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Grade Level Essential Standards
Essential standards are a carefully selected subset of the total list of the grade‐specific and course‐specific standards within each content area that students must know and be able to do by the end of each school year in order to be prepared to enter the next grade level or course. Essential Standards do not represent all that is taught at that grade level, rather they represent the minimum a student must learn to reach high levels of learning.
Essential standards have three key components: Endurance: Knowledge and skills of value beyond a single test date. Leverage: Knowledge and skills of value in multiple disciplines. Readiness For the Next Level of Learning; Knowledge and skills that are necessary for success in the next grade level or in the next level of instruction.
This page is designed to give you an overview of the essential standards students will be learning at each grade level. This overview may assist you when you have conversations about classroom work with your child's teacher and as you reinforce learning concepts at home with your children.
Curriculum is different from academic standards in that standards define what students are expected to learn in a particular subject and grade, and a curriculum defines how teachers will teach to ensure students learn the standards. A highquality, research based curriculum has a significant impact on the quality of student learning.
To learn more about District 41's curriculum resource used to direct standards click the link below:
+ click to Eureka2 Math
+ Elementary Literacy Curriculum Resource
+ Hadley Literacy Curriculum Resource

Kindergarten Essential Skills
Literacy Essential Skills

Writing:

Construct simple sentences.

Capitalize I, capitalize beginning letter, use periods.

Write a narrative with events in order

Write about a topic with some information about the topic

Identify a topic and write an opinion about the topic


Reading Behaviors:

Use sounds and pictures to decode words.

Demonstrate onetoone correspondence.

Retell familiar stories with key details.

Understand concepts of print, including that print conveys a message and is organized from left to right and from top to bottom.


Phonics:

Recognize letters and their sounds.

Read and write CVC (consonant, vowel, consonant) words including words with sh, th, ch.

Segment and blend words.

Recognize kindergarten grade highfrequency words.

Math Essential Skills

Counting and Cardinality:

Count by ones and tens up to 100.

Write and represent numbers from 0 to 20.


Operations and Algebraic Thinking:

Understand that addition is putting together and adding to.

Understand that subtraction is taking apart and taking from.

Identify number pairs to 5.


Numbers in Base Ten:

Compose and decompose numbers from 11 29 into tens, ones, and some further ones.



1st Grade Essential Skills
Literacy Essential Skills
Writing

Write complete sentences.

Write narratives with a beginning, middle, and end.

Write about topics with supporting facts and a conclusion.

Reading Behaviors:

Use strategies for unknown words, such as starting at the left of the word, reading each letter, blending the sounds together and chopping the word into syllables.

Build reading stamina by being able to read for 2030 minutes.

Comprehend stories with sequence and main idea.


Comprehension:

Retell a story by including what occurs in the beginning, middle and end.

Be able to identify a topic of a story and the details that are connected to it.


Phonics:

Read and write words with phonics patterns including digraphs, beginning blends, common endings (ing, ed, s, er), and short and long vowel sounds.

Recognize first grade highfrequency words.

Math Essential Skills
Operations and Algebraic Thinking:

Solve word problems using addition and subtraction within 20.

Fluently add and subtract within 10.


Numbers and Operations  Base Ten:

Count to 120, starting at any number less than 120.

Understand that the two digits of a twodigit number represent amounts of tens and ones.

Given a twodigit number, mentally find 10 more or 10 less than the number without having to count.

Add within 100 and when doing so understand that in adding twodigit numbers, tens are added to tens and ones are added to ones; and sometimes it is necessary to compose a ten.



2nd Grade Essential Skills
Literacy Essential Skills

Writing:

Write a narrative with a beginning, middle and end that includes details to describe characters.

Write an expository and an opinion about a topic with supporting facts and definitions to develop/prove a point and include a conclusion.

Expand on a single sentence through elaboration and word choice.

Organize and group similar information together on a page.


Reading Behaviors:

Choose appropriate books.

Build reading stamina by being able to read for 2030 minutes.

Track comprehension across longer texts.

Use strategies for unknown words, such as blending the sounds together, chopping the words into syllables, separating the base word from the prefix/suffix, and rereading to determine if it makes sense.


Comprehension:

Identify story elements such as the setting, characters, problem and solution.

Retell a story sequence of important events.

Identify a character’s feelings with evidence from the text.

Identify text features such as headings, captions and glossaries and their purpose in informational text.


Phonics:

Read and write words with blends, digraphs, and long vowel patterns.

Recognize second grade highfrequency words.

Math Essential Skills
Operations and Algebraic Thinking:

Fluently add and subtract within 20.

Use addition and subtraction within 100 for word problems involving one and twosteps.


Numbers and Operations  Base Ten:

Understand that the three digits of a threedigit number represent amounts of hundreds, tens and ones.

Skip count by 5s, 10s, and 100s within 1,000.

Read and write numbers to 1,000.

Add and subtract within 1,000 and when doing so understand that one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens and hundreds.


Geometry:

Partition circles and rectangles into two, three, or four equal shares and describe the shares using the words halves, thirds, a half of, a third of, etc., and describe the whole as two halves, three thirds, or four fourths.



3rd Grade Essential Skills
Literacy Essential Skills

Writing:

Write a narrative in an organized sequence with descriptive details and dialogue.

Write an opinion about the topic with organized reasons and supporting details.

Organize and group similar information together on a page and use appropriate paragraphing structure.


Reading Literature and Informational Text:

Identify story elements (character, setting, problem rising action, climax, and resolution), understand their role in the story, and use them to retell the story.

Describe a character using their character traits and motivations with support from the text.

Identify the main idea and determine the important details, leaving out personal opinions and insignificant details.

Use evidence to support claims.


Word Study:

Apply phonics and word analysis skills when decoding words.

Math Essential Skills
Operations and Algebraic Thinking:

Fluently multiply and divide within 100 and be able to recall from memory the products of two onedigit numbers.

Represent and solve problems involving multiplication and division within 100.


Numbers and Operations  Base Ten:

Fluently add and subtract within 1,000.

Round whole numbers to the nearest 10 or 100.


Numbers and Operations  Fractions:

Understand a unit fraction (1/b) as the quantity formed by 1 part when the whole is partitioned into b equal parts, and a fraction a/b as a quantity formed by a unit fractions.

Identify and label fractions on the number.

Compare fractions by reasoning about their size.



4th Grade Essential Skills
Literacy Essential Skills
Writing

Write a narrative in an organized sequence with descriptive details, strongly developed character, transitional words and dialogue

Write about a topic, organize facts and definitions with paragraphs, include quotations

Write an opinion about the topic with organized structure including reasons that are supported by facts and details

Meets grade level conventions expectations
Reading Fiction Text

Increase vocabulary to describe character traits using evidence from the text (moving beyond ‘nice or angry’)

Add theme to story elements and introduce protagonist & antagonist

Determine a theme and give evidence to support your thinking

Write a paragraph using evidence to back up a statement/claim (character, theme, etc)
Reading NonFiction Text

Identify ONE main idea correctly with supporting details

Synthesize information on a topic from two or more sources
Word Study

Know and apply gradelevel phonics and word analysis skills in decoding words.
Math Essential SkillsOperations and Algebraic Thinking

Solve multistep word problems using the four operations with whole numbers
Numbers and OperationsBase Ten

Add, subtract, multiply, and divide multidigit whole numbers

Fluently add and subtract multidigit whole numbers using standard algorithm

Place Value (1s to 1 million)
Numbers and OperationsFractions

Add/subtract fractions with like denominators


5th Grade Essential Skills
Literacy Essential Skills
Writing

Write a narrative in an organized sequence with narrator. Include descriptive details, strongly developed character and character’s response to events.

Write about a topic, organize facts and definitions with paragraphs, include quotations, use text features like headings

Write an opinion about the topic with logically organized reasons that are supported by facts and details

Meets grade level conventions expectations
Reading Fiction Text

Determine a theme using characters’ actions and responses supported by evidence from the text

Identify and interpret figurative language

Write a paragraph stating a claim and using evidence to back up a statement
Reading NonFiction Text

Identify two or more main ideas and supporting details when summarizing text

Synthesize information on a topic from several sources
Word Study

Know and apply gradelevel phonics and word analysis skills in decoding words.
Math Essential SkillsOperations and Algebraic Thinking

Use parentheses, bracket, or braces in numerical expressions, and evaluate expressions with these symbols

Solve multistep real world problems related to the above skills
Numbers and OperationsBase Ten

Add, subtract, multiply, and divide whole numbers and decimals to the thousandths place utilizing place value strategies and standard algorithm

Use place value understanding to round decimals to any place
Numbers and OperationsFractions

Add, subtract, multiply, and divide fractions with unlike denominators and mixed numbers


6th Grade Essential Skills
Literacy Essential Skills
Literacy Habits

Read texts from a wide variety of genres, both independently and with teacher support.

Cite text evidence to support ideas when writing or speaking to support conclusions drawn from the text.

Write in response to literature, informational text, poetry, video, audio and other live versions of text.

Develop and revise writing by planning, revising, and editing.

Determine the meanings of words using a variety of strategies (Latin/Greek roots/affixes; figurative language, etc.
Reading Literature and Informational Text

Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a theme of or central idea of a text and how it is conveyed through particular details; provide a summary of the text free from personal opinions or judgments.

Describe and explain how the plot of a story or drama unfolds in a series of progressive episodes, noting the evolution of characters as the plot develops and resolves.

Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings, and how a specific word choice affects the meaning and tone of a text.

Determine (infer) the author’s point of view or purpose in a text and explain the techniques used to express the author’s perspective and purpose.

Trace and evaluate the argument and specific claims in a text.
Writing

Write arguments to support claims with clear reasons and relevant evidence.

Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and wellstructured event sequences.

Gather relevant information from multiple print and digital sources, assess the credibility of each source, and quote or paraphrase the information and conclusions of others.

Draw evidence from literary or informational texts to support analysis, reflection, and research.
Speaking and Listening

Engage in a range of collaborative discussions with diverse partners on topics, texts, and issues, building on the ideas of others and expressing ideas clearly while providing evidence from a text and posing and responding to questions.
Language

Use knowledge of language arts and its conventions when writing, speaking, reading, or listening.

Determine or clarify the meaning of unknown and multiplemeaning words and phrases by using context clues, syntax, and Greek or Latin affixes and roots.
Math Essential SkillsThe Number System:

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Compute fluently with multidigit numbers and find common factors and multiples.

Apply and extend previous understandings of numbers to the system of rational numbers.
Ratios and Proportional Relationships:

Understand ratio concepts and use ratio reasoning to solve problems.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Use ratio and rate reasoning to solve realworld and mathematical problems.
Expressions and Equations:

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and evaluate numerical expressions involving wholenumber exponents.

Write, read, and evaluate expressions in which letters stand for numbers.

Apply the properties of operations to generate equivalent expressions.

Identify when two expressions are equivalent.

Reason about and solve onevariable equations and inequalities.

Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Represent and analyze quantitative relationships between dependent and independent variables.
Geometry:

Solve realworld and mathematical problems involving area, surface area, and volume.

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.

Draw polygons in the coordinate plane given coordinates for the vertices.

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
Statistics and Probability:

Develop understanding of statistical variability.

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Summarize numerical data sets in relation to their context.


7th Grade Essential Skills
Literacy Essential Skills
Literacy Habits

Read texts from a wide variety of genres, both independently and with teacher support

Cite text relevant evidence to support ideas when writing or speaking to support conclusions drawn from the text.

Determine the meanings of words using a variety of strategies (Latin/Greek roots/affixes; figurative language, etc.)

Write in response to literature, informational text, poetry, video, audio and other live versions of text
Reading Literature and Informational Text

Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a theme of or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.

Analyze the interactions between individuals, events, and ideas, or how particular elements interact within a text (informational, story, or drama).

Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings, repetition of sounds (poetry), and technical meanings, and how a specific word choice affects the meaning and tone of a text.

Analyze and identify the techniques used when an author develops and contrasts the points of view of different characters or narrators in a text.

Determine an author’s point of view or purpose in an informational text and analyze how the author distinguishes his or her position.

Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient.
Writing

Write arguments to support claims with clear reasons and relevant evidence.

Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and wellstructured event sequences.

Gather relevant information from multiple print and digital sources, using effective search terminology, assess the credibility of each source, and quote or paraphrase the data and conclusions of others.

Draw evidence from literary or informational texts to support analysis, reflection, and research.
Speaking and Listening

Engage in a range of collaborative discussions with diverse partners on topics, texts, and issues, building on the ideas of others and expressing ideas clearly while providing evidence from a text, posing and responding to questions, and eliciting elaboration with relevant observations and ideas.
Language

Use knowledge of language arts and its conventions when writing, speaking, reading, or listening.

Determine or clarify the meaning of unknown and multiplemeaning words and phrases by using context clues, syntax, and Greek or Latin affixes and roots.
Math Essential SkillsThe Number System:

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Solve realworld and mathematical problems involving the four operations with rational numbers.
Ratios and Proportional Relationships:

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Recognize and represent proportional relationships between quantities.

Decide whether two quantities are in a proportional relationship.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Represent proportional relationships by equations.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Use proportional relationships to solve multistep ratio and percent problems.
Expressions and Equations:

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
Geometry:

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Describe the twodimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Know the formulas for the area and circumference of a circle and use them to solve problems.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
The Number System:

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Solve realworld and mathematical problems involving the four operations with rational numbers.
Ratios and Proportional Relationships:

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Recognize and represent proportional relationships between quantities.

Decide whether two quantities are in a proportional relationship.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Represent proportional relationships by equations.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Use proportional relationships to solve multistep ratio and percent problems.
Expressions and Equations:

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Statistics and Probability:

Understand that statistics can be used to gain information about a population by examining a sample of the population.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Draw informal comparative inferences about two populations.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood.

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability.

Develop a probability model and use it to find probabilities of events.

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.


8th Grade Literacy Essential Skills
Literacy Essential Skills
Literacy Habits

Read texts from a wide variety of genres, both independently and with teacher support

Cite text evidence from two or more print and digital sources to support ideas when writing or speaking to support conclusions drawn from the text, using appropriate citations and analysis

Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

Determine the meanings of words using a variety of strategies (Latin/Greek roots/affixes; figurative language, etc.)
Reading Literature and Informational Text

Cite the textual evidence that strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a theme of or central idea of a text and analyze its development over the course of the text including the relation to characters, setting, and plot or supporting ideas; provide an objective summary of the text.

Analyze how lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.

Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings or technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.

Analyze the differences in points of view between the characters and the reader/audience; examine how the author uses literary techniques to create a mood.

Determine an author’s point of view or purpose in an informational text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints.

Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient.
Writing

Write arguments to support claims with clear reasons and relevant evidence.

Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and wellstructured event sequences.

Develop a thesis or claim with relevant, wellchosen facts, definitions, concrete details, quotations, or other information and examples.

Gather relevant information from multiple print and digital sources, using effective search terminology, assess the credibility and accuracy of each source, and quote or paraphrase the data and conclusions of others.

Draw evidence from literary or informational texts to support analysis, reflection, and research.
Speaking and Listening

Engage in a range of collaborative discussions with diverse partners on topics, texts, and issues, building on the ideas of others and expressing ideas clearly while providing evidence from a text, posing and responding to questions that connect ideas from several speakers, and eliciting elaboration with relevant observations and ideas.

Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.
Language

Use knowledge of language arts and its conventions when writing, speaking, reading, or listening.

Determine or clarify the meaning of unknown and multiplemeaning words and phrases by using context clues, syntax, and Greek or Latin affixes and roots.


8th Grade Math Essential Skills
Math Essential Skills
The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

Identifying numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats.

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
Expressions and Equations

Work with radicals and integer exponents.

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b

Solve linear equations in one variable.
Expressions and Equations

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.

Solve realworld and mathematical problems leading to two linear equations in two variables.
Functions

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables.

Understand that a function is a rule that assigns to each input exactly has one output.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Use functions to model relationships between quantities.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph.
Geometry

Verify experimentally the properties of rotations, reflections, and translations.

Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures.

Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates.

Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles.

Explain a proof of the Pythagorean Theorem.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.
Statistics and Probability

Describe patterns such as clustering, outliers, positive or negative, linear, and nonlinear.

Understand that straight lines are widely used to model relationships between two quantitative variables.

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.


8th Grade Algebra Essential Skills
Algebra Essential Skills
The Real Number System

Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
Algebra

Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Factor a quadratic expression to reveal the zeros of the function it defines
Algebra

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Use the properties of exponents to transform expressions for exponential functions.

Write expressions in equivalent forms to solve problems, ie: compound interest

Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Understand the relationship between zeros and factors of polynomial.

Use polynomial identities to solve problems.

Rewrite rational expressions. Rewrite simple rational expressions in different forms.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions..

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve equations and inequalities in one variable. Solve quadratic equations in one variable.
Algebra

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

Solve quadratic equations square roots, completing the square, the quadratic formula and factoring.

Solve systems of equations., graphically and algebraically.

Represent and solve equations and inequalities graphically. Explain why the xcoordinates of the points where the graphs of the equations
y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values. Also, where f(x) and/or g(x) are linear, rational, absolute value, exponential, and functions
Functions

Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Interpret functions that arise in applications in terms of the context, a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship increasing, decreasing, positive, or negative, etc.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Graph piecewisedefined functions, including step functions and absolute value functions.
Functions

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available.

Use the process of factoring and completing the square in a quadratic function to show zeros.

Use the properties of exponents to interpret expressions for exponential functions.

Write a function that describes a relationship between two quantities.

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations..

Find inverse functions.

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs.
Statistics and Probability

Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).

Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

Summarize categorical data for two categories in twoway frequency tables.

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
