## Exploding Dots

### 3.4 Multiplication

Lesson materials located below the video overview.

Let’s keep playing with the \(1 \leftarrow 10\) machine. And let’s do a multiplication problem … right now!

You’ve got less than three seconds to write down an absolutely correct speedy answer to this multiplication problem. What’s a good answer?

* *

Can you see that \(6|18|12|3|21\), that is, “six ten thousand, eighteen thousand, twelve hundred and threety twenty-one,” is correct and does the speedy trick?

Here’s what’s going on.

Let’s start with a picture of 26417 in a \(1 \leftarrow 10\) machine. (Is it okay if I just write numbers rather than draw dots?)

* *

We’re being asked to triple this number. * *

* *

Right now we have \(2\) ten-thousands. If we triple this, we’d have \(6\) ten-thousands.

Right now we have \(6\) thousands, and tripling would make this \(18\) thousands.

Also, \(4\) hundreds becomes \(12\) hundreds; \(1\) ten becomes \(3\) tens; and \(7\) ones becomes \(21\) ones.

\(6|18|12|3|21 = 6|19|2|3|21 = 6|19|2|5|1 = 7|9|2|5|1\)

The answer \(79251\) appears.

**2. ***Compute each of the following: \(26417 \times 4\), \(26417 \times 5\), and \(26417 \times 9\).*

*Compute \(26417 \times 10\)and explain why the answer has to be \(264170\). (This answer looks like the original number with the digit zero tacked on to its end.)*

**Extra: ***Care to compute \(26417 \times 11\) and \(26417 \times 12\) too? *(The answer could be “No! I do not care to do this*!”)*

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