English Syllabus for all Levels
Grade K
- Students say aloud ‘gathering words, rhyming words, and rhyming phrases’.
- Lessons are focused on contructing words by learning the sounds of letters that make up words, transitioning from gathering to constructing words.
- Students begin to acquire skills that will allow them to sound out unfamiliar words and, eventually lessen dependence on picture cues.
- Trace letters and words
- Students learn 800 vocabulary words (cumulative)
- Students are introduced to nouns, verbs, and adjectives
- Introduce word types that make up basic elements of simple sentences.
- Prepare students to graduate from the word gathering and constructing exercises to word connecting and arranging.
- Students are introduced to fundamental tools to build sentences
- Students say aloud sentences in multisyllabic words.
- Consonant Combinations
- Changing letter sounds
- Word combinations become more advanced as students work with vowels, the “soft” c and g sounds
Grade 1
- Demonstrate command of the conventions of standard English
grammar and usage when writing or
speaking.
- Print all upper- and lowercase letters.
- Use common, proper, and possessive nouns and in own writing.
- Identify common and proper nouns
- Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop ).
- Use personal, possessive, and indefinite pronouns (e.g., I , me , my ; they , them , their ; anyone , everything) everything ).
- Use verbs to convey a sense of past, present, and future (e.g.,
Yesterday I walked home ; Today I
walk home ; Tomorrow I will walk home ).
- Use regular present-, past-, and/or future-tense verbs correctly orally and in own writing
- Use frequently occurring adjectives.
- Use adjectives orally and in own writing.
- Use frequently occurring conjunctions (e.g., and , but , or , so ,because ).
- Punctuation
- Capitalize dates and names of people.
- Use end punctuation for sentences.
- Identify and use end punctuation, including periods, question marks, and exclamation points in writing
- Use commas in dates and to separate single words in a series
- Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.
- Spell and write one-syllable words using the letter-sound correspondences taught in Grade 1.
- Spell and write high-frequency tricky words.
- Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions.
- Write phonemically plausible spellings for words that cannot be spelled correctly with current code knowledge, e.g., write bote for boat , sum for some , hunee for honey , etc.
- Reading Standards: Ask and answer questions about key details in a text.
- Ask and answer questions (e.g., who , what , where , when ), orally or in writing, requiring literal recall and understanding of the details, and/or facts of a fiction read-aloud s s s
- Answer questions that require making interpretations, judgments, or giving opinions about what is heard in a fiction read-aloud, including answering why questions that require recognizing cause/effect relationships
- Ask and answer questions (e.g., who , what , where , when ), orally or in writing, requiring literal recall and understanding of the details, and/or facts of a fiction text read independently s s s s s s
- Retell stories, including key details, and demonstrate understanding of their central message or lesson.
- Retell fiction read-alouds including key details, and demonstrate understanding of the central message or lesson. Recount fiction read-alouds, including fables and folktales from diverse cultures, identifying the
- Describe characters, settings, and major events in a story, using key details.
- Use narrative language to describe (orally or in writing) characters, setting, things, events, actions, a scene, or facts from a fiction read-aloud
- Use narrative language to describe characters, setting, things, events, actions, a scene, or facts from a fiction text that has been read independently
Grade 2
- 1.1 Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
- 1.2 Answer questions that require making interpretations, judgments, or giving opinions about what is heard in a fiction read-aloud, including answering why questions that require recognizing cause/effect relationships
- 2.1 Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral.
- 2.2 Describe how characters in a fiction text that has been read independently respond to major events and challenges
- 3 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
- Use collective nouns (e.g., group)
- Form and use frequently occurring irregular plural nouns (e.g., feet, children, teeth, mice, fish).
- Form and irregular plural nouns orally and in own writing
- Use reflexive pronouns (e.g., myself, ourselves).
- 4. Use adjectives and adverbs, and choose between them depending on what is to be
- 5. Identify the main purpose of a nonfiction/informational read-aloud, including what the author wants to answer, explain, or describes Identify the main purpose of a nonfiction/informational text read independently.
- 6.1 Determine the meaning of words and phrases in a text relevant to a Grade 2 topic or subject area.
- 6.2 Determine the meaning of unknown words and phrases in nonfiction/informational read-alouds and discussions.
- 6.3 Determine the meaning of unknown words and phrases in nonfiction/informational texts read independently
- 7.1 Know and use various text features (e.g., captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently.
- 7.2 Identify and use text features (e.g., captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a nonfiction/informational
- 8.1 Identify the main purpose of a text, including what the author wants to answer, explain, or describe.
- 8.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
- 8.3 Capitalize holidays, product names, and geographic names.
- 9.1 Use commas in greetings and closings of letters.
- 9.2 Use an apostrophe to form contractions and frequently occurring possessives
- 9.3 Generalize learned spelling patterns when writing words (e.g., cage → badge; boy → boil).
- 9.4 Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. Consult the Individual Code Chart and simple dictionaries to check spelling
Grade 3
- Reading comprehension
- Identify story elements
- Determine the themes of myths, fables, and folktales
- Identify the author’s purpose: mixed media
- Use key details to determine the main idea
- Read about animals
- Identify sensory details
- Determine the meaning of words using synonyms in context
- Use context to identify the meaning of a word
- Choose topic sentences for narrative paragraphs
- Choose the best transition
- Organize information by main idea
- Revise the sentence using a stronger verb
- Is it a complete sentence or a fragment?
- Identify common and proper nouns
- Is the sentence simple or compound?
- Identify coordinating conjunctions
- Create varied sentences based on models
- Form compound words
- Capitalizing the names of people and pets and titles of respect
- Capitalizing the names of places and geographic features
- Greetings and closings of letters
- Capitalizing the names of people and pets and titles of respect
- Capitalizing titles
- Commas: review
- Contractions with “not”
- Form the singular or plural possessive
- Form and use the regular past tense
- Use regular plurals with -s, -es, and -ies
Grade 4
- Conventions of Standard English
- Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
- Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).
- Use relative pronouns: who, whom, whose, which, and that.
- Use relative adverbs
- Use the progressive verb tenses.
- Use modal auxiliaries (e.g., can, may, must) to convey various conditions)
- What does the modal verb show?
- Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).
- Form and use prepositional phrases. Identify prepositions Identify prepositions and their objects Identify prepositional phrases
- Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.
- . Identify the complete subject of a sentence.
- Identify the complete predicate of a sentence.
- Is it a complete sentence, a fragment, or a run-on? (4-JJ.7)
- Correctly use frequently confused words (e.g., to, too, two; there, their).
- Homophones.
- Demonstrate command of the conventions of standard English capitalization,
punctuation, and spelling when writing.
- Use correct capitalization.
- Capitalizing the names of people and pets and titles of respect (4-VV.1) Capitalizing days, months, and holidays, places, geographic features, historical events, periods, documents, proper adjectives, nationalities, and languages. Capitalizing the names of places and geographic features (4-VV.3)
- Use commas and quotation marks to mark direct speech and quotations from
a text.
- Punctuating dialogue Use a comma before a coordinating conjunction in a compound sentence. Use coordinating conjunctions Create compound sentences
- Vocabulary: Spell grade-appropriate words correctly, consulting references as
needed.
- Word pattern analogies
- Word pattern sentences
- Form compound words
- Use the correct homophone
- Use guide words
- Form regular plurals with -s, -es, and -ies
- Use regular plurals with -s, -es, and -ies
- Form regular plurals with -s, -es, -ies, and -ves
- Use regular plurals with -s, -es, -ies, and -ves
- Form and use irregular plurals
- Form the singular or plural possessive
- Identify and correct errors with plural and possessive nouns
- Form and use the regular past tense
- Form and use the irregular past tense
- Pronoun-verb contractions
- Contractions with “not”
Grade 5
- Writing strategies
- Organizing writing
- Put the sentences in order
- Use coordinating conjunctions
- Choose the best transition
- Order items from most general to most specific
- Organize information by main idea
- Remove the sentence that does not belong Introductions and conclusions
- Organize information by main idea
- Choose the best topic sentence
- Choose the best concluding sentence
- Sentence variety
- Create varied sentences based on models
- Editing and revising
- Use the correct frequently confused word
- Correct errors with frequently confused words
- Correct errors with signs
- Research skills
- Identify and correct plagiarism Vocabulary
- Prefixes and suffixes
- Words with pre-
- Words with re-
- Words with sub-
- Words with mis-
- Words with un-, dis-, in-, im-, and non-
- Words with -ful
- Words with -less
- Words with -able and -ible
- Sort words with shared prefixes and suffixes by meaning
- Sort words with shared suffixes by part of speech
- Word pattern analogies
- Word pattern sentences
- Word Roots Greek and Latin roots
- Sort words by shared Greek or Latin roots
- Use Greek and Latin roots as clues to the meanings of words
- Use the meanings of words as clues to the meanings of Greek and Latin roots
- Use words as clues to the meanings of Greek and Latin roots
- Determine the meanings of Greek and Latin roots
- Determine the meanings of words with Greek and Latin roots
- Match words with Greek and Latin roots to their meanings
- Synonyms , Antonyms, Analogies, and Homophones
- Choose the synonym
- Find synonyms in context
- Choose the antonym
- Find antonyms in context
- Analogies
- Homophones
- Multiple-meaning words with pictures
- Idioms and Adages
- Determine the meaning of idioms from context: set 1
- Identify the meaning of idioms and adages: set 1
- Determine the meaning of idioms from context: set 2
- Identify the meaning of idioms and adages: set 2
- Grammar and mechanics
Sentences, fragments, and run-ons- Is the sentence declarative, interrogative, imperative, or exclamatory?
- Identify the complete subject or complete predicate of a sentence
- Identify the simple subject or predicate of a sentence
- Is it a complete sentence or a fragment?
- Is it a complete sentence or a run-on?
- Is it a complete sentence, a fragment, or a run-on?
- Identify dependent and independent clauses
- Is the sentence simple or compound?
- Is the sentence simple, compound, or complex?
- Create compound sentences
- Order the words to create a sentence
- Nouns
- Identify nouns – with abstract nouns
- Identify common and proper nouns
- Form plurals of nouns ending in f, fe, o, and y
- Form and use plurals of nouns ending in f, fe, o, and y
- Form plurals: review
- Form and use plurals: review
- Identify plurals, singular possessives, and plural possessives
- Form the singular or plural possessive
- Identify and correct errors with plural and possessive nouns
- Pronouns
- Identify personal pronouns
- Choose between subject and object personal pronouns
- Replace the noun with a personal pronoun
- Compound subjects and objects with “I” and “me”
- Compound subjects and objects with personal pronouns
- Use possessive pronouns
- Choose between personal and reflexive pronouns
- Use reflexive pronouns
- Identify relative pronouns
- Use relative pronouns: who and whom
- Use relative pronouns: who, whom, whose, which, and that
- Verb types
- Identify main verbs and helping verbs
- What does the modal verb show?
- Use the correct modal verb
- Subject-verb agreement
- Use the correct subject or verb
- Use the correct subject or verb – with compound subjects
- Verb tense
- Is the sentence in the past, present, or future tense?
- Form and use the regular past tense
- Form and use the irregular past tense
- Form and use the simple past, present, and future tense
- Correct inappropriate shifts in verb tense
- Use the progressive verb tenses
- Form the progressive verb tenses
- Choose between the past tense and past participle
- Use the perfect verb tenses
- Form the perfect verb tenses
- Adjectives and adverbs
- Identify adjectives
- Order adjectives
- Identify adverbs
- Use relative adverbs
- Choose between adjectives and adverbs
- Is the word an adjective or adverb?
- Use adjectives to compare
- Spell adjectives that compare
- Use adjectives with more and most
- Use adverbs to compare
- Prepositions
- Identify prepositions
- Identify prepositions and their objects
- Identify prepositional phrases
- Prepositions: review
- Conjunctions
- Identify coordinating conjunctions
- Identify subordinating conjunctions
- Use the correct pair of correlative conjunctions
- Fill in the missing correlative conjunction
- Contractions
- Pronoun-verb contractions
- Contractions with “not”
- Commas
- Commas with a series
- Commas with dates and places
- Commas with direct addresses
- Commas with introductory elements
- Commas with compound and complex sentences
- Commas: review
- Capitalization
- Correct capitalization errors
- Capitalizing titles
- Formatting
- Formatting titles
- Formatting and capitalizing titles
- Formatting street addresses
- Punctuating dialogue
- Abbreviations
- Abbreviate days of the week and months of the year
- Abbreviate people’s titles
- Abbreviate units of measurement
- Abbreviate street names and state names
Grade 6
- Writing
- Organizing writing
- Order topics from broadest to narrowest
- Organize information by main idea
- Transitions with conjunctive adverbs
- Developing and supporting arguments
- Distinguish facts from opinions
- Choose evidence to support a claim
- Identify supporting details in informational texts
- Identify supporting details in literary texts
- Identify counterclaims
- Classify logical fallacies
- Creative techniques
- Use personification
- Create varied sentences based on models
- Editing and revising
- Use the correct frequently confused word
- Correct errors with frequently confused words
- Correct errors with signs
- Correct errors in everyday use
- Suggest appropriate revisions
- Research skills
- Recognize the parts of a Works Cited entry (MLA 8th edition)
- Use in-text citations (MLA 8th edition)
- Identify and correct plagiarism
- Organizing writing
- Vocabulary
- Prefixes and suffixes
- Words with pre-
- Words with re-
- Words with sub-
- Words with mis-
- Words with un-, dis-, in-, im-, and non-
- Words with -ful
- Words with -less
- Words with -able and -ible
- Greek and Latin roots
- Use Greek and Latin roots as clues to the meanings of words
- Use the meanings of words as clues to the meanings of Greek and Latin roots
- Use words as clues to the meanings of Greek and Latin roots
- Determine the meanings of Greek and Latin roots
- Determine the meanings of words with Greek and Latin roots
- Synonyms and antonyms
- Choose the synonym
- Find synonyms in context
- Choose the antonym
- Find antonyms in context
- Homophones
- Use the correct homophone
- Which definition matches the sentence?
- Which sentence matches the definition?
- Idioms and adages
- Determine the meaning of idioms from context: set 1
- Identify the meaning of idioms and adages: set 1
- Determine the meaning of idioms from context: set 2
- Identify the meaning of idioms and adages: set 2
- Word choice and usage
- Describe the difference between related words
- Positive and negative connotation
- Analogies
- Analogies
- Analogies: challenge
- Prefixes and suffixes
- Reference skills
- Alphabetical order
- Use guide words
- Use dictionary entries
- Use dictionary definitions
- Use thesaurus entries
- Grammar and mechanics
- Sentences, fragments, and run-ons
- Is the sentence declarative, interrogative, imperative, or exclamatory?
- Identify the complete subject or complete predicate of a sentence
- Identify the simple subject or simple predicate of a sentence
- Identify the compound subject or compound predicate of a sentence
- Is it a complete sentence or a fragment?
- Is it a complete sentence or a run-on?
- Is it a complete sentence, a fragment, or a run-on?
- Identify dependent and independent clauses
- Is the sentence simple, compound, or complex?
- Nouns
- Identify common and proper nouns
- Form plurals of nouns ending in f, fe, o, and y
- Form and use plurals of nouns ending in f, fe, o, and y
- Form plurals: review
- Form and use plurals: review
- Identify plurals, singular possessives, and plural possessives
- Form the singular or plural possessive
- Identify and correct errors with plural and possessive nouns
- Pronouns and antecedents
- Identify pronouns and their antecedents
- Use the pronoun that agrees with the antecedent
- Identify vague pronoun references
- Identify all of the possible antecedents
- Correct inappropriate shifts in pronoun number and person
- Pronoun types
- Choose between subject and object pronouns
- Compound subjects and objects with “I” and “me”
- Compound subjects and objects with pronouns
- Use possessive pronouns
- Choose between personal and reflexive pronouns
- Use reflexive pronouns
- Is the pronoun reflexive or intensive?
- Identify relative pronouns
- Use relative pronouns: who and whom
- Use relative pronouns: who, whom, whose, which, and that
- Verb types
- Identify main verbs and helping verbs
- Identify transitive and intransitive verbs
- Identify linking verbs, predicate adjectives, and predicate nouns
- What does the modal verb show?
- Use the correct modal verb
- Subject-verb agreement
- Use the correct subject or verb
- Use the correct verb – with compound subjects
- Verb tense
- Irregular past tense: review
- Simple past, present, and future tense: review
- Correct inappropriate shifts in verb tense
- Use the progressive verb tenses
- Form the progressive verb tenses
- Choose between the past tense and past participle
- Use the perfect verb tenses
- Form the perfect verb tenses
- Adjectives and adverbs
- Identify adjectives
- Order adjectives
- Identify adverbs
- Use relative adverbs
- Choose between adjectives and adverbs
- Is the word an adjective or adverb?
- Form and use comparative and superlative adjectives
- Good, better, best, bad, worse, and worst
- Form and use comparative and superlative adverbs
- Well, better, best, badly, worse, and worst
- Prepositions
- Identify prepositions
- Identify prepositions and their objects
- Identify prepositional phrases
- Prepositions: review
- Direct and indirect objects
- Is it a direct object or an indirect object?
- Conjunctions
- Use coordinating conjunctions
- Identify coordinating conjunctions
- Identify subordinating conjunctions
- Use the correct pair of correlative conjunctions
- Fill in the missing correlative conjunction
- Contractions
- Pronoun-verb contractions
- Contractions with “not”
- Punctuation
- Commas with series, dates, and places
- Commas with compound and complex sentences
- Commas with direct addresses, introductory words, interjections, and interrupters
- Commas with coordinate adjectives
- Commas: review
- What does the punctuation suggest?
- Commas with nonrestrictive elements
- Use dashes
- Capitalization
- Correct capitalization errors
- Capitalizing titles
- Formatting
- Formatting titles
- Formatting and capitalizing titles: review
- Formatting street addresses
- Formatting quotations and dialogue
- Sentences, fragments, and run-ons
Level K
• Introduction to numbers
• Counting numbers up to 100 – forward and backward.
• Skip Counting by 2s, 5s & 10s.
• Finding missing numbers.
• Compare numbers > < =
• Writing before and after numbers.
• Sorting numbers – Ascending and Descending order.
• Single digit additions.
• Single digit subtractions.
• Finding missing addends in addition equations.
• Place values – One, tens and hundreds.
• Number Forms – Expanded and Standard forms.
• Introduction to Two-digit additions.
• Introduction to Two-digit subtractions.
• Story problems – Addition & Subtraction.
Level A
• Number and Operations in Base 10.
• Counting numbers by 2s, 5s & 10s.
• Rounding (10s & 100)
• Place values
• Arithmetic Sequence
• Math mountain equations
• Addition Fact Families
• Commutative Properties of Addition
• Mental Math addition
• Regrouping Addition and Subtraction.
• Finding missing addends in addition, subtraction equations.
• Multiplication: 2-digit & 3-digit with 2, 3, & 4.
• Geometry: Recognizing 2D & 3D shapes
Basic properties of 2D shapes. (Sides, Angles & Vertices)
• Money Problems – pennies, nickels, dimes & quarters.
• Time (Clock): Current time
Elapsed time
• Story problems – Addition, Subtraction & Multiplication.
• Math Puzzles.
Level B
- Regrouping 3 – 4-digit addition and subtraction.
- Multiplication: Multiplying 3-, 4- and 5-digit numbers by a single digit.
- Introduction to Division Concept: Simple division and long division by 2, 3, 4 & 5.
- Mental math multiplication with 10s & 100s
- Mental Math addition.
- Mental Math multiplication (with tens eg. 23*20) .
- Introduction to numbers with place values up to 999.
- Rounding 10s & 100s.
- Fact Families: Addition, Multiplication.
- Math Mountain equations.
- Arithmetic Sequence.
- Finding missing addends in equations.
- Fractions: Basics of Fractions (shaded, unshaded, and whole)
Dividing Shapes into equal parts and writing fractions.
Determining Fractions in Number line.
Equivalent Fractions.
Comparing Fractions with Like denominators.
Comparing Fractions with Unlike denominators.
Adding Fractions.
Subtracting Fractions. - Geometry: Introduction to Lines of symmetry.
2D & 3D Properties. - Measurements – Metric system
US customary system
Units Conversion - Story Word Problems : One or two step word problems.
- Time (Add, Subtract & Elapsed time)
- Money & Time Problems.
- Math Puzzles
- Advanced Money Word problems
Level C
- Review of 3 & 4 – digit addition and subtraction.
- Review of 3 digits by 1 digit multiplication.
- Review of simple division and long division below 1000.
- Review of Place values up to 100.
- Place values
- Rounding (10s & 100s)
- Missing numbers with rule
- Missing numbers in equations
- Time (Add, Subtract & Elapsed time)
- Money
- Introduction to numbers with place values up to 1,000,000.
- Multiplication of 3 & 4 – digit numbers with 2-digit number.
- Division with 4 & 5 – digit dividends.
- Introduction to Numbers – Natural numbers, Whole numbers, Prime & Composite numbers.
- Introduction to Multiples, Factors & Factor pairs.
- Prime Factorization.
- Exponents.
- Properties – Commutative, Associative, Identity, Zero, & Distributive properties
- Multi step Story problems (addition, subtraction, multiplication & division).
- Fractions:
Basics of Fractions (shaded, unshaded, and whole)
Dividing Shapes into equal parts and writing fractions.
Determining Fractions in Number line.
Equivalent Fractions.
Comparing Fractions with Like denominators.
Comparing Fractions with Unlike denominators.
Adding Fractions.
Subtracting Fractions.
Word problems. - Introduction to Types of fractions (Proper, Improper & Mixed number).
- Locating the wholes and fractions on a number line.
- Conversion between improper fraction and mixed number.
- Introduction to basic algebraic equations.
- Geometry – 2D & 3D Shapes Properties and Axis of symmetry.
Lines, rays, segments, angles, triangles, quadrilaterals and polygons.
Area & Perimeter Problems – (Rectangle, Square & Irregular shapes)
Word Problems on finding Area and Perimeter. - Measurements – Metric system
US customary system
Units Conversion - Money & Time Problems
- Math Puzzles
- Word Problems
Level D
- Review of number system – Prime & Composite numbers.
- Review of Multiples, Factors & Factor Pairs.
- Review of Prime Factorization.
- Review of multiplication & division with 3 & 4 digit numbers.
- Review of Money & Time.
- Review of Equations and Expressions.
- Multiplication of 5 & 6 digit numbers with 1-digit & 2-digit numbers.
- Division with 5 & 6 digit dividends with 1-digit & 2-digit divisors.
- Divisibility rules for 2, 3, 4, 5, 6, 8, 9,10 & 12.
- Finding Least Common Multiple (LCM) using different methods.
- Finding Greatest Common Factor (GCF) using different methods.
- Fractions
Converting Mixed to Improper and vice versa.
Adding and subtracting fractions and mixed numbers.
Multiplication & Division of fractions.
Adding and subtracting more than 2 fractions using LCM method.
Word problems on Fractions - Introduction to decimals
Decimal numbers – Addition, Subtraction, Multiplication & Division.
Converting fractions to decimals and vice versa. - Introduction to Integers – Numeric expressions.
- Order of Operation – Solving numeric expressions using PEMDAS.
- Introduction to Algebra –
Algebraic expressions: Terms, Variables, Coefficients, Constants.
Solving one step equations
Simplifying the terms.
Simplify the algebraic expressions. - Introduction to Ratios –
Find the Ratios
Simplest form of ratios.
Equivalent Ratios - Introduction to Geometry –
Finding area and perimeter of square, rectangle, Parallelogram, triangle &
Irregular shapes.
Types of Angles. - Measurements – Metric System and US Customary System
Types of Units
Conversion of units - Multi step Story problems (addition, subtraction, multiplication & division).
- Challenging Word Problems
Level E
- Review of Prime Factorization.
- Review of Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 & 12.
- Review of Least Common Multiple (LCM) using different methods.
- Review of Greatest Common Factor (GCF) using different methods.
- Review of Fractions
Multiplication and Division of fractions.
Adding and subtracting more than 2 fractions using LCM method. - Review of Numeric expressions using Order of Operations (PEDMAS).
- Number System
Rational & Irrational numbers.
Decimal numbers – Addition, Subtraction, Multiplication & Division.
Converting fractions to decimals and vice versa.
Operations with Integers. - Introduction to Algebra
Term, Variable, Coefficient & Constant.
Solving single variable algebraic expressions.
Solving algebraic equations using addition, subtraction, multiplication & division
methods.
Solving two-step & multi-step equations.
Applying Distributive property to algebraic equations.
Story problems involving algebra. - Ratios & Proportions.
Introduction to simple Ratios.
Finding missing Ratios.
Introduction to Proportions.
Finding missing variable in Proportion equations.
Word problems on Ratios & Proportions. - Rate Problems.
Introduction to Rate & unit rates.
Word problems on rate. - Distance, Speed & Time.
Introduction to Distance, Speed & Time Formula.
Solving problems using Formula. - Geometry.
Lines.
Area & Perimeter of Square, Rectangle, Triangle, Parallelogram, Trapezoid &
Circle.
Area & Perimeter of regular Polygons.
Area & Perimeter of 3D shapes (cube, prism & cylinder).
Volume of 3D shapes.
Finding Surface area. - Percentages
Level F (Algebra 1)
- Introduction to Polynomials
Adding and subtracting Polynomials.
Multiplying and Dividing Polynomials.
Simplifying the multiple polynomial expressions. - Functions
Domain and Range.
Independent and dependent variables.
Writing Function Rules.
Represent functions as graphs. - Linear Equations & Inequalities
Introduction to coordinate planes.
Graph using intercepts.
Finding Slope and Rate of Change. - Absolute value equations & inequalities
- Compound Inequalities
- Graphing linear equations and inequalities.
- Exponents
- Special Products formulas
Solving equations using Zero-Product property.
Factoring Trinomials. - Quadratic equations.
Understanding Quadratic equations
Solving Quadratic equations by factoring. - System of Linear Equations.
Graphing method of solving equations
Elimination method of solving equations
Substitution method of solving equations
Level G (Geometry)
- Inductive reasoning
- Conjecture
- Counter example
- Conditional Statements – Hypothesis & Conclusion
- Truth Value
- Related Conditional statements – Conditional, Converse, Inverse, & Contrapositive
- Conjunction & Disjunction
- Biconditional (if and only if)
- Deductive reasoning (Law of Detachment & Law of Syllogism)
- Properties of Equality
(Addition, Subtraction, Multiplication, Division, Reflexive, Symmetric, Transitive,
Substitution) - Properties of Congruence
(Reflexive, Symmetric, & Transitive) - Parallel and Skew lines
- Transversal
- Angle pairs formed by Transversals
Alternate interior angles
Same-side interior angles
Corresponding angles
Alternate exterior angles - Formulas
Midpoint
Distance
Midsegment - Postulates:
1) Angles
Corresponding Angles Postulate
Converse of the Corresponding Angles Postulate
Parallel Postulate
Perpendicular Postulate
2) Triangles
Side-Side-Side (SSS) Postulate
Side-Angle-Side (SAS) Postulate
Angle-Side-Angle (ASA) Postulate
Angle-Angle-Side (AAS) Postulate
Hypotenuse-Leg (HL) Theorem - Theorems:
1) Angles
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
All right angles are congruent
If two angles are congruent and supplementary, then each angle is a right angle.
Alternate Interior Angles Theorem
Same-Side Interior Angles theorem
Alternate Exterior Angles Theorem
Converse of the Alternate Interior Angles Theorem
Converse of the Same-Side Interior Angles theorem
Converse of the Alternate Exterior Angles Theorem
If two lines are parallel to the same line, then they are parallel to each other
If two lines are perpendicular to the same line, then they are parallel to each
other.
If a line is perpendicular to one of two parallel lines, then it is also perpendicular
to the other.
2) Triangles
Triangle Angle Sum Theorem
Triangle Exterior Angle Theorem
Third Angles Theorem
Isosceles Triangle Theorem
Converse of the Isosceles Triangle Theorem
Triangle Midsegment Theorem
Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector Theorem
Angle Bisector Theorem
Converse of the Angle Bisector Theorem
Congruency of Perpendicular Bisectors Theorem
Congruency of Angle Bisectors Theorem
Level H (Algebra 2)
- Linear Models
- Scatter Plots
- Relations and Functions
- Absolute Value Functions and Graphs
- Two Variable Inequalities
- Graphing Linear Inequalities
- Quadratic Functions and Transformations
- Standard Form of a Quadratic Function
- Factoring Quadratic Expressions
- Completing the Square
- The Quadratic Formula
- Complex Numbers
- Quadratic Systems
- Polynomials & Polynomial functions:
Polynomial Functions
Polynomials, Linear Factors, and Zeros
Solving Polynomial Equations
Dividing Polynomials
Rational Root Theorem
Conjugate Root Theorem
The fundamental Theorem of Algebra
Binomial Theorem
Pascal’s Triangle - Radical Function & Rational Exponents
Roots and Radical Expressions
Multiplying and Dividing Radical Expressions
Adding and Subtracting Radical Expressions
Multiplying Radical Expressions
Multiplying Conjugates
Rationalizing the Denominator
Rational Exponents
Solving Square Root Equations
Solving Other Radical Equations
Function Operations
Inverse Relations and Functions
Graphing Radical Functions