I love words. Even though I am a mathematics teacher, I often discuss the etymology of a word, or words: sometimes it is of any word used in explaining a topic, or in any conversation with the class; often it occurs with academic vocabulary; and more often, it is for one or more mathematics vocabulary words. Nearly all the time, however, my purpose is to connect the words together to help student understanding.
As we approach linear relationships, and the concept of slope, I often start discussing distance, time, and speed, and how they relate to one another. Most students intuitively understand these concepts.
When I ask if they remember how to express the relationships between these three concepts, most respond that they do not. This leads to a discovery process beginning with the word speed and a discussion of common ways people describe their speed to one another, especially if riding in a car. Most often students respond with miles per hour. From here, I write mph on the board then expand it into miles per hour. A discussion of units and units of measure typically occurs at this juncture; I am a huge fan of dimensional analysis to help students better understand their mathematics.
From miles per hour, we discuss the mathematical symbol(s) used to depict the word per, typically called the fraction bar: —, or dash: ⁄ ; I prefer to use the fraction bar. From here, I write out the following representation for the units of speed.
At this point, I proceed in one of two ways, depending upon whether I wish to make explicit connections between a series of related mathematics vocabulary first, or to emphasize an algebraic representation for one of the relationships between distance, time, and speed. As this post focuses on vocabulary over representations, I will discuss the latter in a later post.
Explicit Vocabulary Connections
If I intend to emphasize the connections between certain mathematics vocabulary, which will become clear in a moment, I ask students for a synonym for speed that they may have heard in earlier math or science classes. Few mention rate, however, at times, some do.
Once the vocabulary word rate is in play, I write out something akin to the following.
Attention then shifts back to the representation of the units for rate at the end of the sentence. When I ask what name students might give to the representation for the units, students respond with fraction most often, and some with the word I sought: ratio.
This allows me to write out the following: rate & ratio asking if anyone notices any similarity between the two words. A few students exclaim rat! To which I say, “Correct!”, which leads to lots of giggling. Once the laughter settles down, I briefly explain the Latin root word, rat or rata, from which both rate and ratio were derived.
With the connection between these two words established, I ask students if they know of any other mathematics vocabulary that includes either of these in whole or in part. As I have a large poster I created in the front of my classroom depicting number sets, students fairly quickly announce rational number; whereupon, I show that ratio is a root word of rational. This leads me to write out a rational number, such as three-fourths, as shown below.
This segment concludes with students observing the connections between the mathematics vocabulary: rate, ratio, and rational number.