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Rewriting Word Problem Statements

Lesson Plans > Mathematics > Algebra > Word Problems

Rewriting Word Problem Statements

When my students are converting statements in a word problem into equations, one of the things they are trained to do is to look for is a linking verb that functions as the equals sign. In most cases, this linking verb is the verb "to be" - "is", "are", "was", "will be" or some other variation on that verb.

Occasionally, however, they'll run across a sentence that, even though they're sure it can be written as an equation, they can't find a linking verb, and they panic. Sometimes it's a sentence as simple as the following:

Fred spends three times as much money as Sue.

In this case, there's only one verb - the verb "spends", and it's a good bet that this functions as the equals sign: F = 3S.

But I don't have my students make that assumption - I work with them through a process of restating the sentence in such a way that the sentence actually has the verb "to be" in it. Here are the steps:

  1. I ask them what their variables are. They will typically tell me they are using F and S.
  2. Now I ask them what their variables represent. They will often (incorrectly) say that F represents Fred and S represents Sue. I point out to them that a variable is a "stand in" for a number, and so unless Fred is a number, F can't represent Fred. This requires them to state more precisely the meanings of their variables. They will eventually arrive at: "F represents the amount of money that Fred spent" and "S represents the amount of money Sue spent."
  3. I then tell them to restate the sentence, and instead of starting with Fred spends, start with their variable description: "The amount of money that Fred spent..."
  4. The student will likely say, "The amount of money that Fred spent is three times the amount of money that Sue spent."

At this point, they have correctly rewritten the sentence in a way that has their magic linking verb "is," and now they feel more comfortable writing their equations.

This situation occurs from time to time, and it's good to get students to work through this process; it accomplishes two purposes. One is that it forces them to state precisely what their variables represent, and it also gives them practice rewriting sentences in equivalent forms.

Here is another example: I bought five more pens than markers.

p = the number of pens I bought
m = the number of markers I bought

Restatement: The number of pens I bought is five more than the number of markers I bought.

Equation: p = m + 5

Lesson by Mr. Twitchell

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