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 cetera. 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 dice. 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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