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Subtraction with Packed Blocks - With Regrouping

Subtraction with packed blocks helps students become very comfortable with the traditional algorithm. They see how the algorithm works. In particular, students see that regrouping (“borrowing”) is simply the unpacking of a large block into ten smaller blocks.

	Let’s start with the problem 45 – 18. The first step is to build the number 45 with packed blocks.
	Next, we must remove 18 blocks and see what remains.
	So far, we’ve taken away 15. We still need to take away 3 more. How can we do this?
	If we open up a block-of-10, we will now have 10 more single blocks. This is the regrouping or “borrowing” step of the formal algorithm.
	Now we can take away 3 more single blocks.
	This gives us a total of 18 that we have taken away.
	Now that we are done taking away the 18, we are left with the answer.
	The answer is 27.

Students should execute many such subtraction problems until they can predict the answer without touching the blocks. When numbers are represented by packed blocks, the subtraction procedure becomes deceptively simple. However, the procedure is meaningless unless students have a solid understanding of the counting view and how to do subtraction in the counting view. On the train, the idea of dealing with the tens (full cars) separately and single blocks (leftover car) separately is not obvious, but becomes very powerful once grasped.