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 student needs only to take a pretest and a post-test on ten math vocabulary terms: (or any ten 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 explanation s 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, denomintor, 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 for instructions.

Suggestions for student work:

Have the students complete work on the remaining four vocabulary words. When they finish their Frayer Models, they can show the teacher, who will check accuracy, and then they can make a wordle for each word.

Control Of Error

Post-test after student complete the work.

Points Of Interest


Direct Aim: learning five new vocabulary words

Indirect Aim: students gain a thorough method for mastering difficult vocabulary.


Use any five words!