Language |
| L.9-10: Knowledge of Language |
| L.9-10.3 | Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. |
| Vocabulary Acquisition and Use |
| L.9-10.5b | Analyze nuances in the meaning of words with similar denotations. |
| L.11-12: Knowledge of Language |
| L.11-12.3 | Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. |
Reading History/Social Studies |
| RH.9-10: Craft and Structure |
| RH.9-10.5 | Analyze how a text uses structure to emphasize key points or advance an explanation or analysis. |
| Key Ideas and Details |
| RH.9-10.1 | Cite specific textual evidence to support analysis of primary and secondary sources, attending to such features as the date and origin of the information. |
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| RH.9-10.2 | Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events or ideas develop over the course of the text. |
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| RH.9-10.3 | Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them. |
| Range of Reading and Level of Text Complexity |
| RH.9-10.10 | By the end of grade 10, read and comprehend history/social studies texts in the grades 9–10 text complexity band independently and proficiently. |
| RH.11-12: Key Ideas and Details |
| RH.11-12.2 | Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas. |
| Range of Reading and Level of Text Complexity |
| RH.11-12.10 | By the end of grade 12, read and comprehend history/social studies texts in the grades 11–CCR text complexity band independently and proficiently. |
Reading Informational |
| RI.9-10: Key Ideas and Details |
| RI.9-10.2 | Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. |
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| RI.9-10.3 | Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them. |
| Range of Reading and Level of Text Complexity |
| RI.9-10.10 | By the end of grade 9, read and comprehend literary nonfiction in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range. |
| RI.11-12: Integration of Knowledge and Ideas |
| RI.11-12.9 | Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features. |
Reading Literature |
| RL.9-10: Craft and Structure |
| RL.9-10.5 | Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise. |
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| RL.9-10.6 | Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature. |
| Integration of Knowledge and Ideas |
| RL.9-10.9 | Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare). |
| Key Ideas and Details |
| RL.9-10.2 | Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. |
| Range of Reading and Level of Text Complexity |
| RL.9-10.10 | By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range. |
| RL.11-12: Range of Reading and Level of Text Complexity |
| RL.11-12.10 | By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. |
Writing |
| W.9-10: Production and Distribution of Writing |
| W.9-10.4 | Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) |
| Research to Build and Present Knowledge |
| W.9-10.9 | Draw evidence from literary or informational texts to support analysis, reflection, and research. |
| Text Types and Purposes |
| W.9-10.1 | Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. |
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| W.9-10.2 | Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. |
Writing HS/S/T |
| WHST.11-12: Research to Build and Present Knowledge |
| WHST.11-12.9 | Draw evidence from informational texts to support analysis, reflection, and research. |
Arithmetic With Polynomials And Rational Expressions |
| HSA.APR: Rewrite Rational Expressions |
| HSA.APR.6 | Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. |
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| HSA.APR.7 | (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. |
Geometric Measurement And Dimension |
| HSG.GMD: Explain Volume Formulas And Use Them To Solve Problems |
| HSG.GMD.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★ |
Interpreting Categorical And Quantitative Data |
| HSS.ID: Interpret Linear Models |
| HSS.ID.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. |
Interpreting Functions |
| HSF.IF: Analyze Functions Using Different Representations |
| HSF.IF.7.a | Graph linear and quadratic functions and show intercepts, maxima, and minima. |
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| HSF.IF.7.d | (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. |
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| HSF.IF.8.b | Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. |
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| HSF.IF.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. |
| Interpret Functions That Arise In Applications In Terms Of The Context |
| HSF.IF.4 | For 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ |
| Understand The Concept Of A Function And Use Function Notation |
| HSF.IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
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| HSF.IF.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. |
Linear, Quadratic, And Exponential Models |
| HSF.LE: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems |
| HSF.LE.3 | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. |
Quantities |
| HSN.Q: Reason Quantitatively And Use Units To Solve Problems. |
| HSN.Q .1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. |
Reasoning With Equations And Inequalities |
| HSA.REI: Represent And Solve Equations And Inequalities Graphically |
| HSA.REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
| Solve Equations And Inequalities In One Variable |
| HSA.REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
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| HSA.REI.4 | Solve quadratic equations in one variable. |
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| HSA.REI.4.b | Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. |
| Solve Systems Of Equations |
| HSA.REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. |
| Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning |
| HSA.REI.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. |
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| HSA.REI.2 | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. |
Seeing Structure In Expressions |
| HSA.SSE: Interpret The Structure Of Expressions |
| HSA.SSE.2 | Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). |
| Write Expressions In Equivalent Forms To Solve Problems |
| HSA.SSE.3.a | Factor a quadratic expression to reveal the zeros of the function it defines. |
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| HSA.SSE.3.c | Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. |
The Complex Number System |
| HSN.CN: Perform Arithmetic Operations With Complex Numbers. |
| HSN.CN.1 | Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. |
| Use Complex Numbers In Polynomial Identities And Equations. |
| HSN.CN.7 | Solve quadratic equations with real coefficients that have complex solutions. |
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| HSN.CN.9 | (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. |
The Real Number System |
| HSN.RN: Extend The Properties Of Exponents To Rational Exponents. |
| HSN.RN.1 | 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. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. |
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| HSN.RN.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. |
| Use Properties Of Rational And Irrational Numbers. |
| HSN.RN.3 | Explain why the sum or product of two 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. |
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