subtrahend, or the number being subtracted, is smaller than the minuend, or the starting quantity. In the example to the right, the subtraction problem is broken up by place value. We subtract one place value at a time, starting with the ones place, moving right to left. The standard Algorithm seems pretty straight forward. Standard Algorithm is the most commonly used strategy, and the strategy most widely accepted by adults since it’s what we learned growing up. Over time, they begin to subtract multi-digit numbers and learn various subtraction strategies. They start with a given quantity and then “take out” or “take away” the amount being subtracted. ![]() When children first start learning about subtraction, they learn that it means to “take away”. ![]()
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