Q&A #6011

Multiplying and dividing by 10

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From: Gail (for Teacher2Teacher Service)
Date: Mar 25, 2001 at 13:32:00
Subject: Re: Multiplying and dividing by 10

Seeing the pattern is so important.  I am glad you are going that route.
What I do when I want my students to see the pattern, or relationship, is
to structure an activity that will give them a chance to collect a lot of
data that will demonstrate the pattern. Then I let them "notice" it...
sometimes with my gentle nudging, of course.

In this case, I would have them suggest numbers they could multiply by
10, 100, or 1000, and then try it out with a calculator or by hand.
Don't tell them there is a shortcut, just let them do the math and collect
the products in a chart of some sort. You could even just write all the
products on the board, haphazardly, and let them notice that some have one
zero, some two, and some three (be sure that the other factor is a non-
multiple of ten at first).  Let them try to figure out why that is
happening...  this zero at the end phenomenon.  Their conjectures about what
is causing the end zeroes will help you know what questions to ask, getting
them to explain what they are thinking will help, too.

Then it is a simple problem to form a generalization for the situation.
"What happens when we multiply by a multiple of ten is..."  Again, I
would let THEM be the ones to verbalize the generalization.  You are
there just to see if it is true, to clarify any mis-comprehension, and to
help refine the language.

If you haven't ever experienced the power of discovery learning, you are
in for a real treat.  :-)

P.S.  A wonderful extension is to wonder aloud (and thus, encourage the
students to, also) about what happens if the multiple of ten is something
like 20, or 200, or 2000  or ...

 -Gail, for the T2T service

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