Math Vocabulary Energizers

S A M P L E C H A P T E R

Mat h Vocabulary Energizers

10 Ways to Get Started

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Contents

1. Vocabulary Energizers: 10 Ways to Get StartedBy Nicki Newtonfrom Daily Math Thinking Routines in Action: Distributed Practices Across the Year K-5

https://www.routledge.com/Daily-Math-Thinking-Routines-in-Action-Distributed-Practices-Across-the/Newton/p/book/9780815349631












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7

Vocabulary Energizers Ten Ways to Get Started

Classrooms where students receive sound word instruction are ones where lessons focus their attention on specifi c words and word-learning strategies, where opportunities to talk about words are many, and where occasions for applying what has been taught with engaging and content-rich texts and with moti-vating purposes occur with regularity and purpose.

—(Kamil & Hiebert, 2005, p. 10)

Math vocabulary is very important. We have to speak it. We have to make it attainable. We should play games where students get to learn it and use it. After the games, I have the students do refl ec-tions. The students should have the math word wall as a reference as well as their own self-authored math dictionary. Teachers should try to do math vocabulary energizers at least once a week as well as having a math workstation where students work with the words.

Oftentimes teachers will tell me that students know the words. We play a quick game of vocabu-lary tic-tac-toe, and teachers are often surprised at how much the students are challenged by the math vocabulary. Students can point it out but they cannot explain it. Knowing the word means that students can explain, give defi nitions, give examples, draw illustrations. Graphic organizers are good formats for these (Research Note, below).

RESEARCH NOTE Graphic organizers help students to unpack the vocabu-lary word. www.aea1.k12.ia.us/en/curriculum_instruction_and_assessment/math/english_language_learner_supports/math_vocabulary/

Math vocabulary is notoriously diffi cult. Researchers have written about the specialized nature of math vocabulary (Gay, 2008; Rubenstein, 2007; Rubenstein & Thompson, 2002). They note that it can be diffi cult for a variety of reasons, some of which are shown in Figures 7.1 and 7.2.

Math Words Can Be Challenging for Several ReasonsEveryday words

Math specifi c

More than one meaning

Homonyms More than one way to say it

Pairs that people confuse

Everydaywords used for math

Modifi ers matter

Right angle versus right answer

AddendMinuendQuotient

A circle is round, but we round numbers

Table and feet

One-quarter/

one-fourth

Area and perimeter

Diamond for rhombus

Corner for vertex

Fraction versus improper fraction

Denominator versus common denominator

Figure 7.1 Challenges of Math Words

http://www.aeal.kl2.ia.us/en/curriculum_Jnstruction__and_assessment/math/engIish_language_learner_supports/math__vocabulary/



198 ◆ Daily Math Thinking Routines

Figure 7.2 Semantic Features

Messy Semantic FeaturesSynonyms Homophones Prepositions Passive Structuresadd, plus, combine, sum

sum, somewhole, holepie, pi

divided into, divided by

Ten books were bought

Taking all of this into account, it is absolutely necessary that we do math vocabulary routines on a weekly basis. Students need multiple opportunities to practice the words through writing, games, and talking. “Math vocabulary is inextricably bound to students’ conceptual understanding of math-ematics” (Dunston & Tyminski, 2013, p. 40). If students don’t understand the words, then they won’t understand the concepts.

Researchers have outlined three ways to teach students specialized vocabulary (Novak, 1998; Novak & Gowin, 1984):

1. Students need to hear words explained and used in conversation and context three to five times.2. Make meaning of words with pictures, models, and diagrams.3. Use graphic organizers to understand the meaning of words.

Some resources are provided below.

Resources*Math Spelling City

Virginia Vocabulary Cards

Granite Illustrated Math Vocabulary Words (in four languages)

Austin Math Vocabulary Graphic Organizers

Vocabulary Strategies for the Mathematics Classroom

More Great Sites

https://www.spellingcity.com/math-vocabulary.html

www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/math_vocab_cards_2.pdf

www.granite schools.org/math-vocabulary/vocabulary-cards/

http://mrwaddell.net/blog/uploadpics/Made4Math-Vocab--Reading-in-Math-research_ 116CA/Building. a.bridge.to.Academic. vocab.in. math.pdf

https://www.eduplace.com/state/pdf/author/chard_ hmm05.pdf

www.broward.k12.fl.us/student support/ese/PDF/MathWord Wall.pdf

www.pps.k12.or.us/curriculum/math/vocabulary/3-5MathVocab.pdf

Here are some routines to teach vocabulary:

1. Alphabet Box2. Frayer Model3. Brainstorm It!4. Word Box

Vocabulary Energizers ◆ 199

5. Charades6. Mystery Word7. Vocabulary Tic-Tac-Toe8. Vocabulary Bingo9. Word of Mouth10. Math Scrabo11. 1-Minute Essay

A B C D EF G H I JK L M N OP Q R S TU V W X YZ

The teacher gives the students an alphabet box to work on during the unit (see Figure 7.5). Every few days they pull out the alphabet box and fill in new words beginning with the letters that are given.

½Definition

A part of a whole

Picture

Examples

Two out of 4

½ of the cake

Non-Examples

The whole cake

2

Routine #1Alphabet Box

Routine #2Frayer Model

The Frayer Model (Frayer, Frederick, & Klausemeier, 1969) is shown in Figure 7.6. For other graphic organizers, see Figure 7.4.


The teacher says a word, and the students have to write words that come to mind when they hear that word. Students record their thinking on their white boards or in thinking notebooks and then share with a neighbor. They have to explain how the word is connected to the starter word. After-wards, the class comes back together and discusses what they wrote and what it means. For example, if the teachers writes “Fraction,” students may write:

• Dividend• Divisor• Piece of• Part of• Numerator• Denominator

This is a quick energizer where each small group has a word box. This is a box with four squares. The teacher says the category, and then each of the students have to fill in one of the squares in the word box (see Figure 7.3).

Figure 7.3 Word Box (Mulgrave-King, 2010 personal communication)

DivisionQuotient DividendDivisor Share

Division

The class is divided into two teams. One person from each team comes up and picks a card. They have to act out the word on the card. Whichever team guesses the word first wins.

Version 1: One of the students volunteers to be the person to try and guess the mystery word (they don’t get to see the word). The teacher writes the mystery word on the board and shows it to the rest of the class. The class gives clues to the volunteer, who then tries to guess the word.

Version 2: The teacher gives a volunteer a mystery word and they have to get the class to guess what word they have. You can put scaffolded hints on the back of the card.

Routine #3Brainstorm IT!

Routine #4Word Box

Routine #5Charades

Routine #6Mystery Word


The students are divided into two teams. One team is the “X”s and the other the “O”s. They pick a number or do rock-paper-scissors to see which team is going to start first. The first team sends some-one up. That person is not on the hotspot. They simply have to pick a word. Then the team is asked a series of questions about the word. They might be asked the definition, to come draw an illustration, and/or to give an example. If they can correctly answer the questions (it is a collaborative effort), then their teammate can mark the spot. If not, the other team gets a chance. Sometimes, teams get one free chance to look up the word in a book. (See versions in Figures 7.4-7.6).

Version 1: This version just involves words.

Figure 7.4 Vocabulary Tic-Tac-Toe (Version 1)

divisor quotient fractionmultiple dividend factorproduct difference remainder

add subtract differenceturn around fact addend sumdoubles ten friends half facts

Possible teacher questions:

1. What does this word mean?2. Can you use it in a sentence?3. Who can illustrate this word?

Version 2: This version involves illustrations.


Routine #7Vocabulary Tic-Tac-Toe



1. Can you name this shape?2. Can you tell me three attributes?3. How is it the same as a ___________?4. How is it different from a ____________?

Version 3: This version is a mix of words, illustrations, and/or definitions.


3/4

This is the name for the bo�om number of the frac�on.

This is the part that is shared out in a division problem.

30 ÷ 10

> < 4 × 5


1. What is this fraction? Come illustrate it. Name a fraction greater than this. Name a fraction smaller than this.

2. What is this symbol? What does it mean? Who wants to stand up and write a statement using numbers with this symbol?

3. Look at this expression. What is the bold number? What is it called? Tell me a word problem using these numbers.

Version 1: The teacher gives the student vocabulary cards and plays bingo by calling out definitions, drawing illustrations, and giving the names (see Figure 7.7).

Routine #8Vocabulary Bingo


Figure 7.7 Vocabulary Bingo

B I N G Ofraction denominator numerator multiply divide

< divisor > dividend

³⁄₄ ¼ ²⁄₄ ½ ⁴⁄₄equivalent

fraction6 THIRDS 5 FOURTHS 2 HALVES 4 FOURTHS

equivalent improper fraction mixed number unit fraction simplify

Sample call-outs:

• B – the symbol that means less than• I – the number that tells how many groups• N – a whole number and a fraction• G – a fraction that is equivalent to ³⁄₆• 0 – the number being divided

Version 2: The teacher writes a list of vocabulary words and the students populate their pre-made boards. Then bingo continues as usual.

Routine #9Word of Mouth

Students mingle around the room and then the teacher says a word. Everyone finds a partner and discusses the word for about 2 minutes. The teacher picks a new word and the students mingle with someone new (see Figure 7.7).

Figure 7.7 Word of Mouth

The teacher draws a Scrabble-type board on a big sheet of chart paper and laminates it. Then once a week the students play as a class. They divide up into teams. The teacher can either give out letters to each team or just let the students figure out math words to make. I start by having the students just submit math words that they can make from the letters on the board. The teacher decides on the amount of points for each square. For example, blue could be double points, purple could be triple points, and red could be a bonus of 10 points (see Figure 7.8).

Routine #10Math Scrabbo

(like Scrabble ...kinda)

The 1-Minute Essay RoutineThis is a quick writing activity whereby students write about a topic for 1 minute. There is a sense of urgency and fun created by the time element.Materials and Tools

Paper and pencil

“I can” statement

I can write about math.Protocol

Overview: Students write about a topic.

1. The teacher tells the students the topic and tells them to use words, numbers, drawings, and diagrams to write about the specific topic.

2. Students start writing for 1 minute.3. After a minute, the teacher tells the

students to switch papers with someone.4. That person adds something to their

partner’s paper.5. Then they switch back and that person

adds some more to their paper.

Purpose:

• Write about mathematics• Explain, discuss, and justify

mathematical understanding

Questions:

• What did you write?• What did your partner add?• What else might you write?

Figure 7.8 Math Scrabbo

*F

R

A

C

M U L T I P L Y

I

O

N

Notes: Scores for different letters: A–J = 1 point; L–S = 2 points; T–Z = 3 points

The teacher puts a starter word on the board. Team 1 puts up the word “multiply.” So, they got M = 2, U = 3, L = 2, T = 3, I = 1, P = 2 (doubled because it’s on a blue square), L = 2, Y = 3 (doubled because it’s on a blue square). Total = 19 points.

Bonus Routine1-Minute Essay

What’s the Math?The 1-Minute Essay should require students at different levels to explore:

Kindergarten• Adding and

subtracting

First Grade• Adding and

subtracting• Properties of addition

Second Grade• Even and odd• Adding and subtracting• Properties of addition• Doubling

Third Grade• Even and odd• Doubling and halving• Adding and

subtracting• Multiplying and

dividing• Properties of addition

and multiplication

Fourth Grade• Prime and composite• Even or odd• Doubling• Adding and

subtracting• Multiplying and


and multiplication

Fifth Grade• Prime and composite• Even or odd• Doubling • Adding and subtracting• Multiplying and


and multiplication

Classroom Vignette: 1-Minute EssayMrs. Jones: Today we are going to do a 1-Minute Essay. OK get ready. I want you to write for

1 minute. Tell me everything you know about fractions. You can use pictures, words, drawings, and diagrams. Go. [One minute passes.]

OK now switch with a partner. Your partner has to add something to your paper. You will have 30 seconds to add something to your partner’s paper. [30 seconds pass.]Now switch back. Add one more thing to your paper. [Time passes.]OK, now let’s talk about what we know.Kate: I wrote that a fraction is a part of a whole.Tim: I wrote that ½ is an example. Then my partner wrote that ³⁄₄ is bigger than ½.Luke: I wrote that ²⁄₄ is equivalent to ½.Maribel: I drew a picture of a circle and then cut it into fourths and then shaded ³⁄₄.Discussion continues with Mrs. Jones taking notes on chart paper.

Fractions

I know that fractions are a part of a whole.1⁄2 is a fraction.3⁄6 is an equivalent fraction.

3⁄4 is bigger than 1⁄2.5⁄4 is also bigger than 1⁄2.

Notes from our 1-minute essay:

A fraction is part of a whole3⁄4 is an example3⁄4 is bigger than 1⁄2

Continued

1-Minute Essays – Third GradeBeginning of the Year

Write about addition, subtraction, multiplication, and division. Multiplication

Multiplication is a way to count fast.Here is an example:3 × 2We have 3 groups of 2.

End of the YearWrite about measuring, geometry and fractions. Parallelograms

Parallelograms are 4-sided figures. They are polygons. They have 2 pairs of parallel sides.

1-Minute Essays – Second Grade

Although you could start 1-minute essays earlier, I really don’t do them until second grade.Beginning of the Year

Write about numbers, addition, and subtraction. Addition

Addition is when you add. It means to put stuff together. Like 2 + 2 is addition.

End of the YearWrite about measuring, geometry, and fractions. Polygons

Polygons are shapes. They have straight sides.This is a polygon.

This is not a polygon.

Figure 7.15

Continued

1-Minute Essays – Fourth GradeBeginning of the Year

Write about addition, subtraction, multiplication, and division.

The teacher could write feedback on a Post-it – for example, asking what are the math words for tops and bottoms.

Adding Fractions

When you add fractions, you just add the tops, not the bottoms if the bottoms are the same. Like ³⁄₄ + ³⁄₄ = ⁶⁄₄

End of the YearWrite about measuring, geometry, and fractions. Lines

There are many diff erent types of line. There are straight lines and curved lines. There are parallel and perpendicular lines.

1-Minute Essays – Fifth GradeBeginning of the Year

Write about addition, subtraction, multiplication, and division.

Teacher might put up a Post-it note asking what is the confusing part.

End of the YearWrite about measuring, geometry, fractions, and decimals.

Measurement

I know that here in the US we use imperial meas-urement. We use ounces, pounds, gallons, pints, inches, and feet. In other places in the world, they use the metric system. They use centime-ters, meters, kilometers, milliliters, and liters. It can all get confusing.

Decimals

Decimals are a part of a whole. We use decimals every day when we use money. 50 cents is half of a dollar. The decimal is .50. You can put decimals on a number line.

.50


SummaryIt is essential that we teach math vocabulary in a planned way. We should not and cannot leave it to chance that the students learn math vocabulary, because math vocabulary is math. We speak math. The vocabulary carries the meaning. So we have to find ways to make it meaningful, engaging, and rigorous. It should be done in routines and in workstations and reinforced in whole-group and small-group lessons.

Questions for Reflection1. What do you currently do to teach math vocabulary?2. Do your students have their own illustrated math dictionaries that they made themselves?3. What does your word wall look like? Is it illustrated? Do the students actively use it?

ReferencesDunston, P., & Tyminski, A. (2013). What’s the big deal about vocabulary? Mathematics Teaching in the

Middle School, 19(1), 38–45.Frayer, D., Frederick, W.C., & Klausmeier, H.J. (1969). A schema for testing the level of concept mastery.

Working Paper No. 16. Madison, WI: University of Wisconsin.Gay, S. (2008). Helping teachers connect vocabulary to conceptual understanding. The Mathematics

Teacher, 102(3), 218–223.Kamil, M., & Hiebert, E.H. (2005). The teaching and learning of vocabulary. In E.H. Hiebert & M.H.

Kamil (Eds.), Teaching and learning vocabulary. Mahway, NJ: Erlbaum, pp. 1–23.Novak, J.D. (1998). Learning, creating and using knowledge: Concept maps as facilitative tools in schools and

corporations. Mahway, NJ: Erlbaum.Novak, J.D., & Gowin, B. (1984). Learning how to learn. Cambridge, UK: Cambridge University Press.Rubenstein, R. (2007). Focused strategies for middle-grades mathematics vocabulary development.

Mathematics Teaching in the Middle School, 13(4), 200–207.Rubenstein, R.N., & Thompson, D.R. (2002). Understanding and supporting children’s mathematical

vocabulary development. Teaching Children Mathematics, 9(2), 107–112.

Documents

Math Vocabulary Energizers