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### A Algebra

- A.SSE Seeing Structure in Expressions
- Interpret the structure of expressions.
- A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
- A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.
- A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.

- A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

- A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
- Write expressions in equivalent forms to solve problems.
- A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
- A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- A.SSE.3c Use the properties of exponents to transform expressions for exponential functions.

- A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

- Interpret the structure of expressions.
- A.APR Arithmetic with Polynomials and Rational Expressions
- Perform arithmetic operations on polynomials.
- A.APR.1 Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- A.APR.1a Focus on polynomial expressions that simplify to forms that are linear or quadratic.

- A.APR.1 Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

- Perform arithmetic operations on polynomials.
- A.CED Creating Equations
- Create equations that describe numbers or relationships.
- A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
- A.CED.1b Focus on applying simple quadratic expressions.

- A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A.CED.2b Focus on applying simple quadratic expressions.

- A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- A.CED.4c Focus on formulas in which the variable of interest is linear or square.

- A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

- Create equations that describe numbers or relationships.
- A.REI Reasoning with Equations and Inequalities
- Solve equations and inequalities in one variable.
- A.REI.4 Solve quadratic equations in one variable.
- A.REI.4a 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. - A.REI.4b Solve quadratic equations as appropriate to the initial form of the equation by inspection, e.g., for
*x*² = 49; taking square roots; completing the square; applying the quadratic formula; or utilizing the Zero-Product Property after factoring. - A.REI.4c Derive the quadratic formula using the method of completing the square.

- A.REI.4a Use the method of completing the square to transform any quadratic equation in

- A.REI.4 Solve quadratic equations in one variable.
- Solve systems of equations.
- A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

- Represent and solve equations and inequalities graphically.
- A.REI.11 Explain why the
*x*-coordinates of the points where the graphs of the equation*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, making tables of values, or finding successive approximations.

- A.REI.11 Explain why the

- Solve equations and inequalities in one variable.

### F Functions

- F.IF Interpreting Functions
- Interpret functions that arise in applications in terms of the context.
- F.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.
- F.IF.4b Focus on linear, quadratic, and exponential functions.

- F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
- F.IF.5b Focus on linear, quadratic, and exponential functions.

- F.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.
- Analyze functions using different representations.
- F.IF.7 Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
- F.IF.7b Graph quadratic functions and indicate intercepts, maxima, and minima.

- F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
*Focus on completing the square to quadratic functions with the leading coefficient of 1.* - F.IF.8b Use the properties of exponents to interpret expressions for exponential functions.
*Focus on exponential functions evaluated at integer inputs.*

- F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
- F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- F.IF.9b Focus on linear, quadratic, and exponential functions.

- F.IF.7 Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.

- Interpret functions that arise in applications in terms of the context.
- F.BF Building Functions
- Build a function that models a relationship between two quantities.
- F.BF.1 Write a function that describes a relationship between two quantities.
- F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from context.
*Focus on situations that exhibit quadratic or exponential relationships.*

- F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from context.

- F.BF.1 Write a function that describes a relationship between two quantities.
- Build new functions from existing functions.
- F.BF.3 Identify the effect on the graph of replacing
*f*(*x*) by*f*(*x*) +*k*,*k**f*(*x*),*f*(*k**x*), and*f*(*x*+*k*) for specific values of*k*(both positive and negative); find the value of*k*given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.- F.BF.3a Focus on transformations of graphs of quadratic functions, except for
*f*(*k**x*).

- F.BF.3a Focus on transformations of graphs of quadratic functions, except for

- F.BF.3 Identify the effect on the graph of replacing

- Build a function that models a relationship between two quantities.
- F.LE Linear, Quadratic, and Exponential Models
- Construct and compare linear, quadratic, and exponential models, and solve problems.
- F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

- Construct and compare linear, quadratic, and exponential models, and solve problems.

### G Geometry

- G.SRT Similarity, Right Triangles, and Trigonometry
- Understand similarity in terms of similarity transformations.
- G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
- G.SRT.1a A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged.
- G.SRT.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

- G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
- G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

- G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
- Prove and apply theorems both formally and informally involving similarity using a variety of methods.
- G.SRT.4 Prove and apply theorems about triangles.
- G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.

- Define trigonometric ratios, and solve problems involving right triangles.
- G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
- G.SRT.8 Solve problems involving right triangles.
- G.SRT.8a Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given.
- G.SRT.8b Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

- Understand similarity in terms of similarity transformations.
- G.C Circles
- Understand and apply theorems about circles.
- G.C.1 Prove that all circles are similar using transformational arguments.

- Find arc lengths and areas of sectors of circles.
- G.C.5 Find arc lengths and areas of sectors of circles.
- G.C.5a Apply similarity to relate the length of an arc intercepted by a central angle to the radius. Use the relationship to solve problems.
- G.C.5b Derive the formula for the area of a sector, and use it to solve problems.

- G.C.5 Find arc lengths and areas of sectors of circles.

- Understand and apply theorems about circles.
- G.GPE Expressing Geometric Properties with Equations
- Translate between the geometric description and the equation for a conic section.
- G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

- Use coordinates to prove simple geometric theorems algebraically and to verify specific geometric statements.
- G.GPE.4 Use coordinates to prove simple geometric theorems algebraically and to verify geometric relationships algebraically, including properties of special triangles, quadrilaterals, and circles.
- G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

- Translate between the geometric description and the equation for a conic section.
- G.GMD Geometric Measurement and Dimension
- Explain volume formulas, and use them to solve problems.
- G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
- G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

- Visualize relationships between two-dimensional and three-dimensional objects.
- G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

- Understand the relationships between lengths, area, and volumes.
- G.GMD.5 Understand how and when changes to the measures of a figure (lengths or angles) result in similar and non-similar figures.
- G.GMD.6 When figures are similar, understand and apply the fact that when a figure is scaled by a factor of
*k*, the effect on lengths, areas, and volumes is that they are multiplied by*k*,*k*², and*k*³, respectively.

- Explain volume formulas, and use them to solve problems.
- G.MG Modeling with Geometry
- Apply geometric concepts in modeling situations.
- G.MG.1 Use geometric shapes, their measures, and their properties to describe objects, e.g., modeling a tree trunk or a human torso as a cylinder.
- G.MG.2 Apply concepts of density based on area and volume in modeling situations, e.g., persons per square mile, BTUs per cubic foot.
- G.MG.3 Apply geometric methods to solve design problems, e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios.

- Apply geometric concepts in modeling situations.

### S Statistics and Probability

- S.CP Conditional Probability and the Rules of Probability
- Understand independence and conditional probability, and use them to interpret data.
- S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
- S.CP.2 Understand that two events A and B are independent if and only if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
- S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
- S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
- S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

- Use the rules of probability to compute probabilities of compound events in a uniform probability model.
- S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
- S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
- S.CP.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)·P(B|A) = P(B)·P(A|B), and interpret the answer in terms of the model.
- S.CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems.

- Understand independence and conditional probability, and use them to interpret data.