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Reading & Writing Process

Students will use a variety of recursive reading and writing processes.

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Algebra

Seeing Structure in Expressions

9-12.A-SSE.1 - 9-12.A-SSE.2 Interpret the structure of expressions.

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9-12.A-SSE.1

Interpret expressions that represent a quantity in terms of its context

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9-12.A-SSE.2

Use the structure of an expression to identify ways to rewrite it

9-12.A-SSE.4 Write expressions in equivalent forms to solve problems.

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9-12.A-SSE.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems

Arithmetic with Polynomials and Rational Expressions

9-12.A-APR.1 Perform arithmetic operations on polynomials.

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9-12.A-APR.1

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

9-12.A-APR.2 - 9-12.A-APR.3 Understand the relationship between zeros and factors of polynomials.

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9-12.A-APR.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x)

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9-12.A-APR.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial

9-12.A-APR.4 - 9-12.A-APR.5 Use polynomial identities to solve problems.

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9-12.A-APR.4

Prove polynomial identities and use them to describe numerical relationships

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9-12.A-APR.5

Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where
x and y are any numbers, with coefficients determined for example by Pascal’s Triangle

9-12.A-APR.6 - 9-12.A-APR.7 Rewrite rational expressions.

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9-12.A-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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9-12.A-APR.7

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtrac- tion, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions

Creating Equations

9-12.A-CED.1 - 9-12.A-CED.4 Create equations that describe numbers or relationships.

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9-12.A-CED.1

Create equations and inequalities in one variable including ones with absolute value and use them to solve problems

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9-12.A-CED.2

Create equations in two or more variables to represent relationships between quantities; graph

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9-12.A-CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context

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9-12.A-CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations

Reasoning with Equations and Inequalities

9-12.A-REI.2 Understand solving equations as a process of reasoning and explain the reasoning.

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9-12.A-REI.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

9-12.A-REI.3.1 Solve equations and inequalities in one variable.

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9-12.A-REI.3.1

Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context

9-12.A-REI.11 Represent and solve equations and inequalities graphically.

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9-12.A-REI.11

xplain why the x-coordinates 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, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions

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