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LA.A1.Algebra I (A1)
Algebra I (A1)
A1:A-APR. Algebra - Arithmetic with Polynomials and Rational Expressions
A1:A-APR.A. Perform arithmetic operations on polynomials.
A1:A-APR.A.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.
A1:A-CED.A. Create equations that describe numbers or relationships.
A1:A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
A1:A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A1:A-CED.A.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
A1:A-CED.A.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.
A1:A-REI. Reasoning with Equations and Inequalities
A1:A-REI.A. Understand solving equations as a process of reasoning and explain the reasoning.
A1:A-REI.A.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.
A1:A-REI.C.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.
A1:A-REI.D. Represent and solve equations and inequalities graphically.
A1:A-REI.D.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
A1:A-REI.D.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
A1:A-SSE. Algebra - Seeing Structure in Expressions
A1:A-SSE.B. Write expressions in equivalent forms to solve problems.
A1:A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A1:A-SSE.B.3.c. Use the properties of exponents to transform expressions for exponential functions emphasizing integer exponents. For example, the growth of bacteria can be modeled by either f(t) = 3^(t+2) or g(t) = 9(3^t) because the expression 3^(t+2) can be rewritten
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
A1:F-BF. Building Functions
A1:F-BF.A. Build a function that models a relationship between two quantities.
A1:F-BF.A.1. Write a linear, quadratic, or exponential function that describes a relationship between two quantities.
A1:F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
A1:F-IF.A. Understand the concept of a function and use function notation.
A1:F-IF.A.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 GuideFunctions
A1:F-IF.A.3. Recognize that sequences are functions whose domain is a subset of the integers. Relate arithmetic sequences to linear functions and geometric sequences to exponential functions.
A1:F-IF.B. Interpret functions that arise in applications in terms of the context.
A1:F-IF.B.4. For linear, piecewise linear (to include absolute value), quadratic, and exponential functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A1:F-IF.B.6. Calculate and interpret the average rate of change of a linear, quadratic, piecewise linear (to include absolute value), and exponential function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A1:F-IF.C. Analyze functions using different representations.
A1:F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
A1:F-IF.C.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A1:F-LE. Linear, Quadratic, and Exponential Models
A1:F-LE.A. Construct and compare linear, quadratic, and exponential models and solve problems.
A1:F-LE.A.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
A1:F-LE.A.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 GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A1:N-RN. Number and Quantity - The Real Number System
A1:N-RN.B. Use properties of rational and irrational numbers.
A1:N-RN.B.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.
A1:S-ID. Statistics and Probability - Interpreting Categorical and Quantitative Data
A1:S-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.
A1:S-ID.B.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.
A2:A-CED.A. Create equations that describe numbers or relationships.
A2:A-CED.A.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.
A2:A-REI. Reasoning with Equations and Inequalities
A2:A-REI.A. Understand solving equations as a process of reasoning and explain the reasoning.
A2:A-REI.A.1. Explain each step in solving an 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.
A2:A-REI.C.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables. With graphic solutions, systems are limited to two variables.
A2:A-REI.D. Represent and solve equations and inequalities graphically.
A2:A-REI.D.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
A2:A-SSE. Algebra - Seeing Structure in Expressions
A2:A-SSE.B. Write expressions in equivalent forms to solve problems.
A2:A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A2:A-SSE.B.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 ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
A2:F-BF. Building Functions
A2:F-BF.A. Build a function that models a relationship between two quantities.
A2:F-BF.A.1. Write a function that describes a relationship between two quantities.
A2:F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
A2:F-IF.B. Interpret functions that arise in applications in terms of the context.
A2:F-IF.B.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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A2:F-IF.B.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.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A2:F-IF.C. Analyze functions using different representations.
A2:F-IF.C.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
A2:F-IF.C.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 exponen
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
A2:N-RN. Number and Quantity - The Real Number System
A2:N-RN.A. Extend the properties of exponents to rational exponents.
A2:N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
GM:G-CO.A. Experiment with transformations in the plane.
GM:G-CO.A.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.
GM:G-CO.A.2. Represent transformations in the plane using, e.g., transparencies, tracing paper, or geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve
GM:G-CO.A.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
GM:G-CO.A.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.
GM:G-CO.B. Understand congruence in terms of rigid motions.
GM:G-CO.B.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
GM:G-CO.C.9. Prove and apply 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
GM:G-GMD.A. Explain volume formulas and use them to solve problems.
GM:G-GMD.A.1. Give an informal argument, e.g., dissection arguments, Cavalieri’s principle, or informal limit arguments, for the formulas for the circumference of a circle; area of a circle; volume of a cylinder, pyramid, and cone.
GM:G-GPE. Expressing Geometric Properties with Equations
GM:G-GPE.B. Use coordinates to prove simple geometric theorems algebraically.
GM:G-GPE.B.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).
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
GM:G-GPE.B.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
GM:G-SRT. Similarity, Right Triangles, and Trigonometry
GM:G-SRT.A. Understand similarity in terms of similarity transformations.
GM:G-SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:
GM:G-SRT.A.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.
GM:G-SRT.A.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
GM:S-CP. Statistics and Probability - Conditional Probability and the Rules of Probability
GM:S-CP.A. Understand independence and conditional probability and use them to interpret data.
GM:S-CP.A.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.