What is an ordered pair?

A pair of numbers that shows the position of a point on a graph

A pair of numbers that represents an equation

Orded pair | Quizalize

Orderd pair and cartesian product

4.5.1 Order Pair Recognition

Volume of prism,orderd pairs and measure of center

Explain that factor pairs can be written in any order

Can you create an evaluation using this information PHONETICS VS. PHONOLOGY Whereas phonetics is the study of sounds that occur in language, phonology is the study of how these sounds are organized and how they function in language. It uses the classifications of sounds derived from phonetics to describe and analyze how sounds occur in speech. STRUCTURALIST PHONEMICS STRUCTURALIST PHONEMICS As linguists began to study sounds in fine detail, they recognized increasingly complex aspects of phonetic organization. For example, the sound /p/ appears in different varieties in English. STRUCTURALIST PHONEMICS One of the varieties of /p/ is indicated by [ph]. This sound is produced with an accompanying puff of air called aspiration, as in the words “pill,” and “peace.” Another sound, indicated by [p•], is produced when there is little or no aspiration; this sound occurs in a word like “spill.” A third major variety for the /p/ sound is the unreleased [p– ], which may occur at the end of a word like “stop.” To deal with these variations for the /p/ sound, the structuralists suggested the existence of an abstract unit which they termed a phoneme. STRUCTURALIST PHONEMICS A phoneme was defined by the structuralists as an abstract phonological unit that represents a class of real sounds, termed the allophones of a phoneme. The phoneme /p/ in English, then, is represented by the allophones [ph], [p•], and [p– ]. STRUCTURALISTS: MINIMAL PAIRS How do we know what these abstract units of sound called phonemes are? In order to find the phonemes of a language, the structuralists developed the concept of the minimal pair, defined as any two words that: a) Contain the same number of segments b) Differ in meaning c) Exhibit only one phonetic difference. STRUCTURALISTS: MINIMAL PAIRS In practical terms, phonemes distinguish meanings; and a phoneme can also be defined as the smallest meaning-distinguishing unit of sound. For instance, the words “pin” /pɪn/ and “bin” /bɪn/ mean different things, and the only one difference in these words occurs in the initial sounds. STRUCTURALISTS: MINIMAL PAIRS By using the concept of a minimal pair, we can determine that the three variations of the /p/ sound do not represent three phonemes. Certainly, it is possible to pronounce the word cap with either an aspirated [ph ] or unreleased [p– ]; however, the two forms [kæph ] and [kæp– ] are not a minimal pair, even though they involve different sounds, because they are identical in meaning. STRUCTURALISTS: FREE VARIATION The two forms [kæph ] and [kæp– ] are, therefore, said to exhibit free variation: that is, the pronunciation may vary without signifying a change in meaning. In other words, we may conclude that the unreleased [p– ] and the aspirated [ph ] are not representations of different phonemes in English; they are, in fact, allophones of one phoneme, /p/. STRUCTURALISTS: COMPLEMENTARY DISTRIBUTION When phonemes have more than one allophone in a language, the allophones are said to be in complementary distribution. Complementary distribution means that the allophones of a phoneme occur in different phonetic environments (that is, with different sounds surrounding them). TRANSFORMATIONAL- GENERATIVE PHONOLOGY TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonology is a relatively recent development in linguistic theory. Chomsky launched Transformational-Generative Grammar in 1957, but the earliest studies within this framework were largely concerned with syntax. A decade later, the first comprehensive transformational-generative treatment of English phonology appeared: Chomsky and Halle’s The Sound Pattern of English (1968). TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonologists strongly oppose the structuralists’ phonemic level. They replace this level by a series of rules that directly relate underlying representations to observed phonetic representations. The central mechanisms in transformational-generative phonology, then, are underlying representations and phonological rules. PHONOLOGICAL RULES A rule is an operational statement in which some linguistic entity is modified, resulting in a new linguistic entity. Rules may add elements, remove elements, or change elements. By using phonological rules, linguists attempt to demonstrate that there is order in linguistic phenomena and that linguistic patterns are systematic. PHONOLOGICAL DERIVATION A phonological derivation is an operation that begins with an underlying representation and, through the application of a set of specific rules, yields the actual sound the speaker produces. The representation of a phonological rule has the following general appearance. /A/ → [B] / C “A” changes to “B” under condition “C” PHONOLOGICAL RULE – EXAMPLE In most Southern dialects, the word ten is pronounced like the word tin. This is not an isolated fact, for den is pronounced like din and Ben is pronounced like bin, and so on. This very general fact can be represented by the phonological rule: /ɛ/ → [I] / ___ [n] den /dɛn/ → /dIn/ Ben /bɛn/ → /bIn/ ten /tɛn/ → /tIn/ /ɛ/ → [I] / ___ [n] - high - low - tense + front + high - tense + front + sonorant + anterior + coronal - continuant NOTATIONAL DEVICES IN PHONOLOGICAL RULES The statement of phonological rules can be complex, and linguists have developed several notational devices for writing them. Often, the following symbols will be necessary for stating the conditions under which rules apply: # indicates a word boundary + indicates an intraword boundary $ indicates a syllable boundary UNDERLYING REPRESENTATIONS AND RELATED ISSUES The transformational-generative description of phonology relates underlying representations to phonetic representations by rules. This can be represented in a simple example: In English, there are certain pairs of words like sign / signature, and malign / malignant that exhibit a regular alternation in their phonetic representations: [g] is present in the second member of the pairs but absent in the first member. UNDERLYING REPRESENTATIONS AND RELATED ISSUES To explain the relatedness of words such as sign / signature, we could claim that the underlying representation of the segment in all such pairs is /g/ and that a rule operates to delete /g/ before syllable-final nasals. Thus, the rule “/g/ is deleted before syllable-final nasal” would appear formally as: + voice - anterior →∅ ____ [+ nasal] $ - coronal UNDERLYING REPRESENTATIONS AND RELATED ISSUES On the left-hand side of the arrow, we place the features needed to uniquely specify /g/ among the consonants; that is, no other consonant has the features [+ voice], [- anterior], and [- coronal]. The symbols → mean that the sound /g/ changes to nothing or more properly “/g/ is deleted.” The horizontal line following the slash mark refers to the position of /g/ - namely, before a segment that is [+nasal]. Finally, this [+nasal] segment occurs before a syllable boundary, as indicated by $. A less formal way of writing this rule would be: /g/ → / _ [+nasal] $ Notice that this rule also helps describe such alternations as phlegm/phlegmatic and paradigm/paradigmatic. Application Activity: Think of other words in which this rule can be applied. Write the sound segments to prove /g/ is deleted. Another example is the process through which the prefix meaning “not” is added to words. This prefix alternates among the forms /Im/, /In/, and /Iŋ/, depending on the point of articulation of the initial segment of the following word. -If the segment begins in the extreme front part of the mouth (labials), the form is /Im/, as in improper. -If the segment begins in the extreme back part of the mouth (velars), the form is /Iŋ/, as in incomplete. -If the segment begins in the mid-region of the mouth (all other sounds), the form is /In/, as in indecent. *Exceptions:Words beginning with /r/ or /l/. Analyze the Word “in + complete,” for example. /n/ → [ŋ] / __ [k] - continuant - continuant - continuant + sonorant → + sonorant - sonorant + anterior - anterior - strident + coronal - coronal - coronal + tense THE VELAR SOFTENING RULE Still another example of alternation in English is found in pairs of words like “electric / electricity,” in which the segments /k/ and /s/ alternate. /k/ changes to [s] only before non- low, front vowels. THE VELAR SOFTENING RULE /k/ → [s] / __ - continuant + continuant - strident → - sonorant V - anterior + anterior - low - coronal + coronal - back

CONCEPT OF INTEGERS What are INTEGERS? Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative (-), positive (+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the value of the integer. POSITIVE INTEGERS Are numbers to the right of zero. Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3. NEGATIVE INTEGERS Are numbers to the left of zero. Are valued less than zero. Express ideas of down or a loss. The sign for a negative integer is (-). This sign is always needed. Opposite Numbers/Integers – are the pairs of integers that have the same absolute value or have the same distance away from zero. ABSOLUTE VALUE The distance of a number from the origin (0) regardless of direction is called absolute value. The absolute value of a number is never negative. The symbol for absolute value is two straight lines surrounding the number or expression for which you wish to indicate absolute value. Examples: I 4 I = 4, +4 is read “ the absolute value of 4 is 4 “ I -3 I = 3, -3 is read “ the absolute value of -3 is 3” - I 3 I = -3, means “ the negative of the absolute value of 3 is -3 “ COMPARING AND ARRANGING INTEGERS Integers can be compared using a number line. As you move to the left along the number line, the integers decrease in value. On the other hand, integers increase in value as you move to the right along the number line. To arrange integers in ascending order is to arrange them from least to greatest. This means that when you use the number line, the smallest the integer is to the left of 0 on the number line. To arrange integers in descending order is to arrange them from greatest to least. This means that when you use the number line, the largest the integer is to the right of 0 on the number line. This is read as “nine is greater than negative 12.” This is read as “negative thirteen is less than negative 5.” This is read as “negative eight is greater than negative 18.”

What are INTEGERS? Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative (-), positive (+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the value of the integer. POSITIVE INTEGERS Are numbers to the right of zero. Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3. NEGATIVE INTEGERS Are numbers to the left of zero. Are valued less than zero. Express ideas of down or a loss. The sign for a negative integer is (-). This sign is always needed. Opposite Numbers/Integers – are the pairs of integers that have the same absolute value or have the same distance away from zero. ABSOLUTE VALUE The distance of a number from the origin (0) regardless of direction is called absolute value. The absolute value of a number is never negative. The symbol for absolute value is two straight lines surrounding the number or expression for which you wish to indicate absolute value. Examples: I 4 I = 4, +4 is read “ the absolute value of 4 is 4 “ I -3 I = 3, -3 is read “ the absolute value of -3 is 3” - I 3 I = -3, means “ the negative of the absolute value of 3 is -3 “ COMPARING AND ARRANGING INTEGERS Integers can be compared using a number line. As you move to the left along the number line, the integers decrease in value. On the other hand, integers increase in value as you move to the right along the number line. To arrange integers in ascending order is to arrange them from least to greatest. This means that when you use the number line, the smallest the integer is to the left of 0 on the number line. To arrange integers in descending order is to arrange them from greatest to least. This means that when you use the number line, the largest the integer is to the right of 0 on the number line. This is read as “nine is greater than negative 12.” This is read as “negative thirteen is less than negative 5.” This is read as “negative eight is greater than negative 18.” R

SB2. Obtain, evaluate, and communicate information to analyze how genetic information is expressed in cells. a. Construct an explanation of how the structures of DNA and RNA lead to the expression of information within the cell via the processes of replication, transcription, and translation. Learning Targets _______Identify the structural components of DNA and RNA Success Criteria _______Can accurately identify the key structural components of DNA (deoxyribose sugar, phosphate group, nitrogenous bases: adenine, thymine, cytosine, guanine). _______Can identify the key structural components of RNA (ribose sugar, phosphate group, nitrogenous bases: adenine, uracil, cytosine, guanine). _______Can describe the differences in the sugar backbone of DNA and RNA (deoxyribose vs. ribose). _______Can identify the double-stranded structure of DNA and the single-stranded structure of RNA. _______Identify the parts of protein synthesis and the location of each process Success Criteria _______Can identify and describe the two main processes of protein synthesis: transcription and translation. _______Can correctly explain that transcription occurs in the nucleus where DNA is transcribed into mRNA. _______Can explain that translation occurs in the cytoplasm at ribosomes where mRNA is translated into amino acid sequences to form proteins. _______Compare and Contrast DNA to RNA Success Criteria _______Can clearly identify similarities between DNA and RNA, such as both being nucleic acids and containing nucleotide structures. _______Can explain differences in DNA and RNA, including sugar types (deoxyribose vs. ribose), strand number (double-stranded DNA vs. single-stranded RNA), and nitrogenous base usage (thymine in DNA vs. uracil in RNA). _______Can describe the function of DNA as genetic storage and the function of RNA in protein synthesis (mRNA, tRNA, rRNA). _______Analyze the reasoning for enzymes usage in both DNA replication and protein synthesis. Success Criteria _______Can identify key enzymes involved in DNA replication (e.g., helicase, DNA polymerase, ligase) and explain their functions (e.g., helicase-unwinding DNA, DNA polymerase-synthesizing new DNA strands, ligase-sealing nicks in the DNA backbone). _______Can identify enzymes involved in protein synthesis (e.g., RNA polymerase) and explain their role in transcribing DNA into mRNA. _______Can analyze why enzymes are essential for speeding up chemical reactions…(ensuring accuracy, and catalyzing steps in replication and protein synthesis) _______Can provide specific examples of how enzyme malfunction can impact genetic replication or protein synthesis. _______Perform the steps of DNA replication and protein synthesis in order to demonstrate their understanding of how the structure of DNA supports the genetic expression in successive generations. Success Criteria _______Can demonstrate a step-by-step understanding of DNA replication, including unwinding, complementary base pairing, and proofreading. _______Can demonstrate the steps of transcription (formation of mRNA from DNA) and translation (conversion of mRNA into a polypeptide). _______Can show how DNA's structure (double helix, base pairing) ensures accurate replication for passing genetic information to offspring. _______Can illustrate how changes in DNA sequence can lead to changes in protein structure and function, thus affecting traits in successive generations.

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