Lesson 5

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Make sure you know you know your basic multiplications of one-digit number (like 8 x 7) with “Numbers Jugging - Times without the Tables.”

So far we’ve covered how to multiply by the number 2 for numbers up to four digits long. We’ve learned a simple way to memorize short numbers when you hear them. We’ve also learned how to use a deck of cards as an “unlimited worksheet.”

You’re going to need that deck of cards again for this lesson, so you might want to get them out, now. Remember, that’s the deck without the Jacks, Queens, or Kings in it. And the Aces count as ones, and the Tens count as zeros.

In this lesson we’ll multiply huge numbers by two. Many of the digits will require us to carry, and some of them will come right after another.

I’d like you to consider this: No digit multiplied by two will ever give you a product that’s higher than eighteen, because nine is the largest digit, and 9 x 2 = 18.

Look at the number 18. The digit in the tens place is 1, so the highest number you could ever have to carry when you multiply by two is 1.

Now look at the multiples of 2 for all the digits. (2, 4, 6, 8, 10, 12, 14, 16 and 18.) If you carry a 1 to any of those numbers, it can’t force that number to go over the number of tens it already has. That means that you will never carry the 1 to a number that ends in 9, which would make the new number have to carry again.

That’s why two is such an easy number to multiply from left to right by. You will never have to look over to the right further than one digit to see if you will have to carry to the digit you are working on, no matter how many digits the number has.

That is not true with the other digits, but we’ll tackle that next week.
We’ll be getting our cards out and doing the example 48, 972 * 2 with them.

Then we’ll try a similar number, a little quicker.

We’ll also talk about tests, and what they mean and don’t mean. It’s more important to be able to evaluate yourself honestly, than worry about someone else’s tests. Because if your standards are higher than the others, their tests will be a breeze.

This leads us to huge multiplications, using an entire deck of cards. You have to get every single digit correct in order to get the entire problem correct.

In this lesson, we’ll also talk about a great way to practice multiplication anywhere, any time, without cards or worksheets, using newspapers, phone numbers, license plates etc.

In the next lesson we tackle multiplication by 3.

For a complete transcript of this podcast, click here.
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