Vocabulary Strategy: Frayer Model Handout 7 Definition Facts Examples Non-examples Mathematical Vocabulary Handout 7 Frayer Model is one type of graphic organizer that can be used to define and clarify terms for students. Point out the importance of listing examples and non-examples. 1

Frayer Model Definition A triangle with at least 2 congruent sides Teaching Reading in Mathematics Mid-continent Research for Education and Learning Definition A triangle with at least 2 congruent sides Facts Is a polygon Has 3 sides Can be turned in different directions Examples Non-examples Isosceles Triangle

Frayer Model Definition Facts Examples Non-examples Factor Teaching Reading in Mathematics Mid-continent Research for Education and Learning Definition -A whole number that divides exactly into a given whole number -A polynomial by which a given polynomial is divisible Facts -Every whole number has at least two factors -Every whole number can be written as a product of prime factors Examples -Factors of 12 are 1, 2, 3, 4, 6, and 12 -(x+1) and (x-1) are factors of x2-1 Non-examples -5 is not a factor of 12 -0 is not a factor of any whole number -(x+1) is not a factor of x2+1 Factor

Frayer Model Essential Characteristics Nonessential Characteristics Handout 8 Teaching Reading in Mathematics Mid-continent Research for Education and Learning Essential Characteristics -Set of ordered pairs with no two pairs having the same first element -Has a domain and range Nonessential Characteristics -May be one-to-one -May be linear (has a straight line graph) -Inverse may be a function Examples -f(x)=2x+1 -y=|x| -Area of a circle with given radius Non-examples -y<x -Perimeter of a rectangle with given area Function Handout 8: How could you use the Frayer Model to differentiate for students that are struggling with essential vocabulary? Have participants share responses. 4

4-Fold Strategy… Have students fold a sheet of colored paper 4 times. Using 4 key vocabulary words, have students list these down the first column. Second column… students will write a “kid friendly” definition Third column… students will show a visual depiction of the word Fourth column… students will write a fill-in-the-blank sentence for the word Have participants complete this activity depending on time. List these terms on the board -binomial expression -polynomial -rational expression -radical expression Materials: -colored paper -markers -scissors Pepper, 2009 5

4-Fold Strategy… Have students cut the rectangles out along the lines. Have students mix up the rectangles. Have students trade their set of rectangles with another student. Student two arranges the rectangles in the correct order for each term. Students will check each other’s work. Do not go to the next slide or handout. Pepper, 2009

Sample 4-Fold Strategy Handout 12 Binomial Expression Expression with two terms connected with a plus or minus sign X + 5 or 2x + 3 The FOIL method is a method for multiplying ___________ expressions. Polynomial Sums of variable and exponent expressions terms 4x2 + 3x - 7 __________ are usually written in decreasing order. Rational Expression Fraction that has polynomial in the numerator and/or the denominator x2 + 1 -------- x2 – 1 Reducing a _________ to lowest terms involves canceling all common factors from the numerator and denominator. Radical Expression Expression with a root √4 = 2 √25 The ________ √25 can be simplified. Handout 12: Depending on your audience. It may be helpful to have some discussion if there was frustration about not knowing these terms. This is how struggling learners feel frequently.

Assessing Math Vocabulary Progress The purpose of progress monitoring is to measure student learning across a period of time on end-of-year goals. Create a master list of essential math vocabulary. Create 10-15 probes by randomly selecting 3-5 words for each probe. (it is ok to choose words that the student hasn’t received instruction on yet) Score probe by awarding one point for correct definition and one point for correct example. This is one example of progress monitoring to guide instruction for individual students and can be given multiple times during the year or during the unit. Have participants discuss other ways they progress monitor for vocabulary in their classrooms. Riccomini & Witzel, 2010 8

Example of a Math Vocabulary Progress-Monitoring Probe Handout 14 Handout 14: This is a simple, but effective way to assess understanding and plan for instruction for the class, groups, and individuals. Riccomini &, 2010 Witzel 9