Parents, these are the standards taught by Beyond Textbooks partner schools. This list is in alphanumeric order, and your school will likely teach them in a different order. For help deciphering the code in front of the standard, please click here.
Alg1.M.A.CED.A.01: The Highly Proficient student can 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.
Alg1.M.A.CED.A.02: The Highly Proficient student can compare and contrast equations and graphs that model linear and exponential relationships. Additionally, they can write or create a system of linear inequalities given a graph or a context, and they can identify the solution set as a region of the coordinate plane that satisfies all inequalities.
Alg1.M.A.REI.A.01: The Highly Proficient student can 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.
Alg1.M.A.REI.B.03: The Highly Proficient student can create, solve and graph linear equations and inequalities in one variable.
Alg1.M.A.S.ID.B.06c: The Highly Proficient student can compare the fit of functions (including exponential) to data and determine which function has the best fit.
Alg1.M.A.S.ID.C.08: The Highly Proficient student can calculate and interpret the correlation coefficient of a set of linear data and determine whether a correlation implies causation.
Alg1.M.A.SSE.A.01a: The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression.
Alg1.M.F.BF.A.01: The Highly Proficient student can write a function that describes a relationship between two quantities.
Alg1.M.F.IF.A.02: The Highly Proficient student can apply and extend knowledge of domain and range to real world contexts and situations. Additionally, they can create a function for a given context where the domain meets certain parameters.
Alg1.M.F.IF.B.04: The Highly Proficient student can create a story or context modeling key features of linear, quadratic, square root, cube root, piecewise, step, absolute value and exponential functions.
Alg1.M.F.IF.B.06: The Highly Proficient student can calculate and describe the rate of change of a graph or table given specific intervals.
Alg1.M.F.IF.C.09: The Highly Proficient student can 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.
Alg1.M.N.Q.A.03: The Highly Proficient student can choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Alg1.M.N.RN.B.03: The Highly Proficient student can explain why the sum or product of two rational numbers are 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.
Alg1.M.S.ID.B.05: The Highly Proficient student can 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.
Alg1.M.S.ID.B.06: The Highly Proficient student can represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or chooses a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals.
Alg1.M.S.ID.C.07: The Highly Proficient student can interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Alg1.M.S.ID.C.09: The Highly Proficient student can distinguish between correlation and causation.
Alg1.M.A.APR.A.01: The Highly Proficient student can use addition, subtraction, and multiplication to create equivalent polynomial expressions.
Alg1.M.A.CED.A.03: The Highly Proficient student can 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Alg1.M.A.REI.C.05: The Highly Proficient student can 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.
Alg1.M.A.REI.C.06: The Highly Proficient student can analyze a system of equations and choose a method to solve exactly and approximately given a context or real-world situation.
Alg1.M.A.REI.D.10: The Highly Proficient student can 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).
Alg1.M.A.REI.D.11: The Highly Proficient student can 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 values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Alg1.M.A.REI.D.12: The Highly Proficient student can create and graph up to three inequalities in two variables and find their solution set.
Alg1.M.F.BF.A.02: The Highly Proficient student can write recursive and explicit formulas for arithmetic and geometric sequences.
Alg1.M.F.IF.C.07a: The Highly Proficient student can graph and compare linear functions.
Alg1.M.F.LE.A.01: The Highly Proficient student can describe the rate of change of a function and can prove that over equal intervals, linear functions grow by equal differences and exponential functions grow by equal factors.
Alg1.M.F.LE.A.02: The Highly Proficient student can create both linear and exponential functions from graphs, patterns, tables, and descriptions of relationships.
Alg1.M.F.LE.A.03: The Highly Proficient student can observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Alg1.M.F.LE.B.05: The Highly Proficient student can interpret the parameters in a linear or exponential function in terms of a context.
Alg1.M.A.APR.B.03: The Highly Proficient student can identify the zeros of a quadratic function graph and use the zeros to construct the quadratic function.
Alg1.M.A.CED.A.04: The Highly Proficient student can 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.
Alg1.M.A.REI.B.04: The Highly Proficient student can determine the most efficient method for solving quadratic equations and justify their choice. The Highly Proficient student can recognize when quadratic equations have no real solutions.
Alg1.M.A.S.ID.A.01: The Highly Proficient student can determine and justify the most appropriate type of data plot for a set of data. The Highly Proficient student can identify advantages and disadvantages of different types of data plots.
Alg1.M.A.S.ID.A.02: The Highly Proficient student can plot multiple data sets and compare and discuss the data plots using measures of center and spread for the data. Additionally, they can explore and manipulate additional data sets and justify which measures are most appropriate for comparison. They will be able to identify advantages and disadvantages of using each type of measure of center and spread.
Alg1.M.A.SSE.A.02: The Highly Proficient student can 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).
Alg1.M.A.SSE.B.03: The Highly Proficient student can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Alg1.M.A.SSE.B.04: The Highly Proficient student can 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. For example, calculate mortgage payments.
Alg1.M.F.IF.A.01: The Highly Proficient student can 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 corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Alg1.M.F.IF.C.07b: The Highly Proficient student can graph and compare linear, quadratic, piecewise, step and absolute value functions in various forms.
Alg1.M.F.IF.C.09: The Highly Proficient student can construct linear, quadratic, piecewise, step, absolute value and exponential functions over integer domains given certain function characteristics or given values greater than or lesser than a given function.
Alg1.M.F.IF.C.08: The Highly Proficient student can write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Alg1.M.N.Q.A.02: The Highly Proficient student can define appropriate quantities for the purpose of descriptive modeling.
Alg1.M.F.IF.A.01: The Highly Proficient student can apply and extend knowledge of domain and range to real world situations and contexts.
Alg1.M.F.IF.A.02: The Highly Proficient student can use function notations, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Alg1.M.F.IF.B.04: The Highly Proficient student can 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.
Alg1.M.F.IF.B.05: The Highly Proficient student can relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person‐hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Alg1.M.F.IF.C.07: The Highly Proficient student can graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Alg1.M.S.ID.A.03: The Highly Proficient student can interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Geo.M.G.CO.A.01: The Highly Proficient student can explain the definition of an angle, circle, perpendicular lines, parallel lines and identify real world examples of each figure.
Geo.M.G.CO.A.02: The Highly Proficient student can 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 angle to those that do not (e.g., translation versus horizontal stretch).
Geo.M.G.CO.A.03: Given a rectangle, parallelogram, trapezoid, or regular polygons, the Highly Proficient student can describe the rotations and reflections that carry it onto itself.
Geo.M.G.CO.A.04: The Highly Proficient student can represent functions to describe transformations using a variety of media and justify statements about rotations, reflections, and translations on the coordinate plane.
Geo.M.G.CO.A.05: The Highly Proficient student can perform 2 or more transformations on a figure, identify the single or series of transformations that map a pre-image to an image, and explain how the order of a sequence of transformations being performed may result in different outcomes.
Geo.M.G.CO.C.09: The Highly Proficient student can prove theorems such as: alternate interior angles are congruent; vertical angles are congruent; consecutive interior angles are supplementary and apply theorems in real world context.
Geo.M.G.CO.D.12: The Highly Proficient student can construct various geometric objects using a variety of tools and methods.
Geo.M.G.CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Geo.M.G.GPE.B.05: The Highly Proficient student can create the equation of a line parallel or perpendicular to a given line that passes through a given point in a context.
Geo.M.G.GPE.B.07: The Highly Proficient student can use coordinates to find the perimeter of polygons and area of triangles and rectangles, and apply them to real world problems.
Geo.M.G.CO.B.06: The Highly Proficient student can 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.
Geo.M.G.CO.B.07: The Highly Proficient student can use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Geo.M.G.CO.B.08: The Highly Proficient student can demonstrate how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions; understands and explains why SSA and AAA are not enough evidence for triangle congruence.
Geo.M.G.CO.C.10: The Highly Proficient student can prove theorems about triangles, and apply them in a real world context. Theorems include: triangle sum theorem, base angles theorem, midsegment theorem, and the medians of a triangle meet at a point.
Geo.M.G.GPE.B.06: The Highly Proficient student can find the point on a directed line segment between two given points that partitions the segment into a given ratio.
Geo.M.G.SRT.A.01: The Highly Proficient student can verify the properties of dilations and locate the center of dilation and find the scale factor given a pair of similar figures on a coordinate plane.
Geo.M.G.SRT.A.02: The Highly Proficient student can prove or disprove that two given figures are similar, using transformations and the definitions of similarity.
Geo.M.G.SRT.B.04: The Highly Proficient student can prove theorems about triangles, and apply them in a real world context. Theorems include: triangle proportionality theorem and converse and the Pythagorean Theorem proved using triangle similarity.
Geo.M.G.SRT.B.05: The Highly Proficient student can solve problems and prove conjectures about congruence or similarity in geometric figures, using congruence and similarity criteria for triangles. Includes problems from context.
Geo.M.G.SRT.C.06: The Highly Proficient student can determine the similarity of right triangles by comparing the trigonometric ratios of the corresponding sides and solve for missing angles of right triangles using sine and cosine.
Geo.M.G.C.A.01: The Highly Proficient student can prove that all circles are similar.
Geo.M.G.C.A.02: The Highly Proficient student can solve problems using relationships among inscribed angles, radii, and chords in circles.
Geo.M.G.C.A.03: The Highly Proficient student can construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Geo.M.G.C.A.04: The Highly Proficient student can construct a tangent line from a point outside a given circle to the circle.
Geo.M.G.C.B.05: The Highly Proficient student can prove that the length of the arc intercepted by an angle is proportional to the radius, with the radian measure of the angle being the constant of proportionality.
Geo.M.G.CO.C.11: The Highly Proficient student can prove theorems about parallelograms and apply them in a real-world context.
Geo.M.G.GMD.A.03: The Highly Proficient student can find the volume of cylinders, pyramids, cones, and spheres in real-life context.
Geo.M.G.GPE.A.01: The Highly Proficient student can write the equation of a circle in center-radius form, given center and radius, given points of tangency, and by completing the square.
Geo.M.G.GPE.B.04: The Highly Proficient student can use coordinates to prove simple geometric theorems algebraically and construct visual representations on the coordinate plane that meet given conditions.
Geo.M.G.SRT.A.03: The Highly Proficient student can use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Geo.M.G.SRT.C.07: The Highly Proficient student can explain and use the relationship between the sine and cosine of complementary angles.
Geo.M.G.SRT.C.08: The Highly Proficient student can model solutions to situations, using trigonometric ratios and the Pythagorean Theorem, by constructing equations that can be used to solve the problem.
Geo.M.G.GMD.A.01: The Highly Proficient student can 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.
Geo.M.G.GMD.A.02: The Highly Proficient student can give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
Geo.M.G.GMD.B.04: The Highly Proficient student can identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Geo.M.G.MG.A.01: The Highly Proficient student can use composite geometric shapes, measures, and properties to model and describe objects.
Geo.M.G.MG.A.02: The Highly Proficient student can apply concepts of density based on area and volume to model real world and mathematical problems.
Geo.M.G.MG.A.03: The Highly Proficient student can design a composite structure to meet constraints and optimization requirements.
Geo.M.G.SRT.D.09: The Highly Proficient student can derive the formula A = ó ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Geo.M.G.SRT.D.10: The Highly Proficient student can prove the Laws of Sines and Cosines and use them to solve problems.
Geo.M.G.SRT.D.11: The Highly Proficient student can apply the law of cosines and sines to find the missing sides and angles of triangles.
Alg2.M.A.APR.B.02a (quadratic): The Highly Proficient student can determine if (x-a) is a factor of a given polynomial and explain why.
Alg2.M.A.REI.B.04b (quadratic): The Highly Proficient student can determine the best method for solving a quadratic and explain whether the graph will have x-intercepts based off these solutions.
Alg2.M.CED.A.01: The Highly Proficient student can 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.
Alg2.M.F.BF.A.01a: The Highly Proficient student can write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
Alg2.M.F.BF.B.03: The Highly Proficient student can identify the effect on the graph of replacing f (x ) by f (x ) + k , k f (x ), f (kx ), 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.
Alg2.M.F.LE.A.02 (linear): The Highly Proficient student can create exponential functions or sequences if provided either a graph, relationship description, or input-output tables.
Alg2.M.F.LE.B.05: The Highly Proficient student can interpret the parameters in a linear or exponential function in terms of a context.
Alg2.M.F.IF.A.03: The Highly Proficient student can 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.
Alg2.M.F.IF.C.07a (quadratic): The Highly Proficient student can graph quadratic functions showing intercepts, maximums and minimums, multiplicity of zeros, domain and range, and increasing and decreasing intervals.
Alg2.M.F.IF.C.07a: The Highly Proficient student can graph linear and quadratic functions and show intercepts, maxima, and minina.
Alg2.M.N.CN.A.01: The Highly Proficient student can know there is a 2 complex number i such that i = −1, and every complex number has the form a + bi with a and b real.
Alg2.M.N.CN.C.07: The Highly Proficient student can solve quadratic equations with real coefficients that have complex solutions.
Alg2.M.N.Q.A.02: Define appropriate quantities for the purpose of descriptive modeling.
Alg2.M.APR.B.02: The Highly Proficient student can 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 ).
Alg2.M.A.APR.B.02b (polynomial): The Highly Proficient student can determine if (x-a) is a factor of a given polynomial and explain why.
Alg2.M.A.APR.B.03 (polynomial): The Highly Proficient student can identify zeros of polynomials by factoring, use the zeros to sketch a graph, and identify and use zeros from a graph to construct the function.
Alg2.M.A.APR.D.06: The Highly Proficient student can 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.
Alg2.M.A.REI.A.01: The Highly Proficient student can 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.
Alg2.M.A.REI.A.02 (radical): The Highly Proficient student can solve radical equations, explain extraneous solutions, and can justify steps by applying and naming properties.
Alg2.M.A.REI.A.02 (rational): The Highly Proficient student can solve rational equations, explain extraneous solutions, and can justify steps by applying and naming properties.
Alg2.M.A.REI.D.11: The Highly Proficient student can 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 values, or find successive approximations. Include cases where f (x ) and/or g (x ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Alg2.M.A.SSE.A.02: The Highly Proficient student can 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).
Alg2.M.F.BF.A.01b: The Highly Proficient student can write a function that describes a relationship between two quantities. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
Alg2.M.F.IF.B.04: For a function that models a relationship between two quantities, The Highly Proficient student can 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.
Alg2.M.F.IF.B.06: The Highly Proficient student can 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.
Alg2.M.F.IF.C.07c: The Highly Proficient student can graph quadratic and polynomial functions showing intercepts, maximums and minimums, and end behavior.
Alg2.M.F.IF.C.07b (radical): The Highly Proficient student can graph square root and cube root functions showing intercepts, maximums and minimums, and increasing and decreasing intervals.
Alg2.M.F.IF.C.07d: The Highly Proficient student can graph rational functions and show the zeros, asymptotes, and end behavior.
Alg2.M.F.IF.C.08: The Highly Proficient student can write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Alg2.M.F.IF.C.09: The Highly Proficient student can 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.
Alg2.M.A.REI.C.06: The Highly Proficient student can solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Alg2.M.A.REI.C.07: The Highly Proficient student can solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
Alg2.M.A.REI.D.11: The Highly Proficient student can find the intersection of two functions set equal to each other and explain why the x-coordinate is the solution.
Alg2.M.A.SSE.B.03: The Highly Proficient student can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 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%.
Alg2.M.A.SSE.B.04: The Highly Proficient student can 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. For example, calculate mortgage payments.
Alg2.M.F.BF.A.02: The Highly Proficient student can write recursive and explicit formulas for arithmetic and geometric sequences.
Alg2.M.F.BF.B.04: The Highly Proficient student can find inverse functions. a. Solve an equation of the form f (x ) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x‐1) for x ≠ 1.
Alg2.M.F.LE.A.02 (exponential): The Highly Proficient student can create exponential functions or sequences if provided either a graph, relationship description, or input-output tables.
Alg2.M.F.LE.A.04: The Highly Proficient student can convert an exponential equation to a logarithmic equation and can use logarithms to solve for variables in a contextual situation.
Alg2.M.F.IF.B.06: The Highly Proficient student can calculate and interpret the rate of change from functions and from real world data.
Alg2.M.F.IF.C.07e: The Highly Proficient student can graph exponential and logarithmic functions showing intercepts, maximums and minimums, end behavior, domain and range, and increasing and decreasing intervals. The Highly Proficient student can use transformations to graph trigonometric functions showing period, midline and amplitude.
Alg2.M.F.IF.C.08b: The Highly Proficient student can write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 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.
Alg2.M.F.IF.C.09b: The Highly Proficient student can 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. 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.
Alg2.M.N.RN.A.01: The Highly Proficient student can 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.
Alg2.M.N.RN.A.02: The Highly Proficient student can rewrite expressions involving radicals and rational exponents using the properties of exponents.
Alg2.M.F.IF.C.07e (trig): The Highly Proficient student can graph exponential and logarithmic functions showing intercepts, maximums and minimums, end behavior, domain and range, and increasing and decreasing intervals. The Highly Proficient student can use transformations to graph trigonometric functions showing period, midline and amplitude.
Alg2.M.F.TF.A.02: The Highly Proficient student can understand that any point on any circle can be identified using trigonometry functions.
Alg2.M.F.TF.A.01: The Highly Proficient student can understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Alg2.M.S.CP.A.01: The Highly Proficient student can describe and make sense of probability events using appropriate set language, such as union, intersection and complement.
Alg2.M.S.CP.A.02: The Highly Proficient student can 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.
Alg2.M.S.CP.A.03: The Highly Proficient student can 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.
Alg2.M.S.CP.A.04: The Highly Proficient student can 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. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
Alg2.M.S.CP.A.05: The Highly Proficient student can explain conditional probability and independence and use them to interpret real-world probabilities.
Alg2.M.S.CP.B.06: The Highly Proficient student can 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.
Alg2.M.S.CP.B.07: The Highly Proficient student can 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.
Alg2.M.S.IC.A.01: The Highly Proficient student can understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population.
Alg2.M.S.IC.A.02: The Highly Proficient student can decide if a specified model is consistent with results from a given data‐ generating process, e.g., using simulation. For example, a model says a spinning coin will fall heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Alg2.M.S.IC.B.03: The Highly Proficient student can recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Alg2.M.S.IC.B.04: The Highly Proficient student can use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
Alg2.M.S.IC.B.06: The Highly Proficient student can evaluate reports based on data.
Alg2.M.S.ID.A.04: The Highly Proficient student can use the mean and standard deviation to fit to a normal distribution.
Alg2.M.S.ID.B.06a: The Highly Proficient student can find and use the best function for data in a scatterplot, including linear and non-linear functions.
Alg3.M.A.APR.B.02: I will be able to apply the Remainder Theorem to determine any zeros of a polynomial function.
Alg3.M.A.APR.B.03: I can identify the zeros of a polynomial and use the zeros to construct a rough graph of the function.
Alg3.M.A.APR.C.05: I will be able to expand a binomial using Binomial expansion, Pascal's triangle, and combinatorial methods.
Alg3.M.A.CED.A.01 Quadratics: I can create equations and inequalities in one variable and use them to solve problems (quadratics).
Alg3.M.A.CED.A.01 Radical: I can create equations and inequalities in one variable and use them to solve problems (radicals).
Alg3.M.F.IF.C.07a: I can graph linear and quadratics functions.
Alg3.M.F.IF.C.07b: I can graph square roots, cube roots, and piecewise-defined functions, including step functions and absolute value functions.
Alg3.M.F.IF.C.07c: I can graph polynomial functions showing intercepts, maximums and minimums, and end behavior.
Alg3.M.F.IF.C.08a: I will be able to factor and complete the square in a quadratic function to show zeros, extreme values, and symmetry of the graph.
Alg3.M.N.CN.A.02: I can add, subtract, and multiply complex numbers.
Alg3.M.N.CN.A.03: I can find the conjugate of a complex number and use the conjugate to find a quotient of a complex number.
Alg3.M.N.RN.A.02: I can rewrite radical expressions to expressions using rational exponent.
Alg3.M.A.APR.D.07: I can simplify rational expressions.
Alg3.M.A.APR.D.06: I can rewrite rational expressions in different forms.
Alg3.M.A.CED.A.01 Rational: I can create equations and inequalities in one variable and use them to solve problems (rational).
Alg3.M.F.IF.C.07d: I can graph rational functions using zeroes, asymptotes, and end behavior.
Alg3.M.F.IF.C.07e (Exponential & Logs): I can graph exponential and logarithmic functions showing intercepts, maximums and minimums, and end behavior.
Alg3.M.F.LE.A.04: I can solve exponential functions by estimating graphically and calculating algebraically.
Alg3.M.A.REI.C.07: I will be able to find the solution(s) of a system of equations.
Alg3.M.A.REI.C.08: I can write a system of linear equations as a single matrix equation.
Alg3.M.A.REI.C.09: I can find the inverse of a matrix and use it to solve a system of linear equations.
Alg3.M.F.BF.A.01c: I can write exponential and logarithmic functions that describe a relationships between two quantities.
Alg3.M.F.BF.B.04a: I can find and write inverse functions.
Alg3.M.F.BF.B.04c: I can find and write inverse values from a table or graph.
Alg3.M.F.BF.B.05: I will be able to understand the relationship between exponents and logarithms and use this relationship to solve problems.
Alg3.M.N.VM.C.08: I can add, subtract and multiply matrices.
Alg3.M.F.IF.C.07e (Trigonometric): I can graph trigonometric functions.
Alg3.M.F.TF.A.01: I understand that radian measure of an angle is the length of the arc on the unit circle encompassed by the angle.
Alg3.M.F.TF.A.02: I can use the unit circle to evaluate trigonometric functions of real numbers and interpret radian measures of angles around the unit circle.
Alg3.M.F.TF.A.03: I can use special triangles to determine the values of sine, cosine, and tangent for ?/3, ?/4, and ?/6.
Alg3.M.G.SRT.C.06: I can understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric.
Alg3.M.G.SRT.C.08: I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
12.M.A.APR.D.07: I can simplify rational expressions.
12.M.F.BF.A.01bc: I can create a function describing the relationship between two quantities using arithmetic operations. I can compose functions that describe relationships between two quantities.
12.M.F.BF.B.03: I can identify transformations for functions using their parent graphs as reference.
12.M.F.BF.B.04: I can find and write inverse functions.
12.M.F.BF.B.05: I can use the relationship between functions exponential and logarithmic functions, which are inverses, to solve problems.
12.M.F.IF.B.06: I can calculate and interpret the rate of change between two variables in a function.
12.M.F.IF.C.07ab: I can graph linear and quadratic functions. I can graph radical, piece-wise and step functions.
12.M.F.IF.C.07cd: I can graph polynomial functions. I can graph rational functions.
12.M.F.IF.C.07e: I can graph exponential and logarithmic functions showing intercepts, maximums and minimums.
12.M.G.GMD.A.02: I can give an informal argument using Cavalieris principle for the formulas for the volume of a sphere and other solid figures. Give an informal argument using Cavalieris principle for the formulas for the volume of a sphere and other solid figures.
12.M.G.GPE.A.01: I can 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.
12.M.G.GPE.A.02: I can derive the equation of a parabola given a focus and directrix.
12.M.G.GPE.A.03: I can derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
12.M.N.CN.A.01-03: I can identify the standard form of a complex number. I can add, subtract, and multiply complex numbers. I can find the conjugate of a complex number and use the conjugate to find a quotient and moduli of a complex number.
12.M.N.CN.C.08: I can extend polynomial identities to complex numbers and write in factored form.
12.M.N.CN.C.09: I can know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
12.M.F.IF.C.07e (trig): I can graph trigonometric functions.
12.M.F.TF.A.01-04: I understand that the radian measure of an angle is the length of the arc on the unit circle subtended by the angle and can apply this. I understand how coordinates for the angles on the unit circle relate to sine and cosine ratios of a right triangle. I can solve problems using special triangles and the unit circle to obtain exact answers. I can use the unit circle to explain symmetry and periodicity of trigonometric functions.
12.M.F.TF.B.05-07: I can choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. I can use domain restrictions on trigonometric functions to construct inverse functions. I can use inverse functions to solve trigonometric equations that arise in modeling contexts and evaluate the solutions using technology, interpreting them in terms of the context.
12.M.F.TF.C.08-09: I can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. I can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
12.M.G.SRT.D.09-11: I can derive and use the formula A = 1?2 ab sin(C) for the area of a triangle. I can prove the Laws of Sines and Cosines and use them to solve problems. I can apply the law of cosines and sines to find unknown measurements.
12.M.N.VM.A.01: I can recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
12.M.N.VM.A.02: I can find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
12.M.N.VM.A.03: I can solve problems involving velocity and other quantities that can be represented by vectors.
12.M.N.VM.A.04: I can add and subtract vectors.
12.M.N.VM.A.05: I can multiply a vector by a scalar.
Parents, these sites are free to use, or have at least some free options. Some may require creating a free account. Once you know the name of the standard your child is working on, try searching within the site for that standard.
ReadWorks - thousands of free reading passages. You can sort by grade, topic, difficulty and more. Create a free account in the upper right corner. | Khan Academy - instructional videos on many standards. Search by subject and standard. | LearnZillion - many resources for students and parents in grades 3-9, ELA and Math. |
Purple Math - informative explanations of many math topics. Searchable by content and standard. | YouTube - try searching for a specific topic, such as "how to add fractions". | Teachers Pay Teachers - many of these resources require purchase, but some are free to view. |
History.com - a great source for Social Studies resources, documents, and video clips. | Text structures: types, outlines, and examples - very useful guidelines on writing and types of writing. | Mood and Tone: a list of words to use when describing mood and tone - descriptive words to pump up the quality of writing. |
Parts of Speech - a good ELA resource based on parts of speech. | The Science Spot - many resources based on science. Searchable by topic and subject. | NewsELA - student-friendly articles based on news and current events. |
Biology Corner - a very detailed source for Biology resources. Mostly high school level, but useful in middle school as well. | Common Lit - many reading resources based on all content areas. Searchable by topic and subject. |
ReadWriteThink - a very powerful website for ELA standards and practice. |
Math Antics - a YouTube channel with great math how-to videos. | Big History Project - a comprehensive "history of the universe" project. |
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