In the previous word problem worksheets, students saw sentences in which the balance point of the word problem statement was the verb "to be." For example:

• The sum of two numbers is 17.
• John's age ten years ago was 30.
• In five years, the population will be 24,000.

It was mentioned that the balance point will not always be the verb "to be," and in the next section, we'll deal with a few of those examples. Before we get there, though, there's another issue that students often struggle with: sometimes the verb "to be" shows up multiple times in a single sentence. Except in rare cases*, a sentence does not have two balance points, which means students have to identify from the structure of the sentence which word is the balance point. Some students intuitively grasp this, and others do not. The process of recognizing the balance point is somewhat grammatical in nature, so students who have a good grasp on the English language will do better than students who do not.

Here is an example of a sentence which contains the verb "to be" twice, but converts into a single equation:

• When Martha's score is increased by 17, the result is 94.

Many students will intuitively grasp that the second "is" represents the balance point. For the students who don't intuitively grasp this, there are two things you can point out which will help the student recognize which is the balance point.

• While the second "is" functions as a linking verb (connecting the first part of the sentence to the second), the first "is" is not an entire verb phrase; it is a helping verb tied to the verb "to increase." Thus, the actual verb phrase is "is increased." If the verb "to be" appears as a helping verb connected to another verb, it cannot be the balance point.
• The word "is" in the first part of the sentence is part of a subordinate clause: "When Martha's score is increased by 17." How do you recognize a subordinate clause? A subordinate clause will begin with a subordinate conjunction. Subordinate conjunctions are words like: when, if, after, because, before, until, and where.

If you recognize either of these conditions:

• "to be" is a helping verb
• "to be" is part of a subordinate clause

That verb is not the balance point of the equation.

The subordinate clause will often tell you something that is being done to the unknown. In the example above, Martha's score is increased by seventeen, so that subordinate clause, as a standalone phrase, can be represented by the expression M + 17.

In the first worksheet below, students are required to find and circle the balance point of the sentence. In the second worksheet, students are also required to solve the equation.

* An example of a sentence with multiple balance points would be something like this: "The sum of two numbers is 13, which is also nine more than the product of the two numbers." This sentence actually converts into more than one equation: x + y = 13 and xy + 9 = 13

Additionally, a subordinate clause can, in some circumstances, provide you with a second balance point, leading to two equations. For example: "Although my age is twice David's, the sum of our ages is only 45." This sentence actually gives us two equations: a = 2d and a + d = 45

In This Unit

• Word Problem Worksheets 1
• Word Problem Worksheets 2
• Word Problem Worksheets 3
• Word Problem Worksheets 4