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Core Subjects - EC-6

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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Core Subjects - EC-6

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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Core Subjects - EC-6

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 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.

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 “lice” and “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 “chunks” of 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, cont’d.

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 students’ phonemic

skills regularly, and plan instruction that

meets students’ individual 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 doesn’t belong – cat,

king or face?

Students: Face doesn’t belong because it

doesn’t 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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1. Oral Language, cont’d.

4. Blending – Students put sounds together to

make a word.

Teacher: What words is /k/ /a/ /t/?

Students: /k/ /a/ /t/ is cat!

5. Segmentation – Students 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. Deletion – Students remove a sound from a

word and identify what remains.

Teacher: What word is clap without /k/?

Students: Clap without /k/ is “lap”.

7. Addition – Students 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. Substitution – Students 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, “She’s a real genius!” may mean “She’s

extremely smart”, or “She’s not very smart”,

Segmentation - breaking a word down

into phonemes (individual sounds)

continued

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Core Subjects - EC-6

1. Oral Language, cont’d.

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 up” or 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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Core Subjects - EC-6

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

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)

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 “lice” and “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.

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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Core Subjects - EC-6

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

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: “Stamp” would 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 students’ phonemic

skills regularly, and plan instruction that

meets students’ individual 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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Core Subjects - EC-6

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:

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 students’ oral 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. Students’ skills 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-

dents’ learning during skill levels.

continued

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Core Subjects - EC-6

8. Vocabulary Development, cont'd.

Finally, use differentiated, explicit activities to

target and build students’ vocabularies 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 words’ parts. 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

115

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Core Subjects - EC-6

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.

124

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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.

125

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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 “a” and “b” are integers and

“b” does 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 “a” and

“b” are 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, cont’d.

• 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 ...

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, cont’d.

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.

= 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.

= 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.

c. π

2 ,

-10

4 ,

1.333..., 4.234 etc.

c. 2.451451451

e. 5.347658953...

continued

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2 (15). Number Concepts and Operations, cont’d.

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)

451

999

2449

999

Numerator

Denominator

5, 3/4 , ,

a. 3.2 - 3+2 x

- 3

10 10 5

b. 2.0004 - 2 + 4 x

-2

1000

1000 250

c. 0.027 = 2 x

+ 7 x

100 1000 1000

a. 3

c. -7

100

Fractional

to Decimal

Conversion

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2 (15). Number Concepts and Operations, cont’d.

• 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.

1 , 5

4 11

- 0.25,

= 0.45

4 11

6 , 7

4 2

2 =

-5

3 7

continued

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2 (15). Number Concepts and Operations, cont’d.

• 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, cont’d.

• 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

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.

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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, cont’d.

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2 (21). History, cont’d.

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 Spain’s territorial claims). Missions were

built to:

• Solidify Spain’s 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.

• Spain’s 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, cont’d.

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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

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 particle’s

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, cont’d.

x(t)

Graph 1 Graph 2

Graph 3

263

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Core Subjects - EC-6

7 (31). Forces and Motion, cont’d.

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

. 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.

• Newton’s 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.

• Newton’s 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

• Newton’s 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

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

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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Core Subjects - EC-6

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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Core Subjects - EC-6

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

320

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Core Subjects - EC-6

stimulates students’ prior 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 Bloom’s

Taxonomy (What if? Is it effective? How

can it be improved? Predict...)

• teach students to apply Bloom’s

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.

321

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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

322

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Core Subjects - EC-6

ground, foreground, proportion, positive and

negative spaces, point of view, eye level view,

worm’s 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

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 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

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