Skills to prepare for Massachusetts MCAS
Find the math, reading and writing skills covered by the Massachusetts MCAS tests at your grade.
Grade 3 MCAS math skills
24 skill groups across 5 topic areasOperations and algebraic thinking
Equal groups, multiplication, division and patterns
Operations and algebraic thinking
Equal groups, multiplication, division and patterns
Interpret multiplication
Explain a whole-number product using equal groups of objects.
Interpret division
Explain a quotient as equal sharing or as finding the number of equal groups.
Solve multiplication and division word problems
Use drawings or equations for equal groups, arrays and measurements within 100.
Find an unknown factor or quotient
Find the missing number in a multiplication or division equation.
Use operation properties
Use changes in order or grouping and the distributive property to make calculations easier.
Use multiplication to solve division
Treat division as finding an unknown factor.
Build multiplication and division fluency
Calculate fluently within 100 and recall products of two one-digit numbers.
Solve problems in two steps
Choose operations, write an equation for an unknown quantity, and check whether the answer is reasonable.
Explain number patterns
Spot relationships in addition or multiplication tables and explain why they work.
Number and operations
Whole-number calculations and beginning fractions
Number and operations
Whole-number calculations and beginning fractions
Round, add and subtract whole numbers
Round to tens or hundreds and calculate sums and differences within 1,000.
Multiply by multiples of ten
Use place value to multiply a one-digit number by 10, 20, and other multiples through 90.
Represent fractions as numbers
Connect equal parts of a whole to fractions and positions on a number line. Grade 3 denominators are 2, 3, 4, 6 and 8.
Compare fractions and find equivalents
Explain simple equivalence, express whole numbers as fractions, and compare fractions sharing a numerator or denominator.
Measurement and data
Time, measurement, graphs, area and perimeter
Measurement and data
Time, measurement, graphs, area and perimeter
Work with time, mass and liquid volume
Read time to the minute, calculate elapsed time, and solve measurement problems with grams, kilograms and liters.
Represent data in graphs and line plots
Use scaled picture and bar graphs; measure to half- and quarter-inches and display the results on line plots.
Understand square units
Explain area as the amount of surface covered by unit squares without gaps or overlaps.
Measure area by counting squares
Count unit squares to determine a figure's area.
Connect area to multiplication
Multiply rectangle side lengths and add areas of non-overlapping rectangles.
Find and compare perimeters
Calculate distances around polygons and distinguish perimeter from area.
Geometry
Shape categories and equal-area parts
Geometry
Shape categories and equal-area parts
Group shapes by shared properties
Recognize quadrilaterals and explain how rectangles, squares and rhombuses fit within that category.
Divide shapes into equal areas
Describe each equal-area part as a unit fraction of the whole shape.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 3 MCAS reading and writing skills
21 skill groups across 5 topic areasLiterary text
Story details, lessons, characters and point of view
Literary text
Story details, lessons, characters and point of view
Support answers with story details
Refer back to the text when answering questions, retelling a story, or explaining its lesson or message.
Connect characters to events
Explain how characters' feelings, motivations and actions shape what happens.
Understand structure and point of view
Explain how chapters, scenes or stanzas build on each other, and distinguish your perspective from the narrator's.
Compare stories and interpret illustrations
Explain what pictures add to a story; compare themes, settings and plots in related stories by the same author.
Informational text
Main ideas, text features and connections between facts
Informational text
Main ideas, text features and connections between facts
Identify a main idea and its supporting details
Answer questions with evidence from the text and explain how key details support the main idea.
Follow relationships and sequences
Explain connections between events, ideas, steps, sentences and paragraphs using sequence or cause and effect.
Use text features
Find information efficiently using headings, keywords, links and other text features.
Distinguish your viewpoint from the author's
Explain how your own point of view differs from the author's.
Connect information across texts and visuals
Use information in the supplied texts, charts, illustrations or diagrams to explain a topic and connect relevant details.
Compare two texts on the same topic
Identify similarities and differences in the key points and details.
Vocabulary
Context clues, word parts and shades of meaning
Vocabulary
Context clues, word parts and shades of meaning
Work out unfamiliar words
Use sentence clues, familiar roots, prefixes, suffixes and reference tools to clarify meaning.
Understand literal and nonliteral language
Explain words in context and distinguish shades of meaning among related words.
Build topic vocabulary
Understand academic and subject words, including language for time and spatial relationships.
Interpret common abbreviations and symbols
Recognize the meaning of abbreviations and symbols used in the passage or its subject area.
Writing from texts
Text-based extended responses
Writing from texts
Text-based extended responses
Write a supported opinion
State an opinion, give supporting reasons, connect the opinion and reasons with linking words, and finish with a conclusion.
Write a clear explanation
Introduce a topic, group related facts and definitions, connect ideas with linking words, and provide a conclusion.
Keep the response focused and organized
Answer the prompt in a focused extended response. Organize the explanation, connect supporting details and use an appropriate ending.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Build and connect complete sentences
Produce, expand and rearrange simple, compound and complex sentences. Match subjects with verbs and pronouns with their antecedents.
Choose verb and descriptive word forms
Use present, past and future tenses, regular and irregular plurals and past-tense verbs, abstract nouns, and comparative or superlative adjectives and adverbs.
Use capitals, possessives and dialogue punctuation
Capitalize titles and number words at sentence beginnings. Use commas in addresses, punctuate dialogue, form possessives and apply spelling patterns.
Choose words for the intended effect
Choose effective words and phrases and distinguish the conventions of written English from conversation.
Grade 4 MCAS math skills
26 skill groups across 5 topic areasOperations and algebraic thinking
Comparisons, multi-step problems, factors and patterns
Operations and algebraic thinking
Comparisons, multi-step problems, factors and patterns
Understand multiplicative comparisons
Represent how many times as much one quantity is as another, using equations and word problems.
Solve multi-step word problems
Choose among the four operations, interpret remainders, and check answers with estimates.
Find factors and multiples
Identify factor pairs, multiples, and prime or composite numbers within 100.
Generate and explain patterns
Follow a number or shape rule and describe features that the rule does not explicitly state.
Number and operations
Larger whole numbers, fraction operations and decimals
Number and operations
Larger whole numbers, fraction operations and decimals
Explain neighboring place values
Explain why a digit represents ten times as much in the place to its left.
Read, write and compare larger whole numbers
Use numerals, words and expanded form through one million and compare values digit by digit.
Round larger whole numbers
Use place value to round a multi-digit whole number to any place.
Add and subtract larger whole numbers
Use standard algorithms fluently for multi-digit sums and differences.
Multiply larger whole numbers
Multiply up to four digits by one digit or two digits by two digits, explaining the strategy with models or equations.
Divide larger whole numbers
Divide up to four digits by one digit and explain quotients and remainders using place value or models.
Explain fraction equivalence and comparisons
Use models or benchmarks to compare fractions referring to the same whole. Grade 4 fraction denominators are 2, 3, 4, 5, 6, 8, 10, 12 and 100.
Add, subtract and multiply fractions
Add or subtract fractions and mixed numbers with like denominators, and multiply a fraction by a whole number.
Connect tenths and hundredths
Express tenths as hundredths and add fractions with denominators 10 and 100.
Write fractions as decimals
Use decimal notation for fractions with denominators 10 or 100.
Compare decimals through hundredths
Use models or place value to compare decimal amounts referring to the same whole.
Measurement and data
Conversions, rectangle measurements, line plots and angles
Measurement and data
Conversions, rectangle measurements, line plots and angles
Convert units and solve measurement problems
Express larger units as smaller units within one system; solve problems involving time, money and other measurements.
Apply area and perimeter formulas
Find rectangle measurements, including a missing side when other information is given.
Calculate with line-plot data
Display measurements in halves, quarters and eighths and answer questions using fraction addition and subtraction.
Understand angle measurement
Connect an angle's size to a fraction of a full turn measured in degrees.
Measure and draw angles
Use a protractor to measure an angle or draw an angle of a specified size.
Find unknown angles
Add or subtract angle measures to find missing parts of a larger angle.
Geometry
Lines, angles, shape properties and symmetry
Geometry
Lines, angles, shape properties and symmetry
Identify lines, angles and shape categories
Recognize parallel and perpendicular lines and classify figures, including right triangles, using line and angle properties.
Recognize lines of symmetry
Identify and draw lines that divide a figure into matching reflected halves.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 4 MCAS reading and writing skills
22 skill groups across 5 topic areasLiterary text
Evidence, theme, character analysis and narration
Literary text
Evidence, theme, character analysis and narration
Explain ideas and inferences with evidence
Use specific details to support an inference, identify a theme, or summarize a story, play or poem.
Describe characters, settings and events in depth
Draw on a character's thoughts, speech and actions rather than giving a general description.
Compare structure and narration
Distinguish poetry, drama and prose, and compare first-person with third-person storytelling.
Compare literary texts
Compare treatments of similar themes, topics and event patterns in stories from different cultures.
Informational text
Summaries, organization, accounts and supporting evidence
Informational text
Summaries, organization, accounts and supporting evidence
Support informational inferences
Refer to details and examples when explaining explicit information or making an inference.
Identify a main idea and summarize
Explain how key details support the main idea and summarize the text.
Explain events, procedures and concepts
Use specific information to explain what happened and why in historical, scientific or technical text.
Recognize structure and compare accounts
Identify organization such as cause and effect, and compare firsthand with secondhand accounts.
Connect information across texts and visuals
Use information in the supplied texts, charts, illustrations or diagrams to explain a topic and connect relevant details.
Combine information from two texts
Bring together relevant facts about the same topic into a coherent explanation.
Vocabulary
Word roots, figurative language and precise meanings
Vocabulary
Word roots, figurative language and precise meanings
Use context and word parts
Use examples, restatements, Greek or Latin roots and reference materials to clarify unfamiliar words.
Interpret figurative and related meanings
Explain similes, metaphors, idioms and mythological references; connect synonyms and antonyms.
Understand academic and topic language
Recognize precise words for actions, emotions and subject-specific ideas.
Interpret common abbreviations and symbols
Recognize the meaning of abbreviations and symbols used in the passage or its subject area.
Writing from texts
Text-based extended responses
Writing from texts
Text-based extended responses
Write a supported opinion
State an opinion and support the reasons with facts and details. Group related ideas, use linking phrases and provide a conclusion.
Write a clear explanation
Organize an explanation in paragraphs or sections. Develop the topic with facts, definitions, concrete details or quotations, and use precise topic vocabulary.
Keep the response focused and organized
Answer the prompt in a focused extended response. Organize the explanation, connect supporting details and use an appropriate ending.
Use evidence rather than unsupported assertions
Select relevant details or quotations from the supplied text or texts and explain how they support the response.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Correct sentence fragments and run-ons
Use subject and predicate knowledge to produce complete sentences. Distinguish frequently confused words such as their and there.
Use phrases, pronouns and helping verbs
Use relative pronouns, relative adverbs, prepositional phrases and progressive verb tenses. Choose a helping verb that conveys the intended possibility, obligation or permission.
Punctuate quotations and compound sentences
Use capitalization, commas and quotation marks correctly. Place a comma before a coordinating conjunction joining complete clauses, and spell correctly.
Make wording and punctuation effective
Choose precise words and purposeful punctuation. Recognize when formal or informal English suits the context.
Grade 5 MCAS math skills
20 skill groups across 5 topic areasOperations and algebraic thinking
Expressions, order of operations and number patterns
Operations and algebraic thinking
Expressions, order of operations and number patterns
Work with numerical expressions
Evaluate calculations with parentheses, brackets and braces, keeping the intended order of operations.
Turn a calculation into an expression
Write expressions from words and explain their meaning without always calculating an answer.
Connect two number patterns
Generate sequences from two rules, explain how their terms relate, and plot corresponding pairs.
Number and operations
Place value, whole numbers, decimals and fractions
Number and operations
Place value, whole numbers, decimals and fractions
Understand place value and powers of ten
Explain how a digit changes value across places and how powers of ten affect whole numbers and decimals.
Read, compare and round decimals
Use words, numerals and expanded form through thousandths; compare values and round to a chosen place.
Multiply and divide larger whole numbers
Use the standard multiplication algorithm. Divide up to four-digit numbers by two-digit numbers, explaining the method.
Calculate with decimals
Use all four operations with decimals to hundredths and explain the reasoning with models or place value.
Add and subtract fractions
Find common denominators, including for mixed numbers. Solve word problems and check answers using estimates.
Understand fractions as division
Express equal-sharing answers as fractions or mixed numbers, connecting the fraction bar to division.
Multiply fractions and explain scaling
Model products and fractional rectangle areas, solve word problems, and explain why a factor can enlarge or reduce a quantity.
Divide with unit fractions
Divide a unit fraction by a whole number, or a whole number by a unit fraction. General fraction-by-fraction division is not a Grade 5 requirement.
Measurement and data
Unit conversions, line plots and volume
Measurement and data
Unit conversions, line plots and volume
Convert measurement units
Switch between units within one measurement system and use conversions in multi-step problems.
Read and create line plots
Plot measurements in halves, quarters and eighths, then use fraction calculations to answer questions about the data.
Measure volume with unit cubes
Connect the space a solid occupies to a count of cubes packed without gaps or overlaps.
Calculate the volume of rectangular prisms
Use length, width and height, or base area and height. Add volumes for shapes made of two non-overlapping prisms.
Geometry
Coordinate points and properties of shapes
Geometry
Coordinate points and properties of shapes
Plot and interpret coordinate points
Use ordered pairs and axes to represent situations in the first quadrant and explain what the coordinates mean.
Classify shapes by their properties
Organize two-dimensional shapes into related groups and explain why a subgroup inherits the properties of its larger category.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 5 MCAS reading and writing skills
21 skill groups across 5 topic areasLiterary text
Quotations, theme, comparisons and narrative perspective
Literary text
Quotations, theme, comparisons and narrative perspective
Support interpretations with accurate quotations
Quote relevant evidence to explain explicit ideas and inferences, identify a theme, and summarize the text.
Compare characters, settings and events
Use specific details to explain similarities, differences and interactions within a story or play.
Explain structure and narrative perspective
Describe how chapters, scenes or stanzas fit together and how the narrator's viewpoint shapes the account.
Compare literary texts
Compare stories in the same genre and explain how they approach similar themes or topics.
Informational text
Multiple main ideas, source comparisons and evidence
Informational text
Multiple main ideas, source comparisons and evidence
Use accurate quotations as evidence
Quote precisely when explaining information or an inference from an informational text.
Explain multiple main ideas
Identify two or more main ideas, connect each with supporting details and summarize the text.
Explain interactions within a text
Explain relationships between individuals, events, ideas or concepts using specific information.
Compare structures and perspectives
Compare the organization of multiple texts and the viewpoints in different accounts of the same topic.
Connect claims with reasons and evidence
Identify which evidence supports each point an author makes.
Connect information across texts and visuals
Use information in the supplied texts, charts, illustrations or diagrams to explain a topic and connect relevant details.
Vocabulary
Context, roots, figurative language and word relationships
Vocabulary
Context, roots, figurative language and word relationships
Resolve unfamiliar or multiple-meaning words
Use context, Greek and Latin word parts, and reference materials to select the right meaning.
Interpret figurative language and word relationships
Explain similes, metaphors, idioms and proverbs, and use synonyms, antonyms or homographs to refine meaning.
Understand academic and subject vocabulary
Interpret topic words and language that signals contrast, addition and other logical relationships.
Interpret common abbreviations and symbols
Recognize the meaning of abbreviations and symbols used in the passage or its subject area.
Writing from texts
Text-based extended responses
Writing from texts
Text-based extended responses
Write a supported opinion
State an opinion and organize the reasons logically. Support each reason with facts and details, link ideas with words or clauses, and provide a related conclusion.
Write a clear explanation
Group information logically, develop it with facts, definitions, examples or quotations, and link ideas within and across categories before concluding.
Keep the response focused and organized
Answer the prompt in a focused extended response. Organize the explanation, connect supporting details and use an appropriate ending.
Use evidence rather than unsupported assertions
Select relevant details or quotations from the supplied text or texts and explain how they support the response.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Control verb tense and voice
Use verb tenses to convey time, sequence, state or condition. Correct inappropriate tense shifts, form perfect tenses and choose active or passive voice for the intended meaning.
Punctuate lists and introductory elements
Use commas in a series, after introductory elements, with direct address and with tag questions. Mark titles of works appropriately and spell correctly.
Improve sentence structure and style
Expand, combine or shorten sentences for clarity and interest. Compare varieties of English used in stories, plays or poems.
Grade 6 MCAS math skills
31 skill groups across 5 topic areasOperations and algebraic thinking
Expressions, equations and variable relationships
Operations and algebraic thinking
Expressions, equations and variable relationships
Evaluate numerical expressions with exponents
Use whole-number powers and the conventional order of operations.
Write and evaluate variable expressions
Translate words into expressions, identify their parts and substitute values for variables.
Generate equivalent expressions
Apply operation properties to rewrite an expression without changing its value.
Recognize equivalent expressions
Decide whether two expressions have the same value for every allowed value of a variable.
Check solutions by substitution
Substitute a value to decide whether an equation or inequality is true.
Use variables for unknown quantities
Write expressions that represent an unknown number or quantities in a situation.
Solve one-step equations
Solve equations of the forms x + p = q and px = q using nonnegative rational numbers.
Represent inequalities
Write constraints such as x > c or x < c and show their infinitely many solutions on a number line.
Connect tables, graphs and equations
Identify which quantity depends on another and represent how the two quantities change together.
Number systems and ratios
Rates, fractions, decimals and signed numbers
Number systems and ratios
Rates, fractions, decimals and signed numbers
Describe ratio relationships
Use ratio language to compare quantities in a situation.
Understand unit rates
Explain a rate with a denominator of one in the context of a ratio relationship.
Solve ratio, rate and percent problems
Use equivalent ratios, tables, graphs or equations, including for percentages and unit conversions.
Divide fractions
Interpret and calculate a quotient of fractions using models or equations.
Divide multi-digit whole numbers
Use the standard division algorithm fluently.
Calculate with decimals
Use standard algorithms for all four decimal operations.
Find common factors and multiples
Use greatest common factors, least common multiples and the distributive property to restructure calculations.
Interpret positive and negative quantities
Explain signed values and the meaning of zero in situations such as temperature or elevation.
Locate signed values and opposites
Use number lines and all four coordinate quadrants to represent rational numbers.
Compare signed numbers and use absolute value
Distinguish order from distance to zero and explain comparisons in context.
Find coordinate distances
Plot points in all quadrants and use absolute value to find horizontal or vertical distances.
Solve problems with density
Use the relationship between mass, volume and density to find an unknown quantity, keeping units consistent.
Geometry
Areas, nets, coordinate figures and volume
Geometry
Areas, nets, coordinate figures and volume
Find polygon areas
Break figures into triangles and rectangles or combine simpler shapes to calculate an area.
Work with volume and surface area
Calculate rectangular-prism volume with fractional side lengths and use nets to find surface area.
Use coordinates to measure shapes
Draw a polygon from its vertices and find side lengths parallel to the coordinate axes.
Statistics and probability
Statistical questions, distributions and data displays
Statistics and probability
Statistical questions, distributions and data displays
Recognize statistical questions
Identify questions that anticipate variability in the data collected to answer them.
Describe a distribution
Explain how numerical data have a center, spread and overall shape.
Distinguish center from variability
Explain what a measure of center summarizes and what a measure of variation summarizes.
Display and summarize measurements
Interpret dot plots, histograms and box plots; calculate suitable measures of center and variability in context.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 6 MCAS reading and writing skills
20 skill groups across 5 topic areasLiterary text
Text evidence, plot development and narrative choices
Literary text
Text evidence, plot development and narrative choices
Support inferences and explain a theme
Use text evidence, connect details to a central message, and summarize without adding personal judgments.
Track plot and character changes
Explain how episodes lead toward a resolution and how characters respond along the way.
Analyze structure and narrator perspective
Explain what a scene or stanza contributes and how the author develops the narrator's viewpoint.
Compare literary texts
Compare texts in different forms or genres and explain how they approach similar themes and topics.
Informational text
Central ideas, development, purpose and claims
Informational text
Central ideas, development, purpose and claims
Support informational inferences with evidence
Cite relevant text evidence for explicit information and inferences.
Trace a central idea and summarize
Explain how details convey a central idea and summarize without personal judgments.
Track how an idea or event develops
Explain how a person, event or concept is introduced, illustrated and elaborated.
Analyze organization and author purpose
Explain how a section contributes to the whole and how the text communicates an author's viewpoint.
Evaluate claims and supporting evidence
Distinguish claims backed by reasons and evidence from unsupported statements.
Connect information across texts and visuals
Connect information from supplied texts and visual displays. Compare accounts and identify important differences in their facts, evidence or interpretations.
Vocabulary
Context, roots, connotation and figurative meaning
Vocabulary
Context, roots, connotation and figurative meaning
Determine precise meanings
Use context, word function, Greek or Latin roots and reference tools, then check that the meaning fits.
Explain word choice and figurative language
Interpret personification and other figures of speech, distinguish connotations, and explain effects on tone.
Understand technical and academic language
Interpret subject vocabulary and unfamiliar terms that are important to understanding the text.
Writing from texts
Text-based extended responses and essays
Writing from texts
Text-based extended responses and essays
Write a supported argument
Introduce a claim and support it with clear reasons and relevant evidence. Organize the argument, connect the reasons and evidence, and maintain an appropriate formal style.
Write a clear explanation
Organize an explanation around relevant facts, definitions, details, quotations and examples. Use transitions, precise vocabulary and a conclusion that follows from the explanation.
Keep the response focused and organized
Develop a focused response or essay based on the supplied text or texts. Organize the analysis with an introduction, connected supporting paragraphs and a conclusion.
Use evidence rather than unsupported assertions
Select relevant details or quotations from the supplied text or texts and explain how they support the response.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Use clauses and modifiers purposefully
Use simple, compound, complex and compound-complex sentences. Explain the role of a phrase or clause and correct misplaced or dangling modifiers.
Set off nonessential information
Use commas, parentheses or dashes for nonrestrictive or parenthetical elements. Spell correctly, recognizing accepted variants.
Maintain a suitable style and tone
Vary sentence patterns for clarity and interest while keeping style and tone consistent.
Grade 7 MCAS math skills
22 skill groups across 5 topic areasOperations and algebraic thinking
Equivalent expressions and multi-step problems
Operations and algebraic thinking
Equivalent expressions and multi-step problems
Rewrite expressions to reveal meaning
Expand, factor or combine linear expressions with rational coefficients and explain what an equivalent form shows.
Solve multi-step numerical problems
Calculate with signed fractions or decimals and use estimates to check whether a result makes sense.
Solve equations and inequalities
Represent a situation with an equation or inequality, solve it, and interpret or graph the solution.
Number systems and ratios
Proportional relationships and rational-number calculations
Number systems and ratios
Proportional relationships and rational-number calculations
Recognize and model proportional relationships
Calculate unit rates involving fractions and connect proportional tables, graphs and equations.
Solve percent and ratio problems
Handle multi-step situations such as discounts, tax, interest or percentage change.
Add and subtract signed rational numbers
Use number lines, opposites and sign rules to calculate with positive and negative fractions or decimals.
Multiply and divide signed rational numbers
Explain sign rules, calculate products and quotients, and connect fractions to terminating or repeating decimals.
Solve rational-number problems
Choose among all four operations in practical and mathematical situations.
Geometry
Scale, circles, angle relationships and solids
Geometry
Scale, circles, angle relationships and solids
Use scale drawings
Calculate actual lengths and areas and reproduce a drawing at a different scale.
Draw shapes with given conditions
Investigate whether specified angles or side lengths determine one triangle, more than one or none.
Describe cross-sections
Identify the flat shapes made by slicing rectangular prisms and pyramids.
Find circle measurements and unknown angles
Use circumference and area formulas and relationships between adjacent, vertical, complementary or supplementary angles.
Calculate measurements of composite figures
Find area, surface area or volume by combining or separating familiar shapes and solids.
Statistics and probability
Sampling, comparing populations and chance
Statistics and probability
Sampling, comparing populations and chance
Use samples to describe populations
Recognize representative sampling and use sample data to estimate population characteristics.
Compare two groups using data
Use centers, variability and the overlap between distributions to make a supported comparison.
Interpret probability
Connect likelihood with a number from zero to one.
Estimate probability from repeated trials
Use long-run relative frequency to estimate likelihood and predict approximate counts.
Use probability models
Build uniform or nonuniform models and compare predicted probabilities with observed frequencies.
Find compound-event probabilities
Organize outcomes using lists, tables or tree diagrams and use simulations when appropriate.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 7 MCAS reading and writing skills
20 skill groups across 5 topic areasLiterary text
Developing themes, interacting elements and viewpoints
Literary text
Developing themes, interacting elements and viewpoints
Use several details to explain a developing theme
Support an interpretation with multiple pieces of evidence and trace the theme across the text.
Connect story elements
Explain how setting, characters and plot influence each other.
Analyze form and contrasting viewpoints
Explain how a poem or play's structure contributes to meaning and how narrators' or characters' perspectives differ.
Compare literary texts
Compare a fictional portrayal of a time, place or character with a historical account of the same period.
Informational text
Multiple ideas, argument quality and interpretations
Informational text
Multiple ideas, argument quality and interpretations
Use several pieces of informational evidence
Support explicit explanations and inferences with multiple relevant details.
Trace two or more central ideas
Analyze how several central ideas develop and provide an objective summary.
Explain interactions among ideas and events
Analyze how people, events and ideas influence one another.
Explain structure and contrasting positions
Show how sections develop ideas and how an author distinguishes a position from competing views.
Judge the strength of an argument
Assess whether reasoning makes sense and whether evidence is relevant and sufficient.
Connect information across texts and visuals
Connect information from supplied texts and visual displays. Compare accounts and identify important differences in their facts, evidence or interpretations.
Vocabulary
Allusions, sound patterns and precise meanings
Vocabulary
Allusions, sound patterns and precise meanings
Verify word meanings from multiple clues
Combine context and word parts with general or specialist reference sources.
Interpret figurative and sound effects
Explain allusions, rhymes or repeated sounds; use word relationships and connotations to clarify meaning.
Explain word choice in nonfiction
Understand technical or academic terms and analyze how wording influences meaning and tone.
Writing from texts
Text-based extended responses and essays
Writing from texts
Text-based extended responses and essays
Write a supported argument
Support a clear claim with logical reasons and relevant evidence, acknowledge opposing claims, and use transitions to show how the claim, reasons and evidence connect.
Write a clear explanation
Organize ideas with suitable structures such as comparison or cause and effect. Develop them with relevant evidence, precise language and transitions that clarify relationships.
Keep the response focused and organized
Develop a focused response or essay based on the supplied text or texts. Organize the analysis with an introduction, connected supporting paragraphs and a conclusion.
Use evidence rather than unsupported assertions
Select relevant details or quotations from the supplied text or texts and explain how they support the response.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Use clear pronoun references and verb tenses
Correct vague pronouns and inappropriate shifts in pronoun number or person. Use phrases, clauses and verb tenses to communicate the intended relationships clearly.
Punctuate coordinate adjectives
Place a comma between coordinate adjectives and spell correctly, recognizing accepted variants.
Adjust sentence patterns and register
Vary phrase or clause placement for meaning and emphasis. Maintain consistent style and tone and adjust nonstandard or overly informal language when the task calls for formal English.
Grade 8 MCAS math skills
25 skill groups across 5 topic areasOperations and algebraic thinking
Linear equations, systems, functions and graphs
Operations and algebraic thinking
Linear equations, systems, functions and graphs
Connect slope, rate and line equations
Compare proportional relationships and explain how slope and an intercept describe a line.
Solve linear equations and systems
Solve equations with rational coefficients, recognize different numbers of solutions, and solve pairs of linear equations.
Recognize a function
Decide whether each input is assigned exactly one output.
Compare functions in different forms
Compare properties shown by tables, graphs, equations or descriptions.
Distinguish linear and nonlinear functions
Recognize a straight-line relationship of the form y = mx + b and explain examples that are not linear.
Model and interpret changing quantities
Build a linear model from data, interpret its starting value and rate, and describe increasing or decreasing portions of a graph.
Number systems and ratios
Irrational numbers, exponents and scientific notation
Number systems and ratios
Irrational numbers, exponents and scientific notation
Distinguish rational and irrational numbers
Connect repeating decimals with fractions and estimate irrational values on a number line.
Use exponents and roots
Apply integer-exponent rules and evaluate square or cube roots of familiar perfect powers.
Calculate in scientific notation
Compare very large or small quantities and perform operations using powers of ten.
Geometry
Transformations, similarity, right triangles and volume
Geometry
Transformations, similarity, right triangles and volume
Describe rigid transformations
Explain which properties of lines, angles and figures are preserved by rotations, reflections and translations.
Recognize congruent figures
Describe a sequence of rigid motions that maps one figure onto another.
Transform figures on a coordinate plane
Describe how translations, reflections, rotations and dilations change coordinates.
Recognize similar figures
Use rigid motions and dilations to explain similarity.
Explain angle relationships
Use informal arguments for triangle angle sums, parallel lines cut by a transversal and angle-angle similarity.
Explain the Pythagorean theorem
Explain a proof of the right-triangle relationship and its converse.
Find right-triangle lengths
Use the Pythagorean theorem to find missing lengths in two or three dimensions.
Find distances between coordinate points
Use the Pythagorean theorem to calculate a distance on a coordinate plane.
Find volumes of curved solids
Calculate the volume of a cylinder, cone or sphere in a practical or mathematical problem.
Statistics and probability
Scatter plots, fitted lines and two-way tables
Statistics and probability
Scatter plots, fitted lines and two-way tables
Interpret scatter plots
Describe clusters, outliers and positive, negative, linear or nonlinear associations in paired data.
Fit and assess a line
Informally fit a straight line to data and judge how closely the points follow it.
Use a linear data model
Interpret slope and intercept in context and use the fitted equation to answer questions.
Compare categories in a two-way table
Use counts and relative frequencies to investigate whether two categorical variables are associated.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 8 MCAS reading and writing skills
20 skill groups across 5 topic areasLiterary text
Strong evidence, dramatic irony and literary connections
Literary text
Strong evidence, dramatic irony and literary connections
Choose the strongest evidence
Select details that best support an inference or show how theme connects to characters, setting and plot.
Explain the impact of dialogue and events
Analyze how a particular line or incident reveals character, prompts a decision or moves the action forward.
Compare structure and analyze dramatic irony
Explain how organization affects style and how differences between reader and character knowledge create effects.
Compare literary texts
Explain how a modern story draws on and transforms themes, events or character types from myths or traditional stories.
Informational text
Developed ideas, counterarguments and conflicting sources
Informational text
Developed ideas, counterarguments and conflicting sources
Choose the strongest informational evidence
Select the evidence that most strongly supports explicit explanations or inferences.
Analyze a central idea's development
Explain how the central idea connects to supporting ideas and provide an objective summary.
Analyze connections and distinctions
Explain comparisons, analogies or categories that connect or distinguish individuals, ideas and events.
Analyze paragraphs and responses to disagreement
Explain the role of particular sentences and how an author addresses conflicting evidence or perspectives.
Evaluate reasoning and relevance
Judge whether claims have sound reasoning and enough relevant support; identify irrelevant evidence.
Connect information across texts and visuals
Connect information from supplied texts and visual displays. Compare accounts and identify important differences in their facts, evidence or interpretations.
Vocabulary
Irony, analogies, allusions and shades of meaning
Vocabulary
Irony, analogies, allusions and shades of meaning
Resolve and verify unfamiliar language
Use context, Greek or Latin word parts and suitable references to select a precise meaning.
Interpret subtle or figurative meanings
Explain verbal irony, puns, connotations and relationships between words in context.
Analyze technical language and word choice
Interpret topic vocabulary and explain how analogies or allusions affect meaning and tone.
Writing from texts
Text-based extended responses and essays
Writing from texts
Text-based extended responses and essays
Write a supported argument
Distinguish a claim from opposing claims and support it with logical reasoning and relevant evidence from accurate, credible sources. Show the relationships among claims, counterclaims, reasons and evidence.
Write a clear explanation
Select and organize relevant content to explain a topic. Use precise language, suitable transitions and a conclusion that reflects the information presented.
Keep the response focused and organized
Develop a focused response or essay based on the supplied text or texts. Organize the analysis with an introduction, connected supporting paragraphs and a conclusion.
Use evidence rather than unsupported assertions
Select relevant details or quotations from the supplied text or texts and explain how they support the response.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Control sentence structure, voice and mood
Coordinate phrases and clauses with correct pronoun agreement. Choose active or passive voice and indicative, imperative, interrogative, conditional or subjunctive mood for the intended meaning.
Mark pauses, breaks and omissions
Use commas, dashes and ellipses purposefully and spell correctly, recognizing accepted variants.
Use verb voice and mood for effect
Choose a verb form that emphasizes the intended actor or action or expresses the intended condition or possibility.
Grade 10 MCAS math skills
45 skill groups across 6 topic areasNumbers, units and precision
Roots, rational exponents and quantitative reasoning
Numbers, units and precision
Roots, rational exponents and quantitative reasoning
Connect roots and rational exponents
Explain fractional powers using roots. Rewrite radical and rational-exponent expressions using exponent rules.
Reason about rational and irrational results
Determine whether a sum or product must be rational or irrational and justify the conclusion.
Choose quantities, units and scales
Define useful variables, keep units consistent in a multi-step problem, and interpret a graph scale or origin in context.
Report appropriate measurement precision
Account for measurement and rounding error. Report significant figures that fit the precision of the measuring tools.
Expressions, equations and inequalities
Algebraic structure, solving and graphical solutions
Expressions, equations and inequalities
Algebraic structure, solving and graphical solutions
Interpret and rewrite expressions
Explain terms, factors and coefficients in context. Use structure, factoring, completing the square or exponent rules to reveal zeros, extreme values or growth.
Calculate with polynomials
Add, subtract and multiply polynomial expressions. Expand products, combine like terms and factor expressions using operation properties.
Create equations and inequalities from a situation
Represent a relationship or constraint with linear, quadratic or exponential equations and inequalities. Interpret whether a solution is viable in context.
Rearrange a formula
Isolate a requested quantity in a formula, treating the other quantities as parameters.
Explain equation-solving steps
Justify transformations of an equation using equality and operation properties rather than giving only a numerical answer.
Solve linear equations and inequalities
Solve one-variable equations and inequalities, including literal coefficients and absolute-value equations or inequalities.
Solve quadratic equations
Choose factoring, square roots, completing the square or the quadratic formula. Recognize non-real solutions and express them in a + bi form.
Solve and justify systems of equations
Solve pairs of linear equations exactly or graphically. Explain why adding a multiple of one equation to another preserves the solution set, and solve a simple linear-quadratic system.
Connect equations to their graphs
Interpret each point on a graph as a solution and an intersection as a shared solution. Estimate solutions to f(x) = g(x) with graphs or tables.
Graph inequalities and feasible regions
Graph a linear inequality as a half-plane, distinguish solid and dashed boundaries, and find the overlap for a system.
Functions and models
Representations, rates of change, sequences and transformations
Functions and models
Representations, rates of change, sequences and transformations
Use functions, domains and notation
Identify whether a relationship assigns exactly one output to each input. Evaluate functions and interpret inputs, outputs and domain restrictions in context.
Represent arithmetic and geometric sequences
Recognize a sequence as a function on integer inputs. Write recursive and explicit rules and connect the two forms.
Interpret key features and rates of change
Use graphs or tables to explain intercepts, increasing and decreasing intervals, maxima, minima and end behavior. Calculate or estimate average rate of change.
Graph and compare function representations
Graph linear, quadratic, exponential, absolute-value and piecewise-defined functions. Compare a feature when one function is given as an equation and another as a graph or table.
Choose a useful form of a function
Use factoring or completing the square to reveal quadratic zeros or a vertex. Use exponent rules to expose an exponential growth or decay rate.
Build a function for a situation
Create a linear, quadratic or exponential rule from the stated relationships. Combine simple functions when the context calls for more than one quantity.
Describe changes to a function graph
Determine the effect of adding or multiplying a constant inside or outside a function, and identify the change from two graphs.
Find an inverse of a linear function
Solve y = f(x) for x and interpret the inverse relationship algebraically or graphically.
Distinguish linear and exponential growth
Recognize equal differences versus equal factors. Construct models from data, compare their growth and interpret starting values, rates and other parameters.
Geometry and measurement
Transformations, proofs, coordinates, circles and right triangles
Geometry and measurement
Transformations, proofs, coordinates, circles and right triangles
Use precise geometric definitions
Reason from definitions of angle, circle, line segment, parallel and perpendicular lines when identifying or justifying a relationship.
Represent rigid motions and symmetry
Draw and describe translations, rotations and reflections. Identify which transformations preserve distance and angle and which carry a figure onto itself.
Use and justify triangle congruence
Connect rigid motions with corresponding equal sides and angles. Apply and explain SSS, SAS and ASA criteria.
Prove relationships in lines and polygons
Justify angle relationships, triangle properties and parallelogram properties. Use theorems and their converses to establish a missing relationship.
Explain geometric constructions
Construct or identify steps for copying and bisecting segments or angles, making parallel or perpendicular lines, and inscribing regular figures.
Use dilations and triangle similarity
Apply scale factors, explain proportional sides and equal corresponding angles, and use AA similarity. Use congruence or similarity to prove triangle relationships or solve for lengths.
Solve right triangles
Use sine, cosine, tangent and the Pythagorean theorem. Explain why side ratios depend on an acute angle and why complementary angles connect sine and cosine.
Use circle theorems
Relate central, inscribed and tangent angles to arcs and chords. Use circle similarity, inscribed or circumscribed circles and properties of cyclic figures.
Calculate arc lengths and sector areas
Connect radians to arc length and radius. Use proportions or formulas to calculate an arc length or sector area.
Connect equations with circles and parabolas
Find a circle equation from its center and radius or complete the square to identify them. Relate a parabola equation to its focus and directrix.
Prove and calculate with coordinates
Use distance and slope to prove geometric properties, divide a segment in a ratio, and calculate perimeters or areas from coordinates.
Explain and apply measurement formulas
Explain formulas for a circle or solid using geometric reasoning. Calculate volumes of cylinders, pyramids, cones and spheres.
Statistics and probability
Distributions, data models and conditional probability
Statistics and probability
Distributions, data models and conditional probability
Compare distributions and outliers
Read dot plots, histograms and box plots. Compare center and spread using suitable statistics, including median, mean, interquartile range or standard deviation, and explain the effect of outliers.
Interpret two-way data tables
Calculate joint, marginal and conditional relative frequencies. Use them to identify an association between two categories.
Fit and interpret a data model
Use a scatterplot to describe an association, fit a suitable model and make predictions. Interpret the slope and intercept of a linear model and use residuals to assess the fit.
Interpret correlation without assuming causation
Interpret a calculated correlation coefficient and distinguish a strong statistical association from evidence of cause and effect.
Represent probability events
Describe outcomes with unions, intersections and complements. Use a sample space or two-way table to calculate an event probability.
Distinguish independence and conditional probability
Restrict the sample space to a known event, calculate conditional probability, and decide whether two events are independent.
Find the probability of either event
Add the probabilities of two events and subtract their overlap. Explain the result using the sample space or a data table.
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Problem solving and mathematical reasoning
Choosing a method, explaining it and checking the result
Plan and solve a multi-step problem
Identify the quantities and constraints, choose useful operations or representations, and carry out the steps needed to answer the question.
Explain why a solution works
Support an answer with equations, diagrams, examples or a logical argument. Identify an error in another solution or explain why a proposed method is valid.
Interpret and check a mathematical model
Connect a calculation, graph or equation to the original situation. Check units, assumptions and whether the result is reasonable.
Grade 10 MCAS reading and writing skills
20 skill groups across 5 topic areasLiterary text
Complex characters, developed themes and author choices
Literary text
Complex characters, developed themes and author choices
Build a well-supported interpretation
Use thorough evidence to trace how a theme emerges, develops and becomes more precise.
Analyze complex character development
Explain conflicting motivations, interactions, and their effects on plot or theme.
Explain structure and cultural perspective
Analyze how event order or pacing creates an effect and how a work reflects a particular cultural viewpoint.
Compare literary texts
Explain how an author draws on and transforms a theme or topic from an earlier source text.
Informational text
Rhetoric, developed claims and reasoning
Informational text
Rhetoric, developed claims and reasoning
Use strong informational evidence
Support explanations and inferences with thorough, relevant text evidence.
Trace a developing central idea
Analyze how an idea emerges, is refined by details and supports an objective summary.
Follow a complex sequence of ideas
Explain how an author introduces, orders and connects ideas or events.
Analyze structure and persuasive choices
Explain how particular passages refine a claim and how rhetoric advances the author's purpose.
Evaluate arguments for validity
Check relevance and sufficiency of evidence and identify false statements or flawed reasoning.
Connect information across texts and visuals
Connect information from supplied texts and visual displays. Compare accounts and identify important differences in their facts, evidence or interpretations.
Vocabulary
Word forms, nuances and cumulative effects
Vocabulary
Word forms, nuances and cumulative effects
Determine and verify precise meanings
Use context, changes in word form and reference sources to clarify meaning, word function or origin.
Analyze figurative language and nuance
Explain euphemism, oxymoron and related meanings, including how a series of word choices shapes tone.
Interpret specialized and academic terms
Resolve unfamiliar subject vocabulary and analyze the cumulative effect of wording in nonfiction.
Writing from texts
Text-based extended responses and essays
Writing from texts
Text-based extended responses and essays
Write a supported argument
Develop a precise claim, distinguish it from opposing claims, and support both claims and counterclaims fairly with relevant evidence. Organize reasoning for the intended audience.
Write a clear explanation
Explain a complex topic with well-chosen facts, examples and quotations. Organize the relationships between ideas, use precise vocabulary and maintain a suitable objective tone.
Keep the response focused and organized
Develop a focused response or essay based on the supplied text or texts. Organize the analysis with an introduction, connected supporting paragraphs and a conclusion.
Use evidence rather than unsupported assertions
Select relevant details or quotations from the supplied text or texts and explain how they support the response.
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Grammar, punctuation and word choice
Massachusetts grade-specific conventions and effective language
Use parallel and varied sentence structures
Arrange phrases and clauses with consistent pronoun reference and logical verb tense. Use parallel structure to connect ideas coherently.
Use semicolons and colons
Connect related independent clauses with a semicolon, introduce a list or quotation with a colon and spell correctly.
Edit for precision and appropriate style
Remove ineffective repetition and make language choices that suit the task, audience and writing type.