Station  11

Division 

What is $3906\div 3$?

That is, how many groups of $3$ can we find in a picture of $3906$?

We can find $1$ at the thousands level, $3$ at the hundreds level, none at the tens level, and $2$ at the ones level.

Try it!

Division by single-digit numbers is all well and good. What about division by multi-digit numbers? People usually call that long division.

Let’s consider the problem $276 \div 12$.

Here is the representation of $276$ in the $1 \leftarrow 10$ machine.

We are looking for groups of twelve in this representation of $276$. Here’s what twelve looks like.

Actually, this is not right as there would be an explosion in our $1\leftarrow 10$ machine. We need to always keep in mind that this really is a picture with all twelve dots residing in the rightmost box.

Okay. So we’re looking for groups of $12$ in our picture of $276$. Do we see any one-dot-next-to-two-dots in the diagram?

Yes. Here’s one.

Try a few new cases to practice!

A challenge:

Let’s do another example. Let’s compute $31824 \div 102$.

Here’s the picture.

Remember, all $102$ dots are physically sitting in the rightmost position of each set we identify.

Here’s my picture of the answer. I used different symbols for each group of $102$ that appears in $31824$. Does my picture make sense?

There are $3$ groups | $1$ group | $2$ groups, that is, there are $312$ groups!