15.2 Quantity Identification and Variable Selection

Quantity Identification and Variable Selection is the step of translation that locates every distinct quantity mentioned in a verbal statement, classifies each as known, unknown, changing, or derived, and assigns a suitable variable to any quantity whose value is not directly given.

Classifying Quantities by Role

Known Quantity Identification

A known quantity is a value stated explicitly in the verbal statement, given as a specific number that can be written directly into the symbolic translation without needing a variable.

Unknown Quantity Identification

An unknown quantity is a value the statement refers to but does not state directly, such as "a number" or "the amount," and this quantity requires a variable to stand in for its unspecified value in the symbolic translation.

Changing Quantity Identification

A changing quantity is one described as varying across a range, such as a distance that increases over time, and this quantity is also represented with a variable, though its role in the symbolic translation is to track variation rather than to be solved for a single specific value.

Reference Quantity Identification

A reference quantity is a value or symbol that another quantity in the statement is explicitly compared against, such as "double the reference number" or "half of a given amount," and identifying it clarifies which quantity the described relationship is measured relative to.

Derived Quantity Identification

A derived quantity is one whose value comes from applying an operation to one or more other quantities already identified in the statement, such as a total formed by adding two named amounts together, and it does not need its own separate variable if it can be expressed directly in terms of quantities already assigned symbols.

Choosing a Variable for an Unknown

Variable Selection for an Unspecified Quantity

Once an unspecified quantity is identified, a single letter is chosen to represent it throughout the entire translation, standing in for whatever specific value that quantity ultimately turns out to have.

Meaningful Variable Naming

Choosing a variable letter that suggests the quantity it represents, such as t for time or d for distance, makes the resulting symbolic expression easier to read and connect back to the original verbal statement, even though any letter could in principle serve the same role.

Keeping Track of Multiple Quantities

Distinct Variables for Distinct Quantities

Every unspecified quantity that is genuinely independent of the others mentioned in the statement is given its own distinct variable, ensuring the symbolic translation can represent each quantity's value separately rather than conflating two different unknowns into one.

One Variable for Repeated References

When a verbal statement refers back to the same unspecified quantity more than once, using phrases like "the number" or "it" to mean the identical quantity already introduced, only one variable is used for every one of those references, rather than introducing a new variable each time.

Carrying Forward Additional Information

Quantity Unit Preservation

When an identified quantity carries a physical unit, such as dollars, hours, or meters, that unit is noted alongside the variable chosen to represent it, ensuring the unit is not lost as the statement is translated into symbolic form.

Variable Meaning Statement

Once a variable has been selected, its meaning is stated explicitly and kept alongside the translated expression or equation, such as "let x represent the number," so that the symbolic form remains clearly connected to the specific quantity from the original verbal statement that it represents.