Vocabulary
Grade Level: 8
Overview:

Polycentric
Morphology is the study of how things are put together, like the
make-up of animals and plants, or the structure of words.
In morphology, morph- means "form" and –ology means "the study
of." So, those who study how something is made or formed are
engaged in morphology. In biology, the morphology of fish might
investigate how the gills work as part of the respiratory system. In
language morphology, you might study how prefixes and suffixes
change a word’s meaning. In mathematics, this literacy strategy can
be applied to study meaningful parts of words. For example the word
triangle has two morphemes, tri- and -angle. These morphemes can
mean three and the relationship of rays respectively; thus, a triangle
is a three-sided or angled figure.

Morphology

Affix

Prefix

Suffix

Root words

Antithesis

Morphemic
 Analysis
Learning morphology, or how to decode a word's meaning by
identifying its component parts, is a great way to maximize student
vocabulary learning. Morphology knowledge also comes in handy on standardized tests, providing the clues you need
to make an educated guess at a word's meaning, or just narrow the options in a multiple choice question.
Morphemic analysis in the mathematics classroom involves selecting words, identifying a morpheme of that word,
defining the morpheme, identifying mathematics words with that morpheme, and relating it to words of general usage
with the same morpheme. Going through this process with students helps them to understand the meanings of specific
words and the relationships between words. For example, tri in tripod means three and tri in triangle means three as
well.
We begin the morphology of math language when we encounter a word in a publication by LIMBS International - the
word is polycentric. This is referring to LIMBS Relief Knee design created by LeTourneau University as biomedical
engineering project. LIMBS International is now an organization that exemplifies the use of human ingenuity,
technology, and compassion, to help people around the world by creating low-cost, yet durable and flexible,
prosthetics to help amputees live a normal life despite the tragedy of losing a leg! They are also creating a way for
people in developing nations not to be dependent on Americans for the repair and maintenance of these prosthetics,
but to fit and fix them in their own country with low-cost parts that can be found at the local store. This is an example
of creating sustainability, empowering developing nations, and partnering globally for the greater good.
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
In this lesson, students will:

Develop 21st century skills of team work, problem solving, and communication

View a video about LIMBS International

Determine or clarify the meaning of unknown and multiple-meaning words and phrases

Use context (e.g., cause/effect relationships and comparisons in text) to determine the meaning of a word/phrase

Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word
(e.g., photograph, photosynthesis)

Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the
pronunciation and determine or clarify the precise meaning of key words and phrases
Students will learn:

How to use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word
(e.g., telegraph, photograph, autograph)

How literacy strategies can help to understand math vocabulary

How to recognize and compare root words and affixes to determine meanings of words in math and other
curriculum content areas

How math language learned in the classroom can help us understand concepts and be applied in the real world

How human ingenuity and compassion, in the form of engineers, scientists, doctors are creating ways for humans
to more positively interact, survive, and thrive in poorer areas of our world
Students will be able to:

Understand the needs of others in less fortunate, developing countries

Appreciate the work of charitable organizations which provide help around the world

Work in teams to brainstorm and create solutions

Use the relationship between particular words (e.g., cause/effect, part/whole, item/category) to better understand
the meanings of words
Levels of Thinking:

Application: Show, practice

Analysis: Compare and contrast

Synthesis: Create, design, discuss
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
Materials:

Website www.Limbs.org

Video - LIMBS Overview (Time – 3:04) and Article - HOW THE LIMBS KNEE WORKS, Listed on the Home Page,
under PROJECTS: KNEE DESIGN

Cardstock, art supplies, paper, pencils

Research materials, Dictionaries, Thesauruses, computer web search capabilities, textbooks
Day 1: Introduction
Teacher says:
Today we are going to talk about literacy, and how the knowledge of language can help you in math, other content areas, and life. Knowledge of language, especially morphology, can help you be more educated, sound more intelligent,
and understand the world around you.
Morphology is the study of how things are put together, like the make-up of animals and plants, or the structure of
words. In morphology, morph- means "form" and –ology means "the study of." So, those who study how something is
made or formed are engaged in morphology. In biology, the morphology of fish might investigate how the gills work as
part of the respiratory system. In language morphology, you might study how prefixes and suffixes change a word’s
meaning. In mathematics, this literacy strategy can be applied to study meaningful parts of words. For example the
word triangle has two morphemes, tri- and -angle. These morphemes can mean three, and the relationship of rays
respectively; thus, a triangle is a three-sided or angled figure.
Learning morphology, or how to decode a word's meaning by identifying its component parts, is a great way to
maximize our vocabulary learning. Morphology knowledge also comes in handy on standardized tests, like the SAT, by
providing the clues you need to make an educated guess at a word's meaning, or just narrow the options in a multiple
choice question.
Teacher says:
Today I am going to show you a video about LIMBS International. During the course of watching this video, I would like
you to make a list of words that fit any and all of the following categories:

Are unfamiliar to you

Have meanings that could be used in multiple content areas (math, science, social studies)

Sound like words we use in math class
Teacher shows video from LIMBS International website.
LIMBS - Promotional Overview Video (on front home page, Time — 3:04)
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
Teacher asks:
What human technology and/or ingenuity is helping the amputees adapt to their environment and their life’s
activities?
Answer: LIMBS International (founded by Roger Gonzalez, an engineering professor who is also the President of the
organization) is creating low-cost, high-quality, prosthetics to help amputees live a normal life despite the tragedy of
losing a leg. They are also creating a way for people in developing nations to fit and fix the prosthetics in their own
country with local, low-cost parts instead of being dependent on Americans for the repair and maintenance. The knee
they have created is durable, flexible, and helps people live normal lives. The knee can bend, which helps people do
normal work and recreational activities.
**If this is your students’ first time learning about LIMBS International, you may want to continue the discussion…If
they have previously learned of LIMBS, you may want to skip this next part and move on until the Lesson
Continues…
Teacher says: LIMBS International is helping people thrive in their environment despite challenges. Some key terms
associated with LIMBS International are:
 Technology
 Sustainability
 Self-sustaining
 Empowering
(Teacher may choose to write these on the board.)
Teacher asks:
1. Who can tell me what those terms mean and how they relate to LIMBS International?
 Discuss as a class.
2. What do these phrases from the LIMBS International Website mean to you?
 Sustainable Solutions for the World
 Design, Create, Test, and Train
Student Activity:
1. Have students individually reflect and respond to the LIMBS International video by writing their thoughts on an index
card, on a piece of paper, or in their journal.

Prompts for their writing: How do you feel about the work LIMBS International is doing? Is this an organization
you might want to help? What charitable organizations have you learned about in the past? How does LIMBS
compare to other charitable organizations you have heard of or been involved with?
2. Have some students share their reflections. You may want to have a short discussion about their reflections.
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
Day 2:
Teacher:
1. What words did you write down when you were watching the video that I asked you to be listening for?

Have a class discussion on how these words relate:
2. If there were words unfamiliar to them, how might they figure out the meaning?

Dictionary, Thesaurus, breaking the word into parts (dissect) and analyzing the parts to come up with a meaning
Pull up the LIMBS International website, and find the KNEE DESIGN, listed under PROJECTS: KNEE DESGIN on the main
page. Scroll down to HOW THE LIMBS KNEE WORKS. Go over this page with the students, it is very interesting and describes how the prosthetic knee is built and how it works!
Hopefully one student comes up with the word polycentric, as one of the words from the video, but it is also on this
page of information – HOW THE LIMBS KNEE WORKS. If not, then the teacher writes the word on the board and asks
students how this word was used in the video.

Answer: This is referring to LIMBS Relief Knee design created by LeTourneau University as biomedical engineering
project. The prosthetic knee design is polycentric.
What does polycentric mean? How do we find out?


Look up poly in a dictionary or on a list of common prefixes: poly means many

Polycentric = many centers
Look up centric in a dictionary or on a list of common prefixes/root words: centric means center, central, having to
do with the center.
Give some class notes or have a discussion explain the concept of morphology. This adds to the discussion you started
in the teacher introduction section, before the class watched the LIMBS video:
Many words are made up of a root (or base word) and a prefix. Some words also have a suffix. For example, the root
word port means to carry or to bear. Attach the prefix ex-, meaning out or out of, and you have the word export,
to carry out. Attach the prefix im-, meaning in or into and you have import, to carry in. Attach the prefix trans-, meaning
across, and you have transport, meaning to carry across. If you attach the suffix -able, meaning able to be, and you
have importable, exportable, and transportable.
The very words prefix and suffix are good examples, too. Pre- means before and fix means to fasten or attach, so quite
literally, a prefix is something attached to the beginning of something else. Suf- is a variant of sub, below or under, so a
suffix is something fastened underneath something else (in this case, behind the root). By learning the common roots
and prefixes (and a few suffixes) you will be able to discern the meaning of many new words almost immediately.
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
The word vocabulary itself grows out of a root word, derived from the Latin root vocare (meaning to name or call).
Knowing that vocare means to call can help you remember that evoke means call to mind, and that convocation means
a group gathered in response to a summons or call.
Words using this root: evoke, provoke, revoke, advocate, invoke, equivocate, unequivocal, vociferous, convocation

Vocabulary: A person’s vocabulary is a set of words in that person’s language they are familiar with; meanings they
can “call to mind”
A morpheme can be defined as the smallest unit of language that has an associated meaning. This small unit cannot be
subdivided into smaller units that have meaning. Thus, the purpose of morphemic analysis is to study the morphemes
of words to aid in understanding the meaning of those words. In mathematics, this literacy strategy can be applied to
study meaningful parts of words.
An affix is a morpheme that is attached to a word stem or root to form a new word.
Morpheme Analysis:
1. Practice some examples of this concept by showing students how to decode the meaning of a multisyllabic word by
first unpacking its meaning through its prefix.

Start with the known. Instead of starting a prefix lesson by explicitly teaching students the meaning of a common
prefix, lead students to first rediscover what they already know. It is likely that if a student meets an unfamiliar
word that begins with a common prefix, they will know other words beginning with that same prefix.

For example, students may not be familiar with the meaning and usage of the word antithesis and they may not
even realize that it begins with the prefix anti- due to its pronunciation (with the stress on the "tith"), but they are
surely familiar with other words beginning with the prefix anti-.
2. On your presentation station, use the wildcard search in an online dictionary, like the one in the Vocabulary.com
Dictionary, by typing anti into the search box and then scrolling through a pull-down list of different words that begin
with anti- .
3. Ask students: Do you know any of these words? Which ones? What do many of these words have in common?
Antifreeze, antianxiety drug, Anti-American, antiapartheid, anticlimactic, antibiotic
4. Encourage students to draw some conclusions based on their prefix research. If students realize that all of the antiwords they know are negative words, they can expect that an unfamiliar anti- word will have a negative element as
well.
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
5. Separate the prefix from its base word, anti + thesis, and have students brainstorm associations with the base word.

In the case of antithesis, students may be familiar with the concept of a "thesis statement" as a writer's main point,
the essence of their message.)
6. Once the word parts have been investigated, have students try to figure out how the different parts come together
to make meaning.

Students' homespun definitions may sound awkward (e.g., antithesis: "something that goes against a main point"),
but that's okay. It's a necessary step in meaningful word exploration to develop a theory about a word's meaning
before confirming or debunking that theory by looking the word up in a dictionary.
7. After students have concocted working definitions of a word, have them test out their theories by evaluating a
handful of sentences containing the word. If students visit the Vocabulary.com word page for antithesis, they will find
many sentence examples that can teach the meaning of antithesis through example:
Susan Boyle, who used to sing in her church choir, is the antithesis of the modern celebrity, with her dowdy
appearance and advancing years.

Those students familiar with Susan Boyle will understand how she is the antithesis of the modern celebrity, and
might in turn realize that the word antithesis is used to represent the opposite of something or someone.
So, we can safely say the prefix anti- means against, so most words that have the prefix anti- will be against or
negative.
8. Once you have gone through several examples like this one, let the students do some activities to reinforce what
they have learned about morphology. Here are several quick activities the students could work on together in groups.
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
Student Activity:
Put the students in pairs or groups and allow them to work together to solve some problems.
Prefix Challenge
1. Explain that a prefix is a group of letters that has been added to the front of a word, thereby changing the meaning
of that word. For example, if you add mid- (a prefix meaning middle) to week, the meaning of the word changes to the
middle of the week.
2. Have the students come up with lists of all of the prefixes they can think of and/or research to find as many prefixes
they can think of:

They should have at least 10: bi, centri, cent, co, dec, deca, deci, di, dodeca, equi, giga, hector, hemi, in, inter, iso,
is, kilo, mid, milli, nona, octo, oct, para, par, penta, pent, per, poly, quad, re, semi, sept, sex, sub, super, tri, trans,
un, under
3. Now have them list words that begin with that prefix.

This could be a race for student groups to come up with as many words under each prefix as possible.
Dog Pile
A dog pile is a sentence made up of several words using the same root word, prefix, or suffix. Creating dog piles is a
good way to learn roots and the meaning of several words at once. Examples:

The porter reported that he transported the import to the airport. [root: port, to carry]

Jane induced Tom to produce the exercise that would reduce his waist. [root: duct, duce: to pull]

To determine whether the autograph on the lithograph was genuine, James was given a polygraph test.

The man was dejected that his project was rejected.

The guard refused to admit the missionary until he got a permit to transmit the missive.
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
Root Canal
A root canal is made by including the meaning of the word's prefix, root, and suffix (if any) in brackets in a sentence.
This is a good game to play with flash cards. The sentence goes on one side and the vocabulary word goes on the other.
Here are a few examples:

Jane felt [down+throw] when she didn’t make the cheerleading squad. [dejected]

The [self+life+writing] of the mountain climber sold a million copies. [autobiography]

The man's [time+measurer] had stopped working at 12 noon. [chronometer]

The barber was tempted to [against+speak] his customer, but kept quiet. [contradict]

The computer virus was called a [many+forms] type because it could change as it spread. [polymorphic]
Neologisms
A neologism is a [neo + logos] new word, a word you make up yourself. If you make up a word on your own that is
unrelated to the classical word roots, prefixes, and suffixes, your hearer or reader will likely not know what you are
talking about. For example, if you say, "I have a blint at home," you won't convey much information because no one
else knows what you mean by a blint until you tell them. But if you say, "I have an omnispect," then your hearer or
reader (if they know word roots and prefixes) can understand something about your meaning. A few examples:

"I feel like retroambulating," Jane said. [walking backwards]

"I could fax or have my secretary call," Joe said, "but I think I will autolog to my customers today." [talk myself]

"We've seen an example, but what we need is an antiparison," the professor said. [join against--a nonexample?]
Learning for LIMBS Grade 8.2 — Math
© LIMBS International
Student Activity Day 3:
Relate this literacy strategy and morphemic analysis to the math classroom. Why do we need to figure out the
meanings of words in math class?

Di — Dissect (When do we dissect? Science, Geometry), Diameter, Divide, Division, Digit, Dihedral

Poly — Polygon, polyhedron, polycentric

Para — parallel, parameter

Per — percent, pertain, perforate
1. Have the students create some kind of graphic organizer to show how morphemes can help us understand meanings
in math class.

One idea is to create a mind map with Math Morphemes in the middle, then morphemes as branches off the
middle, like poly, then words that go with that morpheme, like polygon, polyhedron, polycentric, shooting off from
that, then words or definitions describing the meanings of those words shooting off of that.
Helpful examples of this kind of mind mapping can be seen on the following websites:

Google: Math Mind Mapping Images (See sample at the back of this lesson)

www.visuwords.com

http://www.visualthesaurus.com
The students could also create another type of graphic organizer, chart, table, pictogram, etc.
2. Let the students use their creativity. Allow them to use dictionaries, math textbooks, thesauruses, etc.
3. Walk around the room and check for understanding as they work.
Lesson Conclusion:
End with a discussion on how morpheme analysis can help us comprehend math questions, reading material, and so
on. It is a skill that can be used across the curriculum!
Learning for LIMBS Grade 8.2 — Math
© LIMBS International