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A-APR. Arithmetic with Polynomials and Rational Functions Perform arithmetic operations on polynomials. 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.
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. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constrai
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
A-REI. Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning. A-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.
Solve equations and inequalities in one variable. A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Solve systems of equations. A-REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Represent and solve equations and inequalities graphically. A-REI.11. Explain 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 va
A-REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the correspondin
A-SSE. Seeing Structure in Expressions 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.3.c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.15^(1/12))^12t approximately equals 1.012^12t to reveal the approximate equivalent monthly interest rate if the an Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
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.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-IF. Interpreting Functions Understand the concept of a function and use function notation. F-IF.1. 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f c Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-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 greater than or equal to 1. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
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. Key features include: intercep
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations. F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. F-IF.7.a. Graph linear and quadratic functions and show 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.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 Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-LE. Linear and Exponential Models Construct and compare linear and exponential models and solve problems. F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. F-LE.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
G-CO. Congruence Experiment with transformations in the plane G-CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G-CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
G-CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G-CO.4. Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
G-CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motions G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a rigid motion on a figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Prove geometric theorems G-CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
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, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
G-GMD.3. Use volume formulas for cylinders, pyramids, cones and spheres to solve problems.
G-GPE. Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraically G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G-GPE.7. Use coordinates to compute perimeters of polygons and areas for triangles and rectangles, e.g. using the distance formula.
G-SRT. Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations G-SRT.1. Verify experimentally the properties of dilations: G-SRT.1.a. 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.1.b. 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
Prove theorems involving similarity G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MP-1. Apply geometric concepts in modeling situations
MP-2. Make sense of problems and persevere in solving them.
MP-3. Reason abstractly and quantitatively.
WI.CC.N.Number and Quantity
N-RN. The Real Number System Extend the properties of exponents to rational exponents. N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Use properties of rational and irrational numbers. N-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.
WI.CC.S.Statistics and Probability
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.2. Understand that two events A and B are independent 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-ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal and conditional relative frequencies). Recognize possible associations and trends in the data.
S-ID.6. Represent data on two quantitative variables on a scatter plot and describe how the variables are related. S-ID.6.b. Informally assess the fit of a model function by plotting and analyzing residuals.
S-ID.6.c. Fit a linear function for scatter plots that suggest a linear association.