## Introduction

This tool can be used to identify standards that may not have been taught or were not adequately addressed in the 2019-2020 school year due to disruptions caused by natural disasters and/or COVID-19 school closures.  Teachers are encouraged to complete this audit first and then continue the planning process with the Standards Mapping Tool and the vertical coherence document.

## Kindergarten Math

 Standard Adequately Addressed Inadequately Addressed Not addressed Comments Counting and Cardinality K.CC.A.1 Count to 100 by ones, fives, and tens. Count backward from 10. K.CC.A.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.A.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20. K.CC.B.4.a Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, using one-to-one correspondence. K.CC.B.4.b Recognize that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. K.CC.B.4.c Recognize that each successive number name refers to a quantity that is one greater. K.CC.B.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration. Given a number from 1-20, count out that many objects. K.CC.C.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. K.CC.C.7 Compare two given numbers up to 10, when written as numerals, using the terms greater than, less than, or equal to. Operations and Algebraic Thinking (OA) K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. K.OA.A.2 Add and subtract within 10 to solve contextual problems using objects or drawings to represent the problem. K.OA.A.3 Decompose numbers less than or equal to 10 into addend pairs in more than one way (e.g., 5 = 2 + 3 and 5 = 4 + 1) by using objects or drawings. Record each decomposition using a drawing or writing an equation. K.OA.A.4 Find the number that makes 10, when added to any given number, from 1 to 9 using objects or drawings. Record the answer using a drawing or writing an equation. K.OA.A.5 Fluently add and subtract within 10 using mental strategies. Numbers and Operations in Base Ten (NBT) K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some more ones by using objects or drawings. Record the composition or decomposition using a drawing or by writing an equation. Measurement and Data (MD) K.MD.A.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. K.MD.A.2 Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. K.MD.B.3 Identify the penny, nickel, dime, and quarter and recognize the value of each. K.MD.C.4 Sort a collection of objects into a given category, with 10 or less in each category. Compare the categories by group size. Geometry (G) K.G.A.1 Describe objects in the environment using names of shapes. Describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, between, and next to. K.G.A.2 Correctly name shapes regardless of their orientations or overall size. K.G.A.3 Identify shapes as two-dimensional or three-dimensional. K.G.B.4 Describe similarities and differences between two- and three-dimensional shapes, in different sizes and orientations. K.G.B.5 Model shapes in the world by building and drawing shapes. K.G.B.6 Compose larger shapes using simple shapes and identify smaller shapes within a larger shape.

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

 Standard Adequately Addressed Inadequately Addressed Not addressed Comments The Number System (NS) 8.NS.A.1  Know that numbers that are not rational are called irrational.  Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually or terminates, and convert a decimal expansion which repeats eventually or terminates into a rational number. 8.NS.A.2  Use rational approximations of irrational numbers to compare the size of irrational numbers locating them approximately on a number line diagram.  Estimate the value of irrational expressions such as . For example, by truncating the decimal expansion of , show that is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Expressions and Equations (EE) 8.EE.A.1  Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,   x   =  = = . Expressions and Equations (EE) 8.EE.A.2  Use square root and cube root symbols to represent solutions to equations of the form  = p and  = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that  is irrational. 8.EE.A.3  Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x  and the population of the world as 7 x , and determine that the world population is more than 20 times larger. 8.EE.A.4  Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 8.EE.B.5  Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 8.EE.B.6  Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Expressions and Equations (EE) 8.EE.C.7.a  Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.C.7.b  Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.C.8.a  Analyze and solve systems of two linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8.EE.C.8.b  Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 8.EE.C.8.c  Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Functions (F) 8.F.A.1  Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in 8th grade.) 8.F.A.2  Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and another linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.A.3  Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A =  giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 8.F.B.4  Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values. 8.F.B.5  Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Geometry (G) 8.G.A.1.a   Verify experimentally the properties of rotations, reflections, and translations:  Lines are taken to lines, and line segments to line segments of the same length. 8.G.A.1.b  Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. 8.G.A.1.c  Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. 8.G.A.2  Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.A.3  Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 8.G.B.4  Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.5  Know and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.6  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.C.7  Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. Statistics and Probability (SP) 8.SP.A.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.A.2  Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.A.3  Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP.B.4  Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## Algebra 1

Click here to navigate to the Algebra 1 Math Standards Mapping resource.

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## Algebra 2

Major content of the grade is indicated by the gray shading of the standard’s coding.

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## Geometry

 Standard Adequately Addressed Inadequately Addressed Not addressed Comments Congruence  (G.CO) 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, plane, distance along a line, and distance around a circular arc. G.CO.A.2 Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch). G.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself. G.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Congruence  (G.CO) G.CO.A.5 Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another. 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 determine informally if they are congruent. G.CO.B.7 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. G.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the definition of congruence in terms of rigid motions. G.CO.C.9 Prove theorems about lines and angles. G.CO.C.10 Prove theorems about triangles. G.CO.C.11 Prove theorems about parallelograms. G.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Similarity, Right Triangles, and Trigonometry   (G.SRT) G.SRT.A.1 Verify informally the properties of dilations given by a center and a scale factor. Similarity, Right Triangles, and Trigonometry   (G.SRT) 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 and the proportionality of all corresponding pairs of sides. G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. G.SRT.B.4 Prove theorems about similar triangles. G.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures. G.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.C.8.a  Solve triangles. ★  Know and use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems G.SRT.C.8.b  Solve triangles. ★   Know and use the Law of Sines and Law of Cosines to solve problems in real life situations. Recognize when it is appropriate to use each. Circles   (G.C) G.C.A.1 Recognize that all circles are similar. G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. G.C.A.3 Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context. Circles   (G.C) G.C.B.4 Know the formula and find the area of a sector of a circle in a real-world context. Expressing Geometric Properties with Equations   (G.GPE) G.GPE.A.1 Know and write the equation of a circle of given center and radius using the Pythagorean Theorem. G.GPE.B.2 Use coordinates to prove simple geometric theorems algebraically. G.GPE.B.3 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. G.GPE.B.4 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G.GPE.B.5 Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.★ Geometric Measurement and Dimension   (G.GMD) G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid. G.GMD.A.2 Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.★ Modeling with Geometry   (G.MG) G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects.★ G.MG.A.2 Apply geometric methods to solve real-world problems.★

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## Integrated Math 1

Click here to navigate to the Integrated Math 1 Standards Mapping resource.

 Standard Adequately Addressed Inadequately Addressed Not addressed Comments Quantities* (N.Q) M1.N.Q.A.1 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. M1.N.Q.A.2 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. M1.N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Seeing Structure in Expressions   (A.SSE) M1.A.SSE.A.1.a Interpret expressions that represent a quantity in terms of its context.★  Interpret parts of an expression, such as terms, factors, and coefficients. M1.A.SSE.A.1.b Interpret expressions that represent a quantity in terms of its context.★  Interpret complicated expressions by viewing one or more of their parts as a single entity. Seeing Structure in Expressions (A.SSE) M1.A.SSE.B.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Use the properties of exponents to rewrite exponential expressions. Creating Equations★   (A.CED) M1.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. M1.A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales. M1.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. M1.A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Reasoning with Equations and Inequalities   (A.REI) M1.A.REI.A.1 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. M1.A.REI.B.2 Write and solve a system of linear equations in context. M1.A.REI.C.3 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). Reasoning with Equations and Inequalities   (A.REI) M1.A.REI.C.4 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 approximate solutions using technology. ★ M1.A.REI.C.5 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. Interpreting Functions (F.IF) M1.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 corresponding to the input x. The graph of f is the graph of the equation y = f(x). M1.F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. M1.F.IF.B.3 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. ★ M1.F.IF.B.4 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. ★ Interpreting Functions (F.IF) M1.F.IF.B.5 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.★ M1.F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. a. Graph linear functions and show its intercepts. M1.F.IF.C.7 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Building Functions   (F.BF) M1.F.BF.A.1 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. M1.F.BF.A.2 Write arithmetic and geometric sequences with an explicit formula and use them to model situations.★ Linear and Exponential Models★   (F.LE) M1.F.LE.A.1.a Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. Linear and Exponential Models★   (F.LE) M1.F.LE.A.1.b Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. M1.F.LE.A.1.c Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another. M1.F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. M1.F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly. M1.F.LE.B.4 Interpret the parameters in a linear or exponential function in terms of a context. Congruence   (G.CO) M1.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, plane, distance along a line, and distance around a circular arc. Congruence   (G.CO) M1.G.CO.A.2 Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch). M1.G.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself. M1.G.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. M1.G.CO.A.5 Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another. M1.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 determine informally if they are congruent. M1.G.CO.B.7 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. M1.G.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the definition of congruence in terms of rigid motions. Congruence   (G.CO) M1.G.CO.C.9 Prove theorems about lines and angles. M1.G.CO.C.10 Prove theorems about triangles. M1.G.CO.C.11 Prove theorems about parallelograms. Interpreting Categorical and Quantitative Data   (S.ID) M1.S.ID.A.1 Represent single or multiple data sets with dot plots, histograms, stem plots (stem and leaf), and box plots. M1.S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. M1.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). M1.S.ID.B.4.a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.   Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. M1.S.ID.B.4.b Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit a linear function for a scatter plot that suggests a linear association. M1.S.ID.C.5 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. M1.S.ID.C.6 Compute (using technology) and interpret the correlation coefficient of a linear fit M1.S.ID.C.7 Distinguish between correlation and causation.

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## Integrated Math 2

Click here to navigate to the Integrated Math 2 Standards Mapping resource.

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## Integrated Math 3

Click here to navigate to the Integrated Math 3 Standards Mapping resource.