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Core Subjects - EC-6
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Subject Test I (801):
English Language Arts and Reading and
the Science of Teaching Reading
Competencies 1-13
28% of the test
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Key Words:
Phonology
Morphology
Syntax
Lexicon
Semantics
Discourse
Pragmatics
English Language Proficiency
Standards (ELPS) relating to
listening and speaking
ELA Texas Essential Knowledge
and Skills (TEKS) relating to
listening and speaking
Linguistic Environment
1. Oral Language
Key Descriptors
Knows and teachers basic linguistic concepts, and the devel-
opmental stages in the acquisition of oral language, and rec-
ognizes that individual variations occur within and across
languages, in accordance with the Science of Teaching
Reading (STR).
Plans and implements systematic oral language instruction
based on student assessments.
Recognized when speech or language delays or differences
require evaluations, help, or interventions.
Designs a variety of one-on-one and group activities to build
on students' current oral language skills.
Selects and uses instructional materials and strategies that
promote students' oral language development in accordance
with the STR.
Understands relationships between oral language and literacy
development.
Uses instructional strategies, materials, activities and models
to strengthen students' oral vocabulary and narrative skills in
spoken language for a variety of contexts.
Teaches students how to evaluate the content and effective-
ness of their own spoken messages and the messages of
others.
Recognizes the interrelationships between oral language and
the other components of reading, in accordance with the
STR.
Uses appropriate technologies to develop students' oral com-
munication skills.
D E S C R I P T O R H I G H L I G H T S
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
NOTE: Refer to the lettered descriptors under each Competency in the
ETS/SBEC study material (in the back of this manual). Analyze each
descriptor, and synthesize it down to a paraphrase that is meaningful
to you, using no more than 5 words. List those phrases in order on the
lines above.It will help to letter the lines above. When complete, record
them again on Worksheet 4 in Appendix I.
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15
1. Oral Language
Competency 1:
The teacher understands the importance of oral language, knows the developmental
processes of oral language, and provides children with varied opportunities to develop
listening and speaking skills.
continued
A. LANGUAGE CONCEPTS
Phonology – Phonology (root word
phon” = sound) is the study of sounds.
Phonemes – The smallest part of spoken lan-
guage that makes a difference in the meaning
of words (Examples: Mop – Top, Cat Hat)
Phonological Awareness is the ability to hear
and manipulate sounds and sound chunks
(the overarching category). Phonemic
Awareness is the ability to hear and manipu-
late INDIVIDUAL sounds (a sub-category of
phonological awareness).
Phonological and Phonemic Awareness of
English phonemes are CRITICAL to reading
and language success.
Example: Student: I dont know this word.
Teacher: Sound it out…
Meaning Use what you know about sounds
and the letters that make the sounds to figure
out the new word.
If the student lacks the ability to hear the
sounds, the student will NOT be able to
decode the new word.
Some sounds are not present in all languages,
and some sounds are represented differently
in different languages. (For example, some
children may not be able to distinguish
between the sounds in “liceand rice”.)
Awareness of these differences and the strug-
gles they cause for learners will help teachers
plan instruction that builds students’ knowl-
edge of English phonemes.
Phonological Awareness involves several
categories and, in English, develops in a spe-
cific order, distinguishing and manipulating
sounds from chunks of sound to individual
sounds.
1. When children first learn to hear sounds,
they begin by hearing chunksof sounds.
2. This progresses as they learn to take apart
words into beginning sound (onset) and
word family(rime). (See additional
explanation below.)
3. Finally, children learn to hear individual
sounds (phonemes) and to play with these
sounds, or manipulate them.
IMPORTANT:
Teachers must understand the developmental
stages of phonological awareness (what they
are) as well as their progression (the order in
which they develop), so they can:
• Determine where a child is in their phono-
logical development
• Plan activities that help them build to the
next level
1. Working with Words and Word
“Chunks
Segmenting Words in Sentences -
breaking sentences into individual
words, usually using claps or stomps.
Example: “Clifford” (one clap) ate
(one clap) “pizza(one clap)
Segmenting Words into Syllables -
clapping and breaking words into
smaller parts that include a vowel.
Segmenting Compound Words -
breaking compound words into the
smaller words from which they are
built.
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1. Oral Language, contd.
2. Working with Onsets and Rimes
Distinguishing onsets and rimes - onsets
are the sounds in a syllable that come
before the vowel; rimes are the vowels and
everything else
Example:
Mop Onset /m/, Rime /op/
Flop – Onset /fl/, Rime /op/
Stick Onset /st/, Rime /ick/
Creating rhymes using onsets and rimes
NOTE – These activities must be relevant
and developmentally appropriate. Older stu-
dents will not engage with nursery rhymes;
instead creating poetry, word sorts, and raps
using rhyming words will encourage partici-
pation from students in grades 4-8.
3. Working with Individual Phonemes
Phonemic awareness - the ability to hear AND
manipulate the sound that is spoken
According to the National Reading Panel, there
are eight types of phonemic awareness activities.
Teachers should only introduce and practice two
or three activities at the same time. For each
activity, start with initial consonant sounds, then
work with ending consonant sounds, and finish
with medial vowel sounds. Allow students to
master beginning sounds before moving to end-
ing sounds, etc.
These activities should be a planned part of
your everyday instruction.
They do not take much time, and should be
practiced in the form of discussion, collabora-
tion, or games.
In the upper grades, phonemic activities fit
well into word study, vocabulary lessons, and
spelling.
Teachers should assess studentsphonemic
skills regularly, and plan instruction that
meets studentsindividual needs.
Assessment must be done 1:1 (because in a
group, it is difficult to determine each child’s
ability and needs).
The Eight Phonemic Awareness Activities
1. Isolation - Students hear individual sounds
in words.
Teacher: What’s the first sound you hear in
top”?
Students: The first sound is /t/.
Teacher: What is the last sound you hear?
Students: The last sound is /p/.
2. Identity - Students hear and identify the
same sound in different words.
Teacher: What sound is the same in teacher,
table, and tree?
Students: The beginning sound, /t/.
3. Categorization - Students identify which
word is different in a list of words, based on
sounds.
Teacher: Which word doesnt belong cat,
king or face?
Students: Face doesnt belong because it
doesnt start with /k/.
The two activities that help the kids the most are
BLENDING and SEGMENTING.
These should be practiced and reviewed regularly.
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17
1. Oral Language, contd.
4. BlendingStudents put sounds together to
make a word.
Teacher: What words is /k/ /a/ /t/?
Students: /k/ /a/ /t/ is cat!
5. SegmentationStudents break words into
their individual sounds and/or count the
number of sounds in a word. It is the oppo-
site of blending.
Teacher: How many sounds are in fan”?
Students: /f/ /a/ /n/, three sounds.
6. DeletionStudents remove a sound from a
word and identify what remains.
Teacher: What word is clap without /k/?
Students: Clap without /k/ is “lap”.
7. AdditionStudents create a new word by
adding a sound.
Teacher: What word do you have when you
add /s/ to the beginning of top”?
Students: Stop!
8. SubstitutionStudents change one sound
in a word to a different sound and identify
the new word.
Teacher: I’m thinking of a word that sounds
like man but starts with /r/. What’s my
word?
Students: Ran!
Semantics - Relating to the meaning of words,
groups of words, signs, symbols and phrases.
Semantics is critical to language acquisition.
Semantics studies how meaning is built, under-
stood, deciphered and explained, and includes
topics such as:
how word meanings change over time
how meaning is changed by the addition or
deletion of morphemes
how words may work together to form a
single idea (“drop off”, “turn into”) the
connotations, or variation of meanings
attached to similar words (tired, sleepy;
angry, furious)
similes and metaphors (sings like a bird,
sharp as a tack)
idioms (raining cats and dogs, hungry as a
horse)
Morphology Morphology (root word
morph= change) is the study of how the
meaning of a word is changed when a mor-
pheme (in English, root words, prefixes and suf-
fixes) is added.
Morpheme Morphemes are the smallest unit
of meaning in a language; a part that changes
the meaning.
Examples:
-ed happened in the past, such as talk
-> talked
-ing is happening now, such as fly
-> flying
re- again, such as visit -> revisit
pre- before, such as view -> preview
spect to look (root word)
Discourse - Discourse is a conversation or dia-
logue between two people. It can also relate to
the jargon and vocabulary of a specific group of
people such as doctors or teachers.
Pragmatics - Pragmatics is the way meaning is
implied by context and expressions. For exam-
ple, “Shes a real genius!” may mean “Shes
extremely smart”, or “Shes not very smart”,
Segmentation - breaking a word down
into phonemes (individual sounds)
1
2
3
continued
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1. Oral Language, contd.
depending on the conversation or writing
that surrounds the sentence.
B. TEKS FOR ORAL LANGUAGE
Texas Essential Knowledge and Skills
(TEKS)
Listening
Determine reasons for listening (such as
to get information or solve problems)
Listen critically to interpret and evaluate
Listen responsively to stories and texts
Identify musical elements of language
(such as rhymes and repeated sounds)
Listen and speak to share and experience
culture
Learn and use new vocabulary
Listen to enjoy spoken language
Speaking
Respond appropriately and courteously
Participate in rhymes, songs, conversa-
tions, and discussions
Distinguish and produce sounds in
English
Infer meaning using visuals and actions
Adapt spoken language to audience and
setting
Gain increasing control of grammar when
speaking
C. TYPES OF VOCABULARY AND
RELATIONSHIPS
There are four types of interrelated vocabular-
ies that we all use when we communicate.
They typically develop in the listed order,
and build upon each other.
Gaps or weaknesses in one area yield gaps
and weaknesses in other areas.
Listening vocabulary - the words we need to
know to understand what we hear
Speaking vocabulary - the words we use
when we speak
Reading vocabulary - the words we need to
know to understand what we read
Writing vocabulary - the words we use in
writing
Teaching ELA requires use and develop-
ment of all four areas. Encourage students
to BUILD and USE their vocabularies.
Students may need lesson adaptations
(such as bilingual books, reduced writing
assignments, etc.) to serve their individual
needs.
D. DEVELOPING ORAL LANGUAGE
PROFICIENCY
Language Acquisition – the process of
picking upor acquiring a new language
- Develops similarly for both first language
and second
- Language is built by a desire to commu-
nicate
- Differs from language that is taught
To develop oral language proficiency, learners
should have:
opportunities to acquire and use language
(let students talk, teach students to listen)
a desire to learn and use language
Types of Vocabulary
Gaps in any area affect those that build on it.
Writing vocabulary
Reading vocabulary
Speaking vocabulary
Listening vocabulary
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Key Words:
Onsets and Rimes
Phonemes
Isolation
Identity
Categorization
Blending
Segmenting
Addition
Deletion
Substitution
Key Descriptors
Understands phonological and phonemic awareness and typi-
cal patterns of development.
Understands differences in developmental pattern and
adjusts instruction meet students’ needs, particularly the
needs of English Language Learners (ELLs).
Plans instruction based on formal and informal assessment.
Uses learning games and materials to build phonological
awareness.
Builds teamwork to help each child grow, connecting with
families and other school professionals
Recognized the interrelationships between phonological and
phonemic awareness and the other components of reading in
acordance with the STR (Science of Teaching Reading).
D E S C R I P T O R H I G H L I G H T S
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
NOTE: Refer to the lettered descriptors under each Competency in the
ETS/SBEC study material (in the back of this manual). Analyze each
descriptor, and synthesize it down to a paraphrase that is meaningful
to you, using no more than 5 words. List those phrases in order on the
lines above.It will help to letter the lines above. When complete, record
them again on Worksheet 4 in Appendix I.
2. Phonological and Phonemic Awareness
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2. Phonological and Phonemic Awareness
Competency 2:
The teacher understands phonological and phonemic awareness and employs a variety
of approaches to help students develop phonological and phonemic awareness.
A. LANGUAGE CONCEPTS
PhonologyPhonology (root word phon
= sound) is the study of sounds.
Phonemes – The smallest part of spoken lan-
guage that makes a difference in the meaning
of words (Examples: Mop – Top, Cat Hat)
These two terms are often used interchange-
ably, but they are not the same thing.
Phonological Awareness is the ability to hear
and manipulate sounds and sound chunks
(the over arching category). Phonemic
Awareness is the ability to hear and manipu-
late individual sounds (a sub-category of pho-
nological awareness).
Phonological and Phonemic Awareness of
English phonemes are critical to reading and
language success.
Student: I don’t know this word.
Teacher: Sound it out…
Meaning Use what you know about sounds
and the letters that make the sounds to figure
out the new word.
If the student lacks the ability to hear the
sounds, the student will NOT be able to
decode the new word.
Since phonological awareness is necessary for
spelling, students who lack phonological
skills will also have challenges with spelling.
If a student has trouble spelling, the teacher
must revisit phonological awareness.
Teachers must examine spelling tests to deter-
mine not only whether the child knows the
specific tested words, but also to assess the
child’s phonological skills.
Some sounds are not present in all languages,
and some sounds are represented differently
in different languages. (For example, some
children may not be able to distinguish
between the sounds in “liceand rice”.)
Awareness of these differences and the strug-
gles they cause for learners will help teachers
plan instruction that builds studentsknowl-
edge of English phonemes.
Graphemes – Written letter(s) that represent
a spoken sound. For example, a student
writes the letter “B” when they hear the
sound /b/.
There is no writing in phonological or
Phonemic Awareness. Graphemes come next,
during phonics (where letters and sounds
connect). If a question asks about phonemic
or phonological awareness, the correct answer
will relate to sounds, not writing.
Phonics - Phonics is the understanding that
there is a predictable relationship between
phonemes (the sounds of spoken language)
and graphemes (the letters and spellings that
continued
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2. Phonological and Phonemic Awareness, cont'd.
represent those sounds in written language).
When letters and sounds come together, the
student is developing phonics skills.
B. DEVELOPMENTAL ORDER OF
PHONOLOGICAL AWARENESS
Phonological Awareness involves several cate-
gories and, in English, develops in a specific
order, distinguishing and manipulating
sounds from chunks of sound to individual
sounds.
IMPORTANT:
Test questions will require you to identify
where a child is on the chart above, and
either determine what they have already
mastered, or determine what they need to
work on next.
Teachers must understand the developmental
stages of phonological awareness (what they
are) as well as their progression (the order in
which they develop), so they can:
Determine where a child is in their pho-
nological development.
Plan activities that help them build to the
next level.
When children first learn to hear
sounds, they begin by hearing
chunks” of sounds.
This progresses as they learn to take
apart words into beginning sound
(onset) and “word family” (rime). (See
additional explanation below.)
Finally, children learn to hear individ-
ual sounds (phonemes) and to play
with these sounds, or manipulate
them.
IMPORTANT:
Teachers must understand the develop-
mental stages of phonological awareness
(what they are) as well as their progres-
sion (the order in which they develop), so
they can:
Determine where a child is in their
phonological development
Plan activities that help them build to
the next level
1.
Working with Words and Word
“Chunks
Segmenting Words in Sentences
breaking sentences into individual
words, usually using claps or stomps.
Example“Clifford” (one clap) ate
(one clap) “pizza(one clap)
Segmenting Words into Syllables –
clapping and breaking words into
smaller parts that include a vowel
Segmenting Compound Words –
breaking compound words into the
smaller words from which they are
built
2. Working with Onsets and Rimes
Distinguishing onsets and rimes
onsets are the sounds in a syllable that
come before the vowel; rimes are the
vowel and everything else
Phonological Awareness
1. Sound Chunks
Words in a
sentence
Syllables
2. Onsets and Rimes
Dividing words into
onsets and rimes
Creating rhymes using
onsets and rimes
3. Phonemes
Isolation
Identity
Blending and
Segmenting
Addition and Deletion
Substitution
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2. Phonological and Phonemic Awareness, cont'd.
Example: Mop Onset /m/, Rime /op/
Flop – Onset /fl/, Rime /op/
Stick – Onset /st/, Rime /ick/
If a teacher is playing a game with her children
in which they change beginning sounds in
words, she is working with onsets and rimes.
Example:The farmer in the dell…” becomes
“The farmer in the bell…” then “The farmer
in the pell..." (nonsense words are fine for this
purpose)
Also, if a teacher wants to create an onset and
rime activity, he should select words that have
many rhyming possibilities.
Example: “Stampwould be a better word
choice than six”.
Creating rhymes using onsets and rimes
NOTE – These activities must be relevant and
developmentally appropriate. Older students
will not engage with nursery rhymes; instead
creating poetry, word sorts, and raps using
rhyming words will encourage participation
from students in grades 4-8.
3. Working with Individual Phonemes
Phonemic awareness - the ability to hear
and manipulate the sound that is spoken
According to the National Reading Panel,
there are eight types of phonemic awareness
activities. Teachers should only introduce and
practice two or three activities at the same
time. For each activity, start with initial conso-
nant sounds, then work with ending conso-
nant sounds, and finish with medial vowel
sounds. Allow students to master beginning
sounds before moving to ending sounds, etc.
These activities should be a planned part
of your everyday instruction.
They do not take much time, and should
be practiced in the form of discussion, col-
laboration, or games.
In the upper grades, phonemic activities fit
well into word study, vocabulary lessons,
and spelling.
Teachers should assess studentsphonemic
skills regularly, and plan instruction that
meets studentsindividual needs.
Assessment must be done 1:1 (because in a
group, it is difficult to determine each
child’s ability and needs)
IMPORTANT NOTE: To be successful on
this test, you must know the order in which
each activity develops and what each activity
looks like. You will have to identify where a
child is from a set of evidence, test results, or
observations, and decide what they already
know or what they need to work on. Many
questions focus on these skills.
The Eight Phonemic Awareness Activities
Isolation - Students hear individual
sounds in words.
Teacher: What’s the first sound you hear in
top”?
Students: The first sound is /t/.
Teacher: What is the last sound you hear?
Students: The last sound is /p/.
Identity - Students hear and identify the
same sound in different words.
Teacher: What sound is the same in teach-
er, table, and tree?
Students: The beginning sound, /t/.
Categorization - Students identify which
word is different in a list of words, based
on sounds.
continued
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8. Vocabulary Development
Competency 8:
The teacher knows the importance of vocabulary development and applies that
knowledge to teach reading, listening, speaking and writing.
VOCABULARY DEFINED
Vocabulary, words we must know orally and read
in print to communicate effectively, plays an
important role in learning to read:
As beginning readers, children use the
words they have heard to make sense of the
words they see in print.
Beginning readers have a much more diffi-
cult time reading words that are not already
part of their oral vocabulary.
Readers cannot understand what they are
reading without knowing what most of the
words mean.
Readers must know what most of the
words mean before they can understand
what they reading.
Readers use their oral vocabulary to make
sense of the words they see in print.
As children learn to read more advanced
texts, they must lean the meaning of new
words that are not part of their oral vocab-
ulary.
A. EXPLICIT, SYSTEMATIC INSTRUCTION
Vocabulary is learned systematically (explicit)
and must be taught simple-to-complex, or in
stages so that knowledge builds upon and
relates to prior knowledge. There are four
interrelated types of vocabulary that develop
and build upon each other:
1.
Listening vocabulary—words we need to
know in order to understand what we hear
2. Speaking vocabulary—words we use
when we speak
3. Reading vocabulary—words we need to
know to understand what we read
4. Writing vocabulary—words we use when
writing
A well-written blueprint for teaching vocabu-
lary includes studentsoral and reading vocabu-
laries. First, for new learners, it introduces let-
ters of the alphabet in random order:
4-6 frequently used consonants (M, S, L,
N, R)
2 short vowels (in this order: a, o, u)
Then, the remaining consonants and vowels
As students grow, their vocabulary abilities
should match levels on the Phonological
Awareness chart. Studentsskills develop in
predictable orders and are needed to increase
their vocabularies. These skills should be
assessed by mid-point in kindergarten and in a
1:1 setting. Any gaps between areas affect stu-
dentslearning during skill levels.
continued
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8. Vocabulary Development, cont'd.
Finally, use differentiated, explicit activities to
target and build studentsvocabularies so that
they may learn to communicate effectively:
Language and sound games (Bingo,
Charades, Jeopardy, Memory)
Informal interactions
Onsets
Rhymes and rhyming books
Plays
Skits
Sponge (short) activities
Use vocabulary across-curriculum so students
hear and use new words. Most importantly,
involve community and family members in
helping students practice vocabulary skills!
B. DIRECT AND INDIRECT METHODS
OF TEACHING
Direct Indirect
Explicitly, systematically taught Daily engagement in oral language
Teacher led Student led
Individual words learned; word analysis/ decod-
ing/phonics
Listen to adults read to them
Word Study: Phonics, word structure, mean-
ing, usage, tenses, mophology
Read extensively on their own
Examples: bubble/graphic/semantic maps, con-
notation/denotation, demonstrations, illustra-
tions, word sorts, word walls, Thesaurus, dic-
tionary, glossary, Internet
Examples: discussions, dramatic play,
language play, show and tell, storytelling,
puppet show, pair interview, presentations,
projects, reading forms of literary works
Graphic Organizers
Never have students write words or word parts
repetitiously, or over and over, or require them to
memorize a list of words or wordsparts. Vocabulary,
or word learning, should be fun!
C. USE A WIDE RANGE OF INSTRUCTIONAL
MATERIALS
Present vocabulary development through various instruction-
al materials, and provide strong contextual support for vocab-
ulary development. Students should read varieties of instruc-
tional materials in search of vocabulary words:
Content specific texts
Expository texts
Literature
Magazines
Newspapers
Trade books
Technology
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Subject Test II (802):
Mathematics
Competencies 1-6 (14-19)*
18% of the test
*NOTE: The numbering of these Competencies is based upon how we
number them for the comprehensive Core Subjects EC-6 test prep program,
and also how the SBEC numbers them for the separate Subject Tests. They are
noted as such due to the design of our worksheets in the Appendices.
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2 (15). Number Concepts and Operations
Key Words:
Odd and Even Numbers
Prime Numbers
Composite Numbers
Rational Numbers
Algorithm
Whole Numbers
Natural Numbers
Place Value
Real Numbers
Irrational Numbers
Fractional Numbers
Understands relationships between number proper-
ties, operations, and algorithms for the four basic
operations.
Understands equivalency among representations of
rational numbers.
Selects appropriate representations of real numbers.
Understands number theory.
Understands a variety of models for representing
numbers.
Demonstrates connections between operations and
algorithms.
Uses counting techniques to quantify situations.
Understands place value.
Understands the relative magnitude of whole num-
bers, integers, rational numbers, and real numbers.
D E S C R I P T O R H I G H L I G H T S
Key Descriptors:
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
NOTE: Refer to the lettered descriptors under each
Competency in the ETS/SBEC study material (in the
back of this manual). Analyze each descriptor, and
synthesize it down to a paraphrase that is meaningful
to you, using no more than 5 words. List those phrases
in order on the lines above.It will help to letter the
lines above. When complete, record them again on
Worksheet 4 in Appendix I.
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2 (15). Number Concepts and Operations
A. MATHEMATICAL RELATIONSHIPS
Odd numbers cannot be divided by 2
without having a remainder of 1. A
remainder of 0 is not possible when
dividing an odd number by 2
(Examples: 9, 21, 35).
Even numbers can be divided by 2 with
no remainder (Examples: 2, 4, 16).
Prime numbers have exactly two num-
bers that divide them evenly, 1 and the
actual number itself. 1 is not considered
prime. (Examples: 3, 7, 11). NOTE: To
divide a number evenly means there is a
quotient with a remainder of 0.
Composite numbers have more than
exactly two numbers that divide them
evenly. (Examples: 4, 15, 49)
Number Operations means adding,
subtracting, multiplying, or dividing.
Integers are the set of whole numbers
and their opposites. The number line can
be used to represent the set of integers.
Rational can be expressed in the form:
a/b where “aand “bare integers and
“bdoes not equal 0. They can be
expressed as fractions, decimals (repeat-
ing and terminating), and sometimes,
integers. (Examples: 24, since 48/2; 5.2,
since 26/5; 0.777..., since 7/9)
(Non-examples include: π , 5 These
cannot be written as a/b, where “aand
“bare integers.)
CAUTION: π is sometimes approximated
by the rational numbers 22/7 and 3.14.
These numbers are simply approximations
and are NOT equivalent to π.
An algorithm is a step-by-step proce-
dure used to get a certain result, often
with several steps that repeat. Adding
two numbers together is one kind of
algorithm.
1. Number Concepts
Whole Numbers are the counting num-
bers and 0 (0,1,2,3,4,5, and so on).
Place Value - The location of a digit
within a number determines its value.
The following number shows 8 in the
Ones place 8
Tens place 80
Hundreds place 800
Thousands place 8000
Ten Thousands place 80,000
Hundred Thousands place 800,000
Millions Place 8,000,000
Expanded Form is the sum of a num-
ber’s place values: 1,729 = 1000 + 700 +
20 + 9.
Rounding means estimating the closest
number to a given whole number, with
all zeros to the right of the desired place
value. Examples:
17 rounded to the nearest ten is 20
212 rounded to the nearest hundred is 200
7895 rounded to the nearest thousand is 8000
2. Number Properties
Commutative Property - Changing the
order of numbers being added or multi-
plied gives the same answer (12 + 7 gives
the same answer as 7 + 12, and 3 x 9
gives the same answer as 9 x 3).
Associative Property - The grouping of
the numbers in addition or multiplica-
tion does not change the answer, such as
(2 x 4) x 3 = 2 x (4 x 3).
Distributive Property - Multiplication
and division may be distributed over
addition or subtraction. 10 x (50 + 3) =
(10 x 50) + (10 x 3) and (30-18) / 3 =
30/3 - 18/3.
Competency 2 (15):
The teacher understands concepts related to numbers, operations and algorithms,
and the properties of numbers.
continued
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2 (15). Number Concepts and Operations, contd.
Zero Property of Addition - Adding 0
to a number equals the original number
(43 + 0 = 43 and 0 + 43 = 0).
Zero Property of Multiplication -
Multiplying a number by 0 equals 0
(43 x 0 = 0 and 0 x 43 = 0).
B. DEMONSTRATING EQUIVALENCY
Using concrete models means having
objects, pictures, or diagrams to show
how numbers are added, subtracted,
multiplied, or divided can help young
learners to visualize equivalency between
numerical representations. A teacher
who creates a hands-on activity where
his students put 16 buttons into groups
of 4 to show a division problem is using
a concrete model. Tables and graphs are
other ways to visually show relationships
between math operations such as addi-
tion and subtraction or between number
representations such as decimals to per-
cents.
COMPLEX NUMBERS
REAL NUMBERS
RATIONAL NUMBERS
Values that can be written as ratio of 2 integers
Ex: 5 = 25 = .333... =
INTEGERS
Positive and negative whole numbers
Ex: +5 -13 +23 -1258
WHOLE NUMBERS
Iincludes zero and the set
of natural numbers
IRRATIONAL
NUMBERS
Values that can not be
expressed as a
ratio of 2 integers
Ex: 5 π -2
IMAGINARY
NUMBERS
Square root of a
negative number
Ex: – 4 = 2i
NATURAL
NUMBERS
The counting numbers
Ex: 1, 2, 3, 4 ...
5
8
5
1
1
4
1
3
COMPLEX NUMBERS
Must be written in the form of a + bi , where a and “b are real
numbers. a = real # part , b = imaginary # part
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2 (15). Number Concepts and Operations, contd.
C. CLASSIFICATIONS OF REAL NUMBERS
Set of real numbers denoted by
R contains all
forms and structures of numbers used in math-
ematics. Real numbers can be classified in terms
of accuracy, form, and value. A real number
may be either rational or irrational; positive,
negative or zero.
1. Classifications of Real Numbers in Terms
of Accuracy
Rational Numbers
A rational number is a real number that can be
expressed as a ratio of integers a/b, where a and
b are integers and b 0. Decimals are either
terminating or repeating for rational numbers.
Example. Which of the numbers is rational?
Answers:
a. 2.40 represents a fixed number of digits;
therefore, this number is rational.
b.
= 0.142857142857. This number
contains a repeating decimal part of
0.142857, therefore it is a rational number.
c. π = 3.14159265... The decimal does not
begin to repeat from some point, so it is not a
rational number.
Irrational Numbers
Irrational numbers are not expressible as ratios
of integers. Irrational numbers are always non-
terminating and non-repeating.
Irrational numbers denoted by I contain num-
bers of the forms 5
, 1.23476..., 2, e, π, etc.
Examples: Classify each expression as rational
or irrational. In order to proceed, convert each
expression to decimal form.
Answers:
a. 25 = 5.0. 5.0 has a fixed repeating part
of 0, thus 25
is a rational number.
b.
= 0.75983568565. In this decimal
expansion, there is not a part of the decimal
that repeats; and it is non-terminating;
thus, it is an irrational number.
a. 2.40 b.
1
c. π
7
5
1
2 ,
-10
4 ,
1.333..., 4.234 etc.
1
7
a.
b.
c.
d.
e.
c. 2.451451451
e. 5.347658953...
continued
4
5
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2 (15). Number Concepts and Operations, contd.
c. 2.451451451 contains a repeating part
of 451; therefore it is a rational number. It
can be written as the mixed fraction
or the improper fraction , illustrating it is
indeed a rational number.
d. = 0.80. This value has a repeating part of
0, therefore, it is a rational number.
e. 5.347658953 has no repeating decimal part
therefore, it is an irrational number.
2. Classification of Real Numbers in Terms of
their Forms
Each real number can be expressed in either a
decimal or fractional form.
Decimal Numbers - Decimal numbers
contain a decimal point that separates the
place value of ones from tenths. They can
also contain commas that underline other
place values.
Examples:
a. 2,300.34 b. 0.4553 c. 444,456.09
A decimal point is often used to indicate the
number of significant figures. For example, 20g
can be expressed as 20.00g. The magnitudes of
both values are the same; they differ by the
number of significant figures: the first has one;
the second has four.
Fractional numbers
Fractional numbers do not contain decimal
points. They have a division bar either horizon-
tal
or slashed a/b. The number a is the
numerator, and the number b is the denomina-
tor. A fraction is expressed as
.
A fractional form is not defined if the denomi-
nator is zero.
Converting a Decimal Number to a
Fraction and a Fraction to a Decimal
Number
To convert a decimal to a fraction identify the
place value of each digit.
a. 3.2 b. 2.004 c. 0.027
Answers:
Examples: Convert to decimal form and
classify them as rational or irrational.
Answers: Using the algorithm for division we
get:
a. 3.5 Rational (5 is terminating and 0
repeats)
b. .230 Rational (0 repeats)
c. -7.447368421052632 Rational (terminating)
2
451
999
2449
999
4
5
a
b
Numerator
Denominator
1
5, 3/4 , ,
1
5
-
8
2
a. 3.2 - 3+2 x
1
- 3
2
- 3
1
10 10 5
b. 2.0004 - 2 + 4 x
1
-2
4
-2
1
1000
1000 250
c. 0.027 = 2 x
1
+ 7 x
1
=
27
100 1000 1000
a. 3
1
b.
23
c. -7
34
2
100
76
Fractional
to Decimal
Conversion
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2 (15). Number Concepts and Operations, contd.
Classification of Fractions
Fractions can be classified as proper, improper, and a mixed number.
is called a proper fraction if a < b.
Examples:
Note: when converted to a decimal form, a proper fraction has zero as its place value for ones.
Examples:
is called an improper fraction if a > b
Examples:
Note: Any whole number can be converted into an improper fraction.
Example:
c
is called a mixed number because it contains a whole number and a proper fraction.
Examples:
3. Classification of Real Numbers in Terms of Their Values
All real numbers can be placed on a number line and classified in terms of their values as: natural, whole,
integers, rational, and irrational.
a
b
1 , 5
4 11
1
- 0.25,
5
= 0.45
4 11
a
b
6 , 7
4 2
2 =
2
1
a
b
2
2
,
-5
1
3 7
continued
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2 (15). Number Concepts and Operations, contd.
Natural Numbers
Natural numbers, or counting numbers, are denoted by N where N = {1, 2, 3, 4, ..}. The minimum value
for a natural number is 1 and they increase in value by 1.
The set of natural numbers is infinite. Natural numbers are sometimes called positive or non-negative
integers.
Whole Numbers
Adding zero to the set of natural numbers produces a set of whole numbers denoted by W where
W = {0,1,2,3,4...}. The set of whole numbers is infinite.
0 1 2 3 4
Integers
Whole numbers with their opposites generate a set of integers denoted by Z where
Z = {...-4,-3,-2,
-1,0,1,2,3,4...}. The set of integers is infinite and does not have maximum nor minimum values.
-4 -3 -2 -1 0 1 2 3 4
Rational Numbers
Rational numbers, defined earlier in this section, contain numbers that can be converted into decimal
forms that terminate or contain fixed repeated parts. Rational numbers are denoted by
Q. Some examples
of rational numbers in set Q include : -10 , -1 , -1/2 , 0 , 3.4 , 10. Rational numbers can be placed on a
number line and can be positive or negative.
-4 -3.5 -3 -2 -1 0 1/2 1 2 3 3.76 4
1 2 3 4
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2 (15). Number Concepts and Operations, contd.
Irrational Numbers
If rational numbers are removed from the set of real numbers, irrational numbers will remain;
I = R - Q. Irrational numbers were discussed earlier in this section.
4. Applications of Real Numbers: Decimals, Fractions, Percents, Roots, Power, Scientific Notation
a. Quantities Expressed in Decimal or Fractional Forms
Quantity can be expressed as a fraction or a decimal. A quantity properly described contains a magnitude
and the unit.
Examples:
Mass of 1/20 kilogram = 1/20 kg
Speed of 60 miles per hour = 60 mi/h
Time interval of 3.5 hours = 3.5 h
b. Percent and its Applications
Percent, or part out of 100, represents a ratio of part of a quantity with reference to the whole value.
Example: A class contains 25 students. If 20 students are present, express that in terms of percent.
Answer: Construct a ratio: =
then multiply the ratio by 100: 100 = 80, thus 80% of students are present.
-log40 0 2 e 8
Part
Whole Quantity
20
25
20
25
Number Line Activities
continued
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Subject Test III (803):
Social Studies
Competencies 1-5 (20-24)*
16% of the test
*NOTE: The numbering of these Competencies is based upon how we
number them for the comprehensive Core Subjects EC-6 test prep program,
and also how the SBEC numbers them for the separate Subject Tests. They are
noted as such due to the design of our worksheets in the Appendices.
187
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2 (21). History
I. HISTORY
Texas teachers must be familiar with “histor-
ical points of reference,” which are briefly
outlined below. Familiarize yourself with
these points, paying careful attention to how
each shaped our state and our government.
A. NATIVE AMERICANS
Texas teachers should be able to compare
and contrast various Native American tribes
throughout Texas and the Western
Hemisphere. Below is a list of the prime
attributes of each group.
a. Natives of the Western Hemisphere
The major Native American groups of
the Western Hemisphere were the Incas,
the Mayas, and the Aztecs. The Incan
empire stretched from Ecuador to north-
ern Chile. The Aztecs dominated north-
ern Mexico, while the Mayans flourished
in the rain forests of Guatemala. Their
influence continues today; their positive
achievements included the following:
advanced agricultural methods
tribute systems
advanced communication systems
skilled artisans
highly specialized and stratified
societies
imperial administration
schools
b. Natives of the United States
When the Europeans came to America,
about 10 million Native Americans lived
in all parts of the United States. All lived
off the land and were
hunters
gatherers, or
farmers.
They were resourceful in making tools
and had advanced skills in
horsemanship
farming
buffalo hunting, and
the building of homes.
Many historians count the cooperative
governing systems many nations had in
place to be among their greatest contri-
butions to modern society. In many
parts of America, Native American tribes
met on a regular basis to share news,
methods, and culture, as well as to make
cooperative governmental decisions.
None had a system of writing nor did
they have many scientific advances.
c. Texas Natives
Scientists believe that the earliest Texans
arrived about 11,000 years ago, follow-
ing herds of mammoth and mastodon.
The earliest groups lived in the Gulf
Coastal Plains (Caddo, Coahuiltecans,
Karankawas) and were hunters, fishers,
and farmers. The Plains nations
(Tonkawa, Lipan Apache, Comanche,
Kiowa) were mostly nomadic, skilled
buffalo hunters. The most sedentary
tribes (Pueblo, Jumano, Concho, Tigua)
occupied the Mountains and Basins
region. Contributions from these groups
included:
Caddo - built the first buildings in
Texas - beehive shaped huts made
Competency 2 (21):
The teacher understands and applies knowledge of significant historical events and
developments, multiple historical interpretations and ideas, and relationships
between the past, the present, and the future as defined by the Texas Essential
Knowledge and Skills (TEKS).
continued
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from wooden frames covered with
grass or reeds; also known for
advanced farming methods
Karankawas - created dugout canoes,
small ships carved from the trunks
of trees to facilitate their nomadic
lifestyle (dependent on fishing)
Coahuiltecans - nomadic hunters
and trappers, enslaved Cabeza de
Vaca and other Spanish explorers
Lipan Apaches and Comanche - buf-
falo hunters who tamed wild mus-
tangs, becoming skilled horsemen
Pueblo - built elaborate homes and
cities using adobe (sun-dried mud)
bricks
B. EUROPEAN EXPLORATION AND
COLONIZATION
During the 15th and 16th centuries, Europe
engaged in a strong push for exploration.
England, Spain and France sent explorers to
establish colonies in the Americas.
The French claimed lands in Canada,
around the Great Lakes, and all along
the Mississippi River.
Spain claimed territory that is now
Texas, New Mexico, Arizona, California,
Mexico, and Central and South
America.
England established colonies in the
Caribbean, and thirteen colonies along
the east coast of America.
Colonization had some clearly positive
effects, creating communities and trade
routes that facilitated cultural exchange.
However, these were forged at the expense of
the indigenous peoples of the area; their
populations were ravaged by displacement,
disease, warfare with the Europeans, and
enslavement.
1. Reasons for European Exploration
To locate a new passage to the Far East
(for trade).
To map uncharted areas.
To find treasure (gold, silver, gems, arti-
facts).
To claim new lands and set up colonies.
To convert people to Christianity.
2. Significant Explorers
Columbus (1492, 1493, 1498)
Led expeditions to South
America for Spain.
Landed in South America.
Opened cultural exchange
between the east and the
west (Columbian
exchange).
De Pineda (1519)
Led first expedition into Texas.
Explored Gulf Coasts for Spain (Florida,
Alabama, Louisiana, Texas, and Mexico).
De Vaca (1527 -1535)
Part of a Spanish mission to claim land
along the Gulf, he became stranded in
Florida when his ships did not return
from a supply run to Cuba.
Built rafts and skirted the coast, eventu-
ally wrecking near East Island,
Louisiana; continued on foot with a
slave called Esteban, eventually coming
to Texas.
Encountered Caddo Indians near
Houston; impressed with their sophisti-
cation and tales of wealth inland, he
mapped and wrote about the area in
detail, creating our first written record of
America.
His tales of Cibola, a fabled city of gold,
greatly influenced subsequent explorers
including Coronado and De Soto.
2 (21). History, contd.
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2 (21). History, contd.
Coronado (1540-1542)
Sent by Spain to find
fabled city of gold,
reported by De Vaca.
Traveled much of the
Texas Panhandle.
First Europeans to see
Palo Duro Canyon.
Went home empty handed.
La Salle (1682-1685) A French explorer
Led expedition in 1682 from a French
colony in Canada down the Mississippi
River to the Gulf of Mexico, claiming
land for France on both sides of the river.
In 1684, led another expedition from
France to start a colony at the mouth of
the Mississippi River, sailed past the river
and mistakenly landed in Texas.
Built the first French colony in Texas,
Fort St. Louis, near Galveston.
3. The Thirteen English Colonies
In 1607, the first permanent English col-
ony was established in Jamestown,
Virginia. In less than six months, more
than half of the settlers had died from
disease, starvation, and attacks from
Native Americans.
In 1620, Pilgrims (religious dissidents) set
up a strict, parochial colony of Puritans in
Massachusetts, Plymouth colony.
Roger Williams set up a colony in Rhode
Island that advocated religious freedom
for all, including Native Americans.
William Penn established a colony for
Quakers in Pennsylvania. The Quakers
opposed violence, slavery, and war, and
advocated religious tolerance for all people.
4. Important People
William Bradford - Second governor of
Plymouth colony. In 1621 he ordered the
first Thanksgiving, sharing harvest with
the Wampanoag Indians
Roger Williams - Banished from
Plymouth colony, advocated religious
freedom, established Rhode Island colony.
John Smith - Established trade relations
with the Powhatan Indians; bargained for
food for the starving Plymouth settlers.
Pocahontas - Daughter of the Chief of
the Powhatan Indians; convinced her
father to spare John Smith and help the
settlers.
John Rolfe - Member of Jamestown,
began tobacco industry in America;
married Pocahontas and brought her to
England ensuring peace with the
Powhatan Indians.
Squanto - A Pawtuxet Indian who taught
the Plymouth Pilgrims how to hunt, fish,
and grow crops, thereby saving the lives
of many.
5. The Mayflower Compact
An agreement written on the Mayflower,
a ship which carried the Pilgrims to
America.
This agreement established the governing
laws of the new colonies.
6. Missions, Presidios, and Early Towns
After La Salle built a French colony in Texas,
Spain became worried about protecting their
claims in Texas. They brought Franciscan
monks to build missions - religious settle-
ments in Texas. By 1740, there were more
than 20 missions in Texas. Later they added
forts called Presidios to protect the missions
(and Spains territorial claims). Missions were
built to:
Solidify Spains territorial claims (primary
purpose).
Open and protect trade routes.
Spread the Christian faith to the Native
Americans.
Provide a safe center for working and
learning.
continued
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C. THE FRENCH AND INDIAN WAR
(1754-1763)
This conflict, between British
and French colonies, instigat-
ed issues between the colo-
nists and England, which
eventually led to the
American Revolution.
During the war, most Native
American tribes sided with the French, fear-
ing the British would take their ancestral
homelands. The British won.
Causes of the War
Britain and France were at war, causing
conflict between their colonies in
America.
The British colonies wanted land owned
by the French colonists - for fur trading.
Results of the War
France lost the majority of its territory
and power in North America.
England’s land expanded to include all
of the French lands east of the
Mississippi River, except New Orleans,
which became Spanish territory.
Spains holdings expanded to include all
of the French territory west of the
Mississippi River, and New Orleans.
England tightened its hold on the colo-
nies, restricting freedom and levying
large taxes to help offset the costs of the
war.
D. THE AMERICAN REVOLUTION
(1776-1785)
By 1775, tensions were high between
England and their American colonists.
England had passed laws that prevented
colonists from being elected to Parliament;
at the same time, Parliament passed many
laws that levied taxes on the colonists. Angry
colonists called this taxation without
representation,” which became an instigation
and a battle-cry for the revolt. For nine
years, colonists fought the British
with the aid of France. In 1781,
British general Cornwallis surren-
dered to Washington after the
Battle of Yorktown. The war offi-
cially ended with the Treaty of
Paris in 1783.
Causes of the Revolution
Progressively direct, internal taxes were
levied against the colonists in order to
provide support to mother England. In
order to keep peace with the Native
Americans, Parliament passed The
Proclamation of 1763, a bill that said
colonists could not settle west of the
Appalachian Mountains. Settlers felt this
was a local decision and the government
should not interfere.
In 1765, the Stamp Act was passed,
which levied taxes against the colonists on
almost everything printed on paper - legal
documents, almanacs, diplomas, and
playing cards. This law united the colo-
nists against British rule, and resulted in
many bloody demonstrations and riots.
Parliament passed the Townshend Acts
in 1767, which taxed glass, lead, paper,
paint, and tea. The colonists refused to
buy these items, so the tax was finally
repealed on everything except tea.
In 1768, 4,000 British soldiers were
moved into Boston and the colonists
were required to provide room and
board to the soldiers. On March 5,
1770, several townsmen got into an
argument and threw snowballs at a
group of soldiers. The soldiers opened
fire on the unarmed crowd, killing five
colonists. This became a highly publi-
cized story known as the Boston
Massacre; it fueled the fires for colonial
independence.
2 (21). History, contd.
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229
Subject Test IV (804):
Science
Competencies 1-18 (25-42)*
19% of the test
*NOTE: The numbering of these Competencies is based upon how we
number them for the comprehensive Core Subjects EC-6 test prep program,
and also how the SBEC numbers them for the separate Subject Tests. They are
noted as such due to the design of our worksheets in the Appendices.
230
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1 (25). Safe and Proper Laboratory Processes
Key Words:
Lab Safety
Proper Disposal
Precision
Accuracy
Error
Bias
Metric System
Inquiry-based Instruction
Safety should be the primary concern of the science
teacher, with special attention to injuries, especially to
eyes, and cuts from glass
Understand and be familiar with all substances/mate-
rials in the lab, field, or work area
Understand the proper handling of organisms and
specimens
Teacher should be familiar with and know how to
properly use all science tools and measurement stan-
dards
Teacher should be aware of and communicate to stu-
dents the importance of communication of results,
theories, and hypotheses in science study
Teacher should understand and communicate the
international system of measurement.
D E S C R I P T O R H I G H L I G H T S
Key Descriptors:
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
____________________________
NOTE: Refer to the lettered descriptors under each
Competency in the ETS/SBEC study material (in the
back of this manual). Analyze each descriptor, and
synthesize it down to a paraphrase that is meaningful
to you, using no more than 5 words. List those phrases
in order on the lines above. It will help to letter the
lines above. When complete, record them again on
Worksheet 4 in Appendix I.
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SCIENTISTS AND INVENTORS
Alexander Graham Bell - Invented the telephone.
Rachel Carson - Founder of environmental science.
George Washington Carver - Botanist who was called the "farmers
best friend."
Francis Crick and James Watson - Discovered the structure of the
DNA molecule.
Marie Curie - Physicist who discovered radioactivity.
Leonardo da Vinci - Inventor and artist from the Renaissance.
Thomas Edison - Invented the light bulb, phonograph, and the motion picture.
Albert Einstein - Developed the Theory of Relativity and the equation E=mc
2
.
Henry Ford - Invented the Model T Ford, the first mass produced car.
Ben Franklin - Inventor and Founding Father of the United States.
Galileo - First used the telescope to view the planets and stars.
Jane Goodall - Studied chimpanzees in the wild for many years.
Johannes Gutenberg - Invented the printing press.
Stephen Hawking - Discovered Hawking Radiation and wrote A Brief History in Time.
Antoine Lavoisier - Father of modern chemistry.
Isaac Newton - Discovered the theory of gravity and the three laws of motion.
Louis Pasteur - Discovered pasteurization, vaccines, and founded the science of germ theory.
The Wright Brothers - Invented the first airplane.
TYPES OF SCIENTISTS
While we often talk about a person being a "scientist", there are actually many different types of scientists.
This is because most scientists study and become experts in a specific field of science.
Astronomer - Studies the planets, stars, and galaxies.
Botanist - Studies plant life.
Chemist - Studies chemistry and the behavior, properties, and composition of matter.
Cytologist - Studies cells.
Ecologist - Studies the relationship between living organisms and the environment.
Entomologist - Studies insects.
Geneticist - Studies genes, DNA, and the hereditary characteristics of living organisms.
Geologist - Studies the properties of matter that makes up Earth as well as the forces that shaped it.
Marine biologist - Studies the living organisms that live in the ocean and other bodies of water.
Microbiologist - Studies microscopic life forms such as bacteria and protists.
Meteorologist - Studies the Earth's atmosphere including the weather.
Nuclear physicist - Studies the interactions and make up of the atom.
Ornithologist - Studies birds.
Paleontologist - Studies prehistoric life and fossils including dinosaurs.
Pathologist - Studies diseases caused by pathogens such as bacteria and viruses.
Seismologist - Studies earthquakes and the movements of the Earth's crust.
Zoologist - Studies animals.
2 (26). History and Nature of Science, cont'd.
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and tools should be used to collect, record,
and process data. Science fair projects are a
good example of the process of scientific
investigation in action.
- Students would begin with a question:
Will different colors of crayons lose mass
if heat is applied? Students would form a
hypothesis, explaining whether or not
they believe the crayons would lose mass,
or have less wax, if they were heated.
- To find out, they would need materials
(crayons of different colors) and several
tools: a digital camera, a scale to measure
the mass of the crayons, a hot plate, a
non-stick pan, and a plastic utensil for
scraping the pan. As the crayons were
being melted, students could use the
camera to document the melting and
weighing of each crayon both before and
after heating.
- To better be able to share their data, the
teacher might guide them in using a
computer to create a bar graph showing
the mass of each colored crayon before
and after melting.
- Finally, after gathering their data, the
students would draw a conclusion about
what happened and why, comparing
their data to their hypotheses and
answering the original question. To
complete the project, students could
type up each part of the investigation
and attach it to a display board along
with the pictures, data collection, and
graph, and share their results with their
fellow student scientists.
C. Motion
Scientists use the term motion to refer to a
continuous change in the position of a
body relative to a reference point, as mea-
sured by a particular observer in a particular
frame of reference. There are many ways of
measuring, graphing, and describing chang-
es in motion; most of these ways involve
analyzing the
displacement, acceleration,
and
velocity of an object.
Displacement. A vector quantity that
describes the position of a particle in
reference to an origin, or that particles
change in position. An object can cover
a large distance, but if it ends up in the
same place where it started, its displace-
ment is 0.
Velocity. The speed of an object in a
particular direction. Since speed (a scalar
quantity) and direction are both important
in determining velocity, it is a vector
quantity. Graphs 1 and 2 below have
constant velocity because the slope of
7 (31). Forces and Motion, contd.
A
H
B
x
x(t)
t
x
t
x(t)
x
x(t)
t
Graph 1 Graph 2
Graph 3
263
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7 (31). Forces and Motion, contd.
Data about the physical
properties of objects can
be compiled by putting
them into a graphic form
such as a table to help
explore how they are
related to one another.
Given the table, students
can then discuss and
record how objects com-
pare to one another with
respect to various physi-
cal properties. Early ele-
mentary students can
complete the table as a
whole-class activity, while
students in second grade
and up can likely com-
plete the grid indepen-
dently. To the right is an
example that could be
used in a fourth grade
classroom.
continued
the line is unchanging, while Graph 3
illustrates a particle with changing velocity.
Acceleration. This is a vector quantity
defined as the rate of change of velocity.
It is measured in meters/second
2
. Graph 2
above shows a particle with 0 acceleration,
because there is no change in velocity,
while graphs 1 and 3 both show particles
which are accelerating.
D. FORCE AND MOTION
Sir Isaac Newton was most prob-
ably the first to give a mathemat-
ical definition of force; more
importantly, Newton came up
with three laws which defined
motion in relation to forces act-
ing upon objects and the reaction of objects to
those forces.
Newtons First Law of Motion. This law
states that an object at rest will remain at
rest, while an object in motion at con-
stant velocity will remain in motion at
constant
velocity, unless there is a net force
acting on it. This law is also called The
Law of Inertia.
Newtons Second Law of Motion. When
the net force acting on an object is not
zero, then the object will move in the
direction of the force; in this case, the
acceleration is directly proportional to
the net force and inversely proportional to
the mass of the object. From this relation-
ship, we can derive a very important
equation:
F = net force (measured in N)
m = mass of the object (measured in kilograms)
a = acceleration m/s
2
Newtons Third Law of Motion. When
one object exerts a force on another object,
the second object will exert a force on the
first object that is equal in magnitude but
opposite in direction. From this law, we
get the famous phrase, "For every action,
there is an equal and opposite reaction."
This is an example of action-reaction forces.
a = F
m
or F = ma
Object Size Shape Temperature Hardness Mass Conduction
Ice cube 2 cm Rectangular
prism
32° F Hard 5g No
Cotton ball 3 cm Sphere 70° F Soft 1g No
Metal spoon 12 cm Bowl on one
end with
handle
90° F (in
cocoa)
Very hard 45g Yes
Hot Cocoa
(prepared)
50cm
3
Liquid
(shape of
container)
100° F Liquid 150g No
Crayon 6 cm Cylindrical
with point
70°F Soft (easily
scratched)
7g No
285
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11 (35). Structure and Function of Living Things, cont'd.
Muscular system. Muscles are responsible for
your body’s every move; they are also responsi-
ble for the physical actions of your internal
organs such as the pounding of your lungs and
the movement of food through your digestive
system. Muscles can also generate heat to keep
you warm.
Nervous system. This
system is responsible
for sending messages
throughout your body.
It is divided into the
central nervous system
(CNS) and the periph-
eral nervous system
(PNS). The first is
made up of the brain
and spinal cord and has
the job of receiving
information from the
body and sending out
instructions; the latter
is made up of all the
nerves and has the job
of transmitting the
messages to and from
the CNS.
Digestive system. This
system has the job of breaking down food into
chemicals that the body can use for fuel.
Respiratory system. This is the system that is
responsible for taking oxygen into the body and
releasing carbon dioxide out of the body. Our
cells need oxygen in order to perform cellular
respiration.
Circulatory system. This system is made of the
heart and all the vessels that transport blood
around the body. Circulation is necessary to
transport oxygen and nutrients to all the cells
of the body.
Urinary system. This system controls the
amount of water and salts that are found in the
body and what is taken out as waste; it also acts
as a filtering mechanism for the blood.
Endocrine system. This system regulates, coor-
dinates, and controls a number of bodily func-
tions by the release of
chemicals called hor-
mones.
Integumentary system.
This is composed of
skin, hair, nails, oil and
sweat glands. This sys-
tem not only covers the
body, but it acts as a
protective wrapping, it
insulates against wear
and tear, it keeps germs
and excess water out, it
keeps the body’s fluids
and salts in, and it acts
as a temperature regula-
tor.
Immune system. This
system defends against
millions of bacteria,
microbes, viruses, tox-
ins, and parasites that
come into contact with the body on a regular
basis.
Reproductive. This system is responsible for
ensuring the survival of the species by produc-
tion of offspring.
Respiratory System
319
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1 (43). Visual Arts
Competency 1 (43):
The teacher understands the concepts, processes, and skills involved in the
creation, appreciation, and evaluation of art and uses that knowledge to plan
and implement effective and engaging visual arts instruction.
A. THE VALUE OF ART
All children need a variety of experiences to
assist them in exploring their environment.
Through art, children learn to value their
own uniqueness and to appreciate the indi-
viduality of others. Art allows us to commu-
nicate powerful ideas creatively, on many lev-
els. Art promotes
Personal Development - creative expres-
sion, self-discovery, self-esteem and self-
concept
Social Development - children learn to
cooperate during group art projects
Physical Development - small muscles,
eye-hand coordination, dexterity, and a
sense of rhythm are developed as chil-
dren engage in art activities
Language Development - vocabulary is
increased as the children talk about their
art projects; drawing contributes to the
development of writing
Cognitive Development - art contributes
to thinking skills in many areas, includ-
ing classification, symbolic representa-
tion, and spatial relationships
B. FOSTERING CREATIVITY
Students should be allowed to explore and
create with as few limits as pos-
sible! Genuine creative thinking
consists of flights of fancy tem-
pered by practical limitations,
and is a requirement for success
in modern society. In a world
that is becoming increasingly
technological, creativity is tan-
tamount to success. Students
will develop their creative skills
in an environment that fosters mental flexi-
bility. Respect for the individual and his
ideas are more than a democratic principle;
it is a cardinal code of conduct for the teach-
er who expects genuine, sustained interest
from students. Simply put, students should
be allowed to explore and create with as few
limits as possible. Students should be
allowed choice of topic, choice of design,
and choice of tools as much as possible. Use
of patterns and examples limits creativity.
C. DEVELOPING PERCEPTION AND
VISUAL LITERACY
Visual literacy refers to the way we use our
senses and perceive the world. It is the ability
to identify the visual and tactile qualities of
the environment. The development of visual
literacy is fundamental to learning. Visual
literacy allows students to:
interpret symbols and understand symbol-
ism
communicate ideas more effectively
comprehend artworks
visually analyze their environment
Students with weak visual perception strug-
gle in many areas. Visual Arts education pro-
vides unique opportuni-
ties for students to build
visual perception skills.
Students can build visu-
al perception skills by:
drawing and creating
images from observa
tion
cooperative discussion
prior to activities that
continued
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Core Subjects - EC-6
stimulates studentsprior knowledge
creating artworks and images from their
imagination
* creating artworks that demonstrate the
student’s thoughts and beliefs - works that
include symbolism and contain a message
multi-sensory experiences - activities in
which artworks are based on things they
see, feel, taste, smell, or hear.
D. CRITICAL THINKING AND THE
VISUAL ARTS
Few venues offer finer opportunities for criti-
cal thinking and problem solving. In the
study of art, students must constantly seek
innovative ways to express their thoughts and
ideas. They must consider
the world around them
from many perspectives.
They must focus on min-
ute detail, while still con-
sidering the overall com-
position. To capitalize on
these opportunities,
teachers should include
elements of critical think-
ing in every art lesson
with methods such as:
cooperative discussion prior to activities
that examines projects and issues from
many angles
allowing students to make informed
choices about how they will create their
artworks, including choices about tools
and techniques they will use
lead student discussions on the merits and
shortfalls of various tools and techniques
as related to the work at hand
question students regarding their choices
and the choices of other (professional and
peer) artists and artworks; use higher
order questioning from Blooms
Taxonomy (What if? Is it effective? How
can it be improved? Predict...)
teach students to apply Blooms
Taxonomy to their own works and to cre-
ate effective questions for themselves—to
evaluate their own works
include self-reflection activities as a rou-
tine part of every lesson by having stu-
dents explain or justify their choices and
the messages of their works, creating an
artist’s statement, and by displaying the
works
teach students to respectfully evaluate
their own works, the works of their peers,
and the works of professional artists.
E. THE ELEMENTS OF ART
The elements of art are apparent in all living
systems. They have practical applications in
mathematics, assist readers with comprehen-
sion and inference, and provide a myriad of
opportunities for written expression.
1. Line
Lines are the most basic element of art. They
take on many forms including horizontal,
straight, diagonal, vertical, zigzag, curved and
wavy. Lines create the underlying concepts
and boundaries for works of art.
2. Texture
Texture brings clarity and depth to art.
Textures may be soft, smooth, rough, bumpy
or silky.
3. Shape
Basic shapes create the form for objects in art.
Shapes include circles, triangles, organic
shapes, geometric shapes, rectangles, symbols
and letters, ovals, squares and diamonds.
4. Form
Art moves from basic shapes to three dimen-
sional forms with the addition of geometric
figures. These add depth and perspective to
art. Form includes geometric shapes, cones,
1 (43). Visual Arts, cont'd.
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Core Subjects - EC-6
1 (43). Visual Arts, cont'd.
spheres, pyramids and trian-
gular prisms, rectangular
prisms, cubes, cylinders, and
organic forms (forms found
in nature).
5. Color
Color is used in three ways:
to describe things, as a sym-
bol, and to convey feelings
or set the mood. Primary
colors blend to create sec-
ondary colors, which in turn
blend to create intermediate
colors. Complimentary col-
ors—those that oppose each
other on the color wheel—
affect each other, causing the
colors to be more vibrant.
When complementary colors
are together, they create con-
trast. Analogous colors—col-
ors that are positioned next
to each other on the color
wheel—create a sense of har-
mony. Colors can be com-
plementary, cool, warm, pri-
mary, secondary, or interme-
diate.
6. Value
Value is created through the
blending of colors, and is
used to enhance art and cre-
ate specific effects. Colors
mixed with white are lighter, and create high-
lights in art, giving depth and dimension.
Colors mixed with black are darker, and cre-
ate shadows and contrasts. Shadows and high-
lights are used to create focal points, or cen-
ters of attention. Values include shadows, tints
(colors mixed with white), shades (colors
mixed with black), and light to dark effects.
7. Space
Space is a critical element of art, as it allows
the artist to create works with perspective.
Perspective allows art viewers to see depictions
from different angles. It is created with over-
lapping shapes, proportion (the size of one
object in comparison to another object), and
shadows. By drawing items in the foreground
of the artwork larger than those in the back-
ground, the artist gives their work depth.
Space elements include background, middle
continued
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Core Subjects - EC-6
ground, foreground, proportion, positive and
negative spaces, point of view, eye level view,
worms eye view and bird’s eye view.
F. THE PRINCIPLES OF ART
1. Unity
Unity is creating a bond between all the parts
of a work, giving the work a balanced sense of
wholeness. Unity is created using repeated
lines, textures, colors, shapes and forms.
2. Variety
Variety allows artists to give their work con-
trast, to create depth, and to engender emo-
tion. Variety is formed by the use of different
lines, textures, colors, shapes and forms.
3. Emphasis
Emphasis is the process whereby an artist
makes one element of a piece of art capture the
viewer’s attention. Artists create emphasis by
adjusting the size of the objects in their works,
and with shading and highlighting techniques.
4. Pattern
Patterns create movement and rhythm. To cre-
ate harmony in artworks, patterns should
match each other and not clash. Artists create
unity through patterns of repeated lines and
shapes. Patterns of curved lines and compli-
mentary colors can create a sense of move-
ment. Pattern is used to show proportion and
to create balance—symmetrical, asymmetrical,
and physical.
5. Harmony
Harmony is created when elements of a work
blend and flow together into a cohesive state-
ment. Harmony is created by the use of analo-
gous colors (colors that are beside each other
on the color wheel), tints (colors mixed with
white) and shades (colors mixed with black).
6. Conflict
Conflict is created when complementary colors
meet and create a contrast. Conflict is also cre-
ated using arbitrary colors, colors that do not
normally occur in nature (e.g., a green dog).
G. A VARIETY OF MEDIA
Elementary students should be exposed to and
use a variety of media, including
Crayon, pencil, colored pencil, pen
Paint - acrylic paint, oil paint, tempera,
Water color
Pastel, oil pastel
Collage and paper crafts
Clay and fresco
Print-making (lithography)
Fabric crafts including yarn and beads
Teachers should be familiar with these tools
and the methods for clean-up and storage of
them.
H. A VARIETY OF ART TECHNIQUES
Elementary students should be exposed to and
use a variety of art methods, including
Drawing
Painting
Printmaking
Construction (assembling artworks from
found objects, cutting and pasting, collage,
etc.)
1 (43). Visual Arts, cont'd.
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Core Subjects EC-6 - Addendum/Seminar Packet
Competency Definitions
1. Oral Language
2. Phonological and Phonemic
Awareness
3. Alphabetic Principle
4. Literacy Development
5. Word Analysis and
Identification Skills
6. Fluency Reading
7. Reading Comprehension and
Applications
8. Vocabulary Development
9. Reading, Inquiry, Research
10. Writing Conventions
11. Written Communication
12. Viewing and Representing
13. Assessment of Developing
Literacy
1(14). Mathematics Instruction
2(15). Number Concepts and
Operations
Competency 1
The teacher understands the importance of oral language, knows the developmental
processes of oral language, and provides children with varied opportunities to develop
listening and speaking skills.
Competency 2
The teacher understands phonological and phonemic awareness and employs a variety of
approaches to help students develop phonological and phonemic awareness.
Competency 3
The teacher understands the importance of the alphabetic principle for reading English and
provides instruction that helps students understand the relationship between spoken
language and printed words.
Competency 4
The teacher understands that literacy develops over time, progressing from emergent to
proficient stages, and uses a variety of approaches to support the development of students’
literacy.
Competency 5
The teacher understands the importance of word identification skills (including decoding,
blending, structural analysis, sight word vocabulary, and contextual analysis) and provides
many opportunities for students to practice and improve word identification skills.
Competency 6
The teacher understands the importance of fluency for reading comprehension and
provides many opportunities for students to improve their reading fluency.
Competency 7
The teacher understands the importance of reading for understanding, knows the compo-
nents and processes of reading comprehension, and teaches students strategies for
improving their comprehension, including using a variety of texts and contexts.
Competency 8
The teacher knows the importance of vocabulary development and applies that knowledge
to teach reading, listening, speaking and writing.
Competency 9
The teacher understands the importance of research and inquiry skills to students’
academic success and provides students with instruction that promotes their acquisition
and effective use of those study skills in the content areas.
Competency 10
The teacher understands the conventions of writing in English and provides instruction that
helps students develop proficiency in applying writing conventions.
Competency 11
The teacher understands that writing to communicate is a developmental process and
provides instruction that promotes students’ competence in written communication.
Competency 12
The teacher understands skills for interpreting, analyzing, evaluating, and producing visual
images and messages in various media and provides students with opportunities to
develop skills in this area.
Competency 13
The teacher understands the basic principles of literacy assessment and uses a variety of
assessments to guide literacy instruction.
Competency 1(14)
The teacher understands how students learn mathematical skills and uses that knowledge
to plan, organize, and implement instruction and assess learning.
Competency 2(15)
The teacher understands concepts related to numbers, operations and algorithms, and the
properties of numbers.
S ub jec t Te s t I ( 8 01): EL AR a nd t he S ci ec ne o f Te achi ng Rea din g
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S ub Te s t II (8 02 )
389
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Core Subjects EC-6 - Addendum/Seminar Packet
Competency Definitions
3(16). Patterns and Algebra
4(17). Geometry and
Measurement
5(18). Probability and Statistics
6(19). Mathematical Processes
1(20). Social Science Instruction
2(21). History
3(22). Geography and Culture
4(23). Economics
5(24). Government and Citizenship
1(25). Safe and Proper Laboratory
Processes
2(26). History and Nature of
Science
3(27). Impact of Science on Daily
Life
4(28). Concepts and Processes
in Science
5(29). Students as Learners and
Science Instruction
6(30). Science Assessments
7(31). Forces and Motion
8(32). Physical and Chemical
Properties of Matter
Competency 3(16)
The teacher understands concepts related to patterns, relations, functions, and algebraic
reasoning.
Competency 4(17)
The teacher understands concepts and principles of geometry and measurement.
Competency 5(18)
The teacher understands concepts related to probability and statistics and their
applications.
Competency 6(19)
The teacher understands mathematical processes and knows how to reason
mathematically, solve mathematical problems, and make mathematical connections within
and outside of mathematics.
Competency 1(20)
The teacher understands and applies social science knowledge and skills to plan, organize,
and implement instruction and assess learning.
Competency 2(21)
The teacher understands and applies knowledge of significant historical events and devel-
opments, multiple historical interpretations and ideas, and relationships between the past,
the present, and the future as defined by the Texas Essential Knowledge and Skills (TEKS).
Competency 3(22)
The teacher understands and applies knowledge of geographic relationships involving
people, places, and environments in Texas, the United States, and the world; and also
understands and applies knowledge of cultural development, adaptation, diversity, and
interactions among science, technology, and society as defined by the Texas Essential
Knowledge and Skills (TEKS).
Competency 4(23)
The teacher understands and applies knowledge of economic systems and how people
organize economic systems to produce, distribute, and consume goods and services.
Competency 5(24)
The teacher understands and applies knowledge of concepts of government, democracy,
and citizenship, including ways that individuals and groups achieve their goals through
political systems.
Competency 1(25)
The teacher understands how to manage learning activities, tools, materials, equipment,
and technologies to ensure the safety of all students.
Competency 2(26)
The teacher understands the history and nature of science, the process and role of scien-
tific inquiry, and the role of inquiry in science instruction.
Competency 3(27)
The teacher understands how science impacts the daily lives of students and
interacts with and influences personal and societal decisions.
Competency 4(28)
The teacher knows and understands the unifying concepts and processes that are common
to all sciences.
Competency 5(29)
The teacher has theoretical and practical knowledge about teaching science and about how
students learn science.
Competency 6(30)
The teacher knows the varied and appropriate assessments and assessment practices for
monitoring science learning in laboratory, field, and classroom settings.
Competency 7(31)
The teacher understands forces and motion and their relationships.
Competency 8(32)
The teacher understands the physical and chemical properties of and changes in matter.
S ub j ec t Te st II (8 02 ):
M at h em a t ic s
Copy this chart and carry it with you for easy study. See the study module; it breaks down these definitions into phrasing for better understanding.
S ub jec t Te s t II I (803) :
S oc ia l S tu di e s
S ub jec t Te s t IV ( 804 ):
S ci en ce