Q&A #466

Understanding word problems

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From: Marielouise (for Teacher2Teacher Service)
Date: Aug 02, 1998 at 22:07:18
Subject: Re: Understanding word problems

I think that you are right on target when you say that "this probably
represents a gap in their verbal education."   Students always are perplexed
when I tell them that reading is more important than mathematics!

You asked  for some assistance.  I hesitate when you asked for procedures or
helping students to understand when to add, subtract, etc.   I know that many
teachers use clue words:  "and"  for  adding,  "less than" for subtraction,
"of" for multiplying, etc.  I believe that this teaching of clue words is
doing the students a disservice.

Instead teach that there are strategies to attach word problems: I draw a
picture, label it with words and numbers if known.  If you are talking about
10 cows, draw rectangles to represent the cows.  Don't label them 1 to 10 but
rather 1 cow, 1 cow, ...1 cow.

II  make a table asking what happens now (I used the zero 0 for the o in now
to show that the time from now is zero), what happens in 1 unit of time or
event, what happens in one more unit of time or event, that is two from now.
Sometimes you ask the question in a different manner.   For example, what is
the perimeter when each side of the square is 1?  What happens when each side
of the square is 1?  What happens when each side of the square is 2?  et

III.  Look for a simple problem that is similar to it.  First solve the
simple problem.

Marilyn Burns writes interesting problems for the elementary grades.   One
that might intrigue adults is the following  (you will have to have some dice
to do this)   First look at a die and make some observations about it.  (they
should notice that only the numbers from 1 to 6 are on the die.  They should
also notice that the numbers on the opposite side when put together equal 7.)

Ask them if they can figure out:  "what the sum of all the numbers that can
be seen if they stack three dice on top of each other?"   This is a nice
problem to so by looking at a smaller problem:  first look at the top die.
Then look at the top two dice.  Then look at all three.  Suggest that they
think what the number would be if they put those three on top of two more

One of the goals of mathematics is to solve problems.  I think it is best
done by doing interesting problems.

Another interesting problem: Take a small handful of beans.   In how many
different ways can you separate the beans into groups so that with each
separation there is the same number of beans in each group.   Here again,
start with a simpler problem:  first use only 6 beans; then use 8 beans, then
use 9 beans.   Gradually work up to using 24 or 36.  Then stop!   Hopefully
after several days the student sees division/multiplication.

 -Marielouise, for the Teacher2Teacher service

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