Only Grade 10 mathematics is shown here. Current and transition frameworks remain separate. A provisional target is not proof that every clause is taught or assessed.
Mathematics · 2017 framework
High school · 160 / 160 statements targeted
| Standard | Instruction status | Source text |
|---|---|---|
| math-2017:N.RN.1 | Provisional target; review pending | 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 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^3 = 5^((1/3)3) to hold, so (5^(1/3))^3 must equal 5. |
| math-2017:N.RN.2 | Provisional target; review pending | Rewrite expressions involving radicals and rational exponents using the properties of exponents. |
| math-2017:N.RN.3 | Provisional target; review pending | 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. |
| math-2017:N.Q.1 | Provisional target; review pending | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. |
| math-2017:N.Q.2 | Provisional target; review pending | Define appropriate quantities for the purpose of descriptive modeling. |
| math-2017:N.Q.3 | Provisional target; review pending | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. |
| math-2017:N.CN.1 | Provisional target; review pending | Know there is a complex number 𝑖𝑖 such that 𝑖𝑖^2 = −1, and every complex number has the form 𝑎𝑎 + 𝑏𝑏𝑏𝑏 with 𝑎𝑎 and 𝑏𝑏 real. |
| math-2017:N.CN.2 | Provisional target; review pending | Use the relation 𝑖𝑖^2= −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. |
| math-2017:N.CN.3 | Provisional target; review pending | Find the conjugate of a complex number; use conjugates to find magnitudes and quotients of complex numbers. |
| math-2017:N.CN.4 | Provisional target; review pending | Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. |
| math-2017:N.CN.5 | Provisional target; review pending | Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (−1 + 𝑖𝑖√3)³ = 8 because (−1 + 𝑖𝑖√3) has magnitude 2 and argument 120°. |
| math-2017:N.CN.6 | Provisional target; review pending | Calculate the distance between numbers in the complex plane as the magnitude of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. |
| math-2017:N.CN.7 | Provisional target; review pending | Solve quadratic equations with real coefficients that have complex solutions. |
| math-2017:N.CN.8 | Provisional target; review pending | Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2 𝑖𝑖)(x − 2 𝑖𝑖). |
| math-2017:N.CN.9 | Provisional target; review pending | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. |
| math-2017:N.VM.1 | Provisional target; review pending | 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, e.g., 𝒗𝒗, | 𝒗𝒗 |, ||𝒗𝒗||, 𝑣𝑣⃗. |
| math-2017:N.VM.2 | Provisional target; review pending | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. |
| math-2017:N.VM.3 | Provisional target; review pending | Solve problems involving velocity and other quantities that can be represented by vectors. |
| math-2017:N.VM.4 | Provisional target; review pending | Add and subtract vectors. |
| math-2017:N.VM.5 | Provisional target; review pending | Multiply a vector by a scalar. |
| math-2017:N.VM.6 | Provisional target; review pending | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. |
| math-2017:N.VM.7 | Provisional target; review pending | Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. |
| math-2017:N.VM.8 | Provisional target; review pending | Add, subtract, and multiply matrices of appropriate dimensions. |
| math-2017:N.VM.9 | Provisional target; review pending | Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. |
| math-2017:N.VM.10 | Provisional target; review pending | Understand that the zero and identity matrices play a role in matrix addition and multiplication analogous to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. |
| math-2017:N.VM.11 | Provisional target; review pending | Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. |
| math-2017:N.VM.12 | Provisional target; review pending | Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. |
| math-2017:A.SSE.1 | Provisional target; review pending | Interpret expressions that represent a quantity in terms of its context. |
| math-2017:A.SSE.2 | Provisional target; review pending | Use the structure of an expression to identify ways to rewrite it. For example, to factor 3x(x − 5) + 2(x − 5), students should recognize that the "x − 5" is common to both expressions being added, so it simplifies to (3x + 2)(x − 5); or see x^4 − y^4 as (x^2)^2 − (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 − y^2)(x^2 + y^2). |
| math-2017:A.SSE.3 | Provisional target; review pending | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. |
| math-2017:A.SSE.4 | Provisional target; review pending | 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. |
| math-2017:A.APR.1 | Provisional target; review pending | 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. |
| math-2017:A.APR.2 | Provisional target; review pending | Understand and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x − a is p(a). In particular, p(a) = 0 if and only if (x - a) is a factor of p(x). |
| math-2017:A.APR.3 | Provisional target; review pending | Identify zeros of polynomials, when factoring is reasonable, and use the zeros to construct a rough graph of the function defined by the polynomial. |
| math-2017:A.APR.4 | Provisional target; review pending | Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² − y²)² + (2xy)² can be used to generate Pythagorean triples. |
| math-2017:A.APR.5 | Provisional target; review pending | 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. For example by using coefficients determined for by Pascal's Triangle. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument. |
| math-2017:A.APR.6 | Provisional target; review pending | 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. |
| math-2017:A.APR.7 | Provisional target; review pending | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. |
| math-2017:A.CED.1 | Provisional target; review pending | Create equations and inequalities in one variable and use them to solve problems. Include equations and inequalities arising from linear, quadratic, simple rational, and exponential functions. |
| math-2017:A.CED.2 | Provisional target; review pending | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. |
| math-2017:A.CED.3 | Provisional target; review pending | 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. (A1, M1) |
| math-2017:A.CED.4 | Provisional target; review pending | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. |
| math-2017:A.REI.1 | Provisional target; review pending | 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. |
| math-2017:A.REI.2 | Provisional target; review pending | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. |
| math-2017:A.REI.3 | Provisional target; review pending | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
| math-2017:A.REI.4 | Provisional target; review pending | Solve quadratic equations in one variable. |
| math-2017:A.REI.5 | Provisional target; review pending | Verify 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. |
| math-2017:A.REI.6 | Provisional target; review pending | Solve systems of linear equations algebraically and graphically. |
| math-2017:A.REI.7 | Provisional target; review pending | 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. |
| math-2017:A.REI.8 | Provisional target; review pending | Represent a system of linear equations as a single matrix equation in a vector variable. |
| math-2017:A.REI.9 | Provisional target; review pending | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). |
| math-2017:A.REI.10 | Provisional target; review pending | 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). |
| math-2017:A.REI.11 | Provisional target; review pending | 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. |
| math-2017:A.REI.12 | Provisional target; review pending | 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 corresponding half-planes. |
| math-2017:F.IF.1 | Provisional target; review pending | 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). |
| math-2017:F.IF.2 | Provisional target; review pending | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
| math-2017:F.IF.3 | Provisional target; review pending | 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. |
| math-2017:F.IF.4 | Provisional target; review pending | 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 the following: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (A2, M3) |
| math-2017:F.IF.5 | Provisional target; review pending | 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. |
| math-2017:F.IF.6 | Provisional target; review pending | 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. (A2, M3) |
| math-2017:F.IF.7 | Provisional target; review pending | 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. |
| math-2017:F.IF.8 | Provisional target; review pending | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. |
| math-2017:F.IF.9 | Provisional target; review pending | 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. (A2, M3) |
| math-2017:F.BF.1 | Provisional target; review pending | Write a function that describes a relationship between two quantities. |
| math-2017:F.BF.2 | Provisional target; review pending | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. |
| math-2017:F.BF.3 | Provisional target; review pending | Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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. (A2, M3) |
| math-2017:F.BF.4 | Provisional target; review pending | Find inverse functions. |
| math-2017:F.BF.5 | Provisional target; review pending | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. |
| math-2017:F.LE.1 | Provisional target; review pending | Distinguish between situations that can be modeled with linear functions and with exponential functions. |
| math-2017:F.LE.2 | Provisional target; review pending | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). |
| math-2017:F.LE.3 | Provisional target; review pending | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. (A1, M2) |
| math-2017:F.LE.4 | Provisional target; review pending | For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. |
| math-2017:F.LE.5 | Provisional target; review pending | Interpret the parameters in a linear or exponential function in terms of a context. |
| math-2017:F.TF.1 | Provisional target; review pending | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. |
| math-2017:F.TF.2 | Provisional target; review pending | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. |
| math-2017:F.TF.3 | Provisional target; review pending | Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π − x, π + x, and 2π − x in terms of their values for x, where x is any real number. |
| math-2017:F.TF.4 | Provisional target; review pending | Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. |
| math-2017:F.TF.5 | Provisional target; review pending | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. |
| math-2017:F.TF.6 | Provisional target; review pending | Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. |
| math-2017:F.TF.7 | Provisional target; review pending | Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. |
| math-2017:F.TF.8 | Provisional target; review pending | Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1, and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. |
| math-2017:F.TF.9 | Provisional target; review pending | Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems. |
| math-2017:G.CO.1 | Provisional target; review pending | Know precise definitions of ray, angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and arc length. |
| math-2017:G.CO.2 | Provisional target; review pending | 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. |
| math-2017:G.CO.3 | Provisional target; review pending | Identify the symmetries of a figure, which are the rotations and reflections that carry it onto itself. |
| math-2017:G.CO.4 | Provisional target; review pending | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. |
| math-2017:G.CO.5 | Provisional target; review pending | Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using items such as graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. |
| math-2017:G.CO.6 | Provisional target; review pending | 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. |
| math-2017:G.CO.7 | Provisional target; review pending | 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. |
| math-2017:G.CO.8 | Provisional target; review pending | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. |
| math-2017:G.CO.9 | Provisional target; review pending | Prove and apply theorems about lines and angles. Theorems include but are not restricted to the following: 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 segment are exactly those equidistant from the segment's endpoints. |
| math-2017:G.CO.10 | Provisional target; review pending | Prove and apply theorems about triangles. Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. |
| math-2017:G.CO.11 | Provisional target; review pending | Prove and apply theorems about parallelograms. Theorems include but are not restricted to the following: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. |
| math-2017:G.CO.12 | Provisional target; review pending | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. |
| math-2017:G.CO.13 | Provisional target; review pending | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. |
| math-2017:G.CO.14 | Provisional target; review pending | Classify two-dimensional figures in a hierarchy based on properties. |
| math-2017:G.SRT.1 | Provisional target; review pending | Verify experimentally the properties of dilations given by a center and a scale factor: |
| math-2017:G.SRT.2 | Provisional target; review pending | 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. |
| math-2017:G.SRT.3 | Provisional target; review pending | Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. |
| math-2017:G.SRT.4 | Provisional target; review pending | Prove and apply theorems about triangles. Theorems include but are not restricted to the following: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. |
| math-2017:G.SRT.5 | Provisional target; review pending | Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles. |
| math-2017:G.SRT.6 | Provisional target; review pending | 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. |
| math-2017:G.SRT.7 | Provisional target; review pending | Explain and use the relationship between the sine and cosine of complementary angles. |
| math-2017:G.SRT.8 | Provisional target; review pending | Solve problems involving right triangles. |
| math-2017:G.SRT.9 | Provisional target; review pending | Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. |
| math-2017:G.SRT.10 | Provisional target; review pending | Explain proofs of the Laws of Sines and Cosines and use the Laws to solve problems. |
| math-2017:G.SRT.11 | Provisional target; review pending | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles, e.g., surveying problems, resultant forces. |
| math-2017:G.C.1 | Provisional target; review pending | Prove that all circles are similar using transformational arguments. |
| math-2017:G.C.2 | Provisional target; review pending | Identify and describe relationships among angles, radii, chords, tangents, and arcs and use them to solve problems. Include the relationship between central, inscribed, and circumscribed angles and their intercepted arcs; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. |
| math-2017:G.C.3 | Provisional target; review pending | Construct the inscribed and circumscribed circles of a triangle; prove and apply the property that opposite angles are supplementary for a quadrilateral inscribed in a circle. |
| math-2017:G.C.4 | Provisional target; review pending | Construct a tangent line from a point outside a given circle to the circle. |
| math-2017:G.C.5 | Provisional target; review pending | Find arc lengths and areas of sectors of circles. |
| math-2017:G.C.6 | Provisional target; review pending | Derive formulas that relate degrees and radians, and convert between the two. (A2, M3) |
| math-2017:G.GPE.1 | Provisional target; review pending | 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. |
| math-2017:G.GPE.2 | Provisional target; review pending | Derive the equation of a parabola given a focus and directrix. |
| math-2017:G.GPE.3 | Provisional target; review pending | 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. |
| math-2017:G.GPE.4 | Provisional target; review pending | Use coordinates to prove simple geometric theorems algebraically and to verify geometric relationships algebraically, including properties of special triangles, quadrilaterals, and circles. For example, determine if a figure defined by four given points in the coordinate plane is a rectangle; determine if a specific point lies on a given circle. (G, M2) |
| math-2017:G.GPE.5 | Provisional target; review pending | Justify 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. |
| math-2017:G.GPE.6 | Provisional target; review pending | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. |
| math-2017:G.GPE.7 | Provisional target; review pending | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. |
| math-2017:G.GMD.1 | Provisional target; review pending | 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. Use dissection arguments, Cavalieri's principle, and informal limit arguments. |
| math-2017:G.GMD.2 | Provisional target; review pending | Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. |
| math-2017:G.GMD.3 | Provisional target; review pending | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. |
| math-2017:G.GMD.4 | Provisional target; review pending | Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. |
| math-2017:G.GMD.5 | Provisional target; review pending | Understand how and when changes to the measures of a figure (lengths or angles) result in similar and non-similar figures. |
| math-2017:G.GMD.6 | Provisional target; review pending | 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. |
| math-2017:G.MG.1 | Provisional target; review pending | Use geometric shapes, their measures, and their properties to describe objects, e.g., modeling a tree trunk or a human torso as a cylinder. |
| math-2017:G.MG.2 | Provisional target; review pending | Apply concepts of density based on area and volume in modeling situations, e.g., persons per square mile, BTUs per cubic foot. |
| math-2017:G.MG.3 | Provisional target; review pending | 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. |
| math-2017:S.ID.1 | Provisional target; review pending | Represent data with plots on the real number line (dot plots, histograms, and box plots) in the context of real-world applications using the GAISE model. |
| math-2017:S.ID.2 | Provisional target; review pending | In the context of real-world applications by using the GAISE model, use statistics appropriate to the shape of the data distribution to compare center (median and mean) and spread (mean absolute deviation, interquartile range, and standard deviation) of two or more different data sets. |
| math-2017:S.ID.3 | Provisional target; review pending | In the context of real-world applications by using the GAISE model, interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
| math-2017:S.ID.4 | Provisional target; review pending | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. |
| math-2017:S.ID.5 | Provisional target; review pending | 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. |
| math-2017:S.ID.6 | Provisional target; review pending | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. |
| math-2017:S.ID.7 | Provisional target; review pending | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. |
| math-2017:S.ID.8 | Provisional target; review pending | Compute (using technology) and interpret the correlation coefficient of a linear fit. |
| math-2017:S.ID.9 | Provisional target; review pending | Distinguish between correlation and causation. |
| math-2017:S.IC.1 | Provisional target; review pending | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. |
| math-2017:S.IC.2 | Provisional target; review pending | 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 falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? |
| math-2017:S.IC.3 | Provisional target; review pending | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. |
| math-2017:S.IC.4 | Provisional target; review pending | 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. |
| math-2017:S.IC.5 | Provisional target; review pending | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between sample statistics are statistically significant. |
| math-2017:S.IC.6 | Provisional target; review pending | Evaluate reports based on data. |
| math-2017:S.CP.1 | Provisional target; review pending | 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"). |
| math-2017:S.CP.2 | Provisional target; review pending | 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. |
| math-2017:S.CP.3 | Provisional target; review pending | 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. |
| math-2017:S.CP.4 | Provisional target; review pending | 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. |
| math-2017:S.CP.5 | Provisional target; review pending | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. |
| math-2017:S.CP.6 | Provisional target; review pending | 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. |
| math-2017:S.CP.7 | Provisional target; review pending | 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. |
| math-2017:S.CP.8 | Provisional target; review pending | 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. |
| math-2017:S.CP.9 | Provisional target; review pending | Use permutations and combinations to compute probabilities of compound events and solve problems. |
| math-2017:S.MD.1 | Provisional target; review pending | Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. |
| math-2017:S.MD.2 | Provisional target; review pending | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. |
| math-2017:S.MD.3 | Provisional target; review pending | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. |
| math-2017:S.MD.4 | Provisional target; review pending | Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? |
| math-2017:S.MD.5 | Provisional target; review pending | Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. |
| math-2017:S.MD.6 | Provisional target; review pending | Use probabilities to make fair decisions, e.g., drawing by lots, using a random number generator. |
| math-2017:S.MD.7 | Provisional target; review pending | Analyze decisions and strategies using probability concepts, e.g., product testing, medical testing, pulling a hockey goalie at the end of a game. |