Key Words to Suggest What Operation to Use

Date: 12/08/2005 at 20:36:28
From: Sonya
Subject: How do I explain which math operation to use?

My daughter cannot decipher which operation to use in word problems.
Key words like "in all" and "all together" let her know to use 
addition.  Are there any key words or phrases that give her a hint
when to use division?

Date: 12/08/2005 at 22:47:27
From: Doctor Peterson
Subject: Re: How do I explain which math operation to use?

Hi, Sonya.

There are lists of key words, but I prefer not to lean too heavily on
them.  In your example, there's a good chance that the operation will
be multiplication (for example, if there are 4 girls and they have 3
apples each, how many apples do they have "in all"?) or division
(there are 4 girls and they have 12 apples in all; how many does each
have?).  Of course, in these examples, the word "each" suggests that
there is multiplication involved, and the division is just a 
multiplication in reverse, so keywords are not useless!

I like to connect math operations to physical or mental ACTIONS, 
rather than just to words.  Then the words of a problem just describe
the actions, which tell us what operations to do.

In my first example, we can picture the 4 girls each placing her 3
apples in a row; that action is repeated 4 times, and the repetition
suggests multiplication.  (The key word "each" suggests the 
repetition!)

In my second example, we can picture the same actions, but this time
we don't know how many apples there will be in each row, so the
problem is to undo a multiplication: how many are in each group?  And
that question you ask yourself indicates division.  Or, alternatively,
we can imagine acting out an investigation to find how many each has:
we take the 12 apples and divide them among the girls, giving each 1,
then 2, then 3 until we've used up the apples.  This action of
parceling out is also represented by division.

The key to this is to focus on MEANING: what does each operation mean,
and what situations call for it?  Then you can connect those
situations with the appropriate operation.  How to do this for a
specific child may depend on her style of thinking.  My suggestions
have been partly visual and partly "kinesthetic" (involving motion, if
only imaginary).  There may be other ways to "visualize" the actions
of a problem.  But one way or another, I think she has to experience
enough mathematical activities (counting things out, moving things
around, and so on) to get a natural sense of what operations mean in
action.

Here is a discussion of some of the same ideas:

  Organizing a Word Problem
    http://mathforum.org/library/drmath/view/59203.html 

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/