## 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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