Using Doubling to Multiply
Date: 02/20/2002 at 09:28:37 From: Ron Javenes Subject: Using doubling to multiply My 4th grade grandson comes home with a math worksheet. One of the problems he has to solve is, "Can you think of a way to use doubling to multiply 6 x 7? Explain your answer." Please explain to me the term "doubling to multiply" and how it would work with 6 x 7. Thank you.
Date: 02/20/2002 at 12:55:27 From: Doctor Peterson Subject: Re: Using doubling to multiply Hi, Ron. I think this is just an opportunity for him to invent a way to use doubling in order to multiply two numbers without having to know the multiplication table. Such methods have been used for a long time in various cultures; the so-called "Russian peasant multiplication" and "Egyptian multiplication" are examples: Russian Peasant Multiplication http://mathforum.org/dr.math/faq/faq.peasant.html Russian Peasant Method of Multiplication http://mathforum.org/dr.math/problems/brown10.7.98.html Egyptian Method of Multiplication http://mathforum.org/dr.math/problems/shelley.6.26.96.html But you don't want to do research and dig too deep. Let's just look at what he might think of himself, and how you can guide him. You want to multiply 7 by 6. If you double 7, you have multiplied it by 2: 2*7 = 14 If you double it again, you've multiplied 7 by 4: 2*2*7 = 28 If you double it yet again, you've gone too far and multiplied it by 8: 2*2*2*7 = 56 How can we use these numbers to find 6 times 7? Well, 6 is 2+4, so 6*7 is (2+4)*7, which we can find as 2*7 + 4*7. (Technically, this is called the distributive property.) Put more simply, 2 sevens plus 4 sevens is 6 sevens, which is what you want. So you can just add 14 (2 sevens) and 28 (4 sevens) to get 42, which is 6*7. You'll want to give hints to gete him moving in this direction. He might think of ways that are just as good on his own; for instance, he might want to multiply 6 by 7, and do it as 8 sixes minus 1 six. That's fine! The idea is to get him thinking and inventing if possible. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 02/22/2002 at 12:25:11 From: Ron Javenes Subject: Using doubling to multiply Thank you for the answer to my question...I understand why they want young minds to explore different ways to solve a problem. But old minds sometimes have a problem understanding why something so simple can become so complex. Have a nice day, Ron
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.