Division with Packed Blocks

Introducing division to students and teaching them the formal algorithm is simple and effective with Digi-Block. The unique design of the blocks allows students to perform large division problems by simply asking them to make equal piles -- before they know the algorithm. However, the blocks lead the children to do the division problems in-line with the algorithm. So, when the algorithm is introduced, it appears very natural to students. Indeed, they might even discover it for themselves!

	Let’s do 500/4. Start by building the dividend, 500, with packed blocks.
	Now, we want to make four equal piles. We can put one block-of-100 in each pile.
	We are left with a block-of-100. In order to keep dividing, we must open up this block. Then we can share the blocks-of-10.
	We can give each group two blocks-of-10 from the block-of-100. Now, each pile has one block-of-100 and two blocks-of-10.
	We still have two more blocks-of-10 that must be divided equally. We must open these blocks, as well, to get to the single blocks.
	Each pile gets 5 single blocks, and we are done. Each pile has 1 block-of-100, two blocks - of-10 and five single blocks.
	We can set the digits to the answer, 125.

Notice how the design of the blocks within blocks leads the children to start dividing the largest blocks first. Then when they can no longer divide up the largest blocks, the students are led to dividing up smaller and smaller blocks sequentially. This is the division algorithm.

Let’s do another division problem. This time, we’ll show how closely our work with the blocks mimics the formal algorithm.

	Let’s do 432/3. We start by building 432. We wish to divide the blocks into three equal piles.
	We want to make three equal piles. First, let’s divide the biggest blocks. We can put one block-of-100 in each pile.
	In order to keep dividing, we must open the remaining block-of-100.
	We now have 13 blocks-of-10.
	We can put 4 blocks-of-10 in each pile. There is 1 block-of-10 that doesn’t divide.
	So we must open this block-of-10. This leaves us with 12 single blocks.
	Each pile gets 4 single blocks. We are done dividing. Each group has 144: 1 bock-of-100, 4 blocks-of-10, and 4 single blocks.