Translating Words into Mathematical Symbols

from:  The Sourcebook for Teaching Science

One of the greatest challenges in working with science word problems is to translate them into symbolic form.  The lists that follow include a variety of words often found in science word problems.   Identify each of the terms as addition (+), subtraction (-), multiplication (´), division (¸), power (xy), unknown (?), equal (=), or parentheses ( ) by placing the appropriate symbol after the term. Some terms may imply a specific type of the process.  For example, triple implies multiplication by three, not just multiplication.  Other terms can mean different things depending upon the way in which the sentence is written.  For example, if one is instructed to “calculate percent”, then division of the part by the whole and multiplication by 100 is implied, while if one is instructed to "take the percent of something", then multiplication by a decimal is implied. Always look at the context when interpreting a word problem, as there is not always a one to one correspondence between math words and symbols.  In this exercise use the most common meaning of the word. Figure 14.1 shows how the Ideal Gas Law can be mapped from natural language to symbolic form.  Note how much simpler the symbolic form is than the natural language form.

Activity 14.1.1– Translating words into mathematics symbols – part 1

Translate each of the following into its most likely mathematical meaning and indicate with the appropriate symbol: (+), subtraction (-), multiplication (x), division (/), power (xy), unknown (?), equal (=), or parentheses ( ).  

See data.  See summary of data.

Discuss class results.  Do words translate into sybols in a 1:1 manner, or can a word mean different things depending upon context.  Provide sample sentences in the quickwrite for words that may mean more than one thing.