The Six Steps of Vocabulary Development: Math Terms

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Students need math notebooks & a pencil. If you have a Smartboard, or an LCD projector, you can show students how to create Wordles. See "Presentation" and "Links" below for the procedure for creating a Wordle.


The students need only to take a pretest and a post-test on fifteen math vocabulary terms: (or any fifteen vocabulary words you choose). Results of the pre-test determine what words to practice. The teacher needs to know the six steps of vocabulary development. Step 1: Present a description, explanation or example of a new word. Step 2: Present students with a graphic organizer representation of the new term or phrase. Step 3: Ask students to generate their own explanation or description and to draw the word or phrase. Step 4: Ask students to create their own graphic or nonlinguistic representations and engage in strategies to deepen their understanding of the word or phrase. Step 5: Students review and discuss the accuracy of their explanations and representations with each other. Places they can review eachother's work: notebook entries, graphic organizers, and art work. Step 6: Engage students in vocabulary games they create for themselves.


1. I gave students a pretest on fifteen math words or phrases kids often do not know: number sentence, product, prime number, range, numerator, area, sum, quotient, median, mean, symmetry, difference, estimate, mode, denominator, perimeter.

2. Out of 31 students, three students scored quite low. Others I allowed to practice the words together to learn what the terms they had missed, and I kept three for a vocabulary lesson.

3. First, I isolated five words each of the students had missed: product, quotient, mean, mode, and range. It is recommended that you don't have more than five vocabulary words in a single lesson. I wrote these words in red on cards. I wrote the definitions in black on separate cards for matching, later.

4. Step one: I demonstrated each word. Product, using the multiplication board; quotient, using a simple problem (6 divided by 2=3) with the quotient highlighted in red; mean, mode, and range I demonstrated with cube towers: 2 cubes, 3 cubes, 6 cubes, 7 cubes, 7 cubes. Mean was easy: I evened out the towers. The mean is 5. "Mean is the average number in a data set." Lay out the numbers 2,3,6,7,7 in front of the corresponding cube towers. "Range is the difference between highest and lowest." I subtracted 2 from 7 to get the range of 5. Mode is the most frequent number in a data set, therefore 7. Three period lesson with words and definitions.

5. Step two: I gave students each five copies of the "Frayer Model," a graphic organizer. You can easily create one of these for yourself. Make a table in Word with four boxes taking up about 2/3 of the page. Place an oval in the center where students will write the particular vocabulary word. In the boxes type: "Defiinition" (upper left); "Characteristics" (upper right); "Examples" (lower left), and "Non-examples" (lower right). Below make another box and type, "Draw a picture of the word." Note: non-examples are for pure fun, anything the word is not. I modeled the use of the Frayer model by using a word I was currently wondering about, that I didn't know: Stentorian. In "Three Cups of Tea," the writer referred to Time Magazine's style as "stentorian."

6. Steps three and four. The students fill out the Frayer model for one word.

7. Step five: students share what they have done and revise for accuracy.

8. Step six. I show students how to create a wordle. Wordles are great fun. Go to These are colorful displays in which you'll type words and definitions, synonyms, associations. Students can create different backgrounds, layouts, randomize the result, etc. Very fun. Words enlarge depending on the number of times you type them. If you want to link words in a phrase place a + sign in between them, or quotation marks around the phrase.

Suggestions for Student Work:

Have the students finish the remaining four vocabulary words using the Frayer model. When they finish, they check in with the teacher for corrections. Then, they can make their words and definitions into a Wordle.

Control Of Error


Points Of Interest

The final step, making a Wordle, can be applied to many different subject areas.


Direct Aim: to learn five new vocabulary words

Indirect Aim: to develop a thorough process for learning difficult vocabulary.


Use any five vocabulary words!