Standards are the floor. Mastery and understanding are the goal.

Explore how each subject becomes a coherent sequence of knowledge, reasoning, practice, and transfer—not a disconnected checklist.

Grade 9 Math

46 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Real Number System · CCSS.Math.Content.HS.N-RN.A.1

Explain rational exponents

Independently explain how the definition of a rational exponent follows from extending the properties of integer exponents, so that expressions like 5^(1/3) mean the cube root of 5. across representations and contexts.

Component progression

  1. 1I can use the pattern in integer exponent rules (e.g. (5^(1/3))^3 = 5^1) to explain what a fractional exponent must mean.
  2. 2I can rewrite expressions between radical form and rational-exponent form (e.g. cube root of 5 = 5^(1/3), x^(2/3) = (cube root of x)^2).
  3. 3I can explain, using integer exponent properties as evidence, why a^(m/n) must equal the nth root of a^m.
Real Number System · CCSS.Math.Content.HS.N-RN.A.2

Rewrite radical and rational-exponent expressions

Independently rewrite expressions involving radicals and rational exponents using the properties of exponents. across representations and contexts.

Component progression

  1. 1I can simplify radical expressions by factoring out perfect powers matching the index.
  2. 2I can rewrite expressions fluently between radical notation and rational-exponent notation.
  3. 3I can use exponent properties (product, quotient, power rules) to simplify expressions containing rational exponents or radicals.
Real Number System · CCSS.Math.Content.HS.N-RN.B.3

Classify results of operations on rational and irrational numbers

Independently explain why the sum or product of two rational numbers is rational, why the sum of a rational number and an irrational number is irrational, and why the product of a nonzero rational number and an irrational number is irrational. across representations and contexts.

Component progression

  1. 1I can determine whether a given number can be written as a ratio of integers, and classify it as rational or irrational.
  2. 2I can explain, with examples, why rational numbers are closed under addition and multiplication.
  3. 3I can construct an argument (e.g. by contradiction) for why adding a nonzero rational number to an irrational number, or multiplying a nonzero rational number by an irrational number, produces an irrational result.
Real Number System · CCSS.Math.Content.HS.N-Q.A.1

Use units to guide problem solving

Independently 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. across representations and contexts.

Component progression

  1. 1I can carry units through each step of a multi-step problem, cancelling and combining them the way the arithmetic combines the numbers.
  2. 2I can verify that every term in a formula has consistent units, and use unit analysis to catch a setup error.
  3. 3I can choose a scale and origin for a graph or data display that appropriately shows the values and relationships of interest.
Real Number System · CCSS.Math.Content.HS.N-Q.A.2

Define appropriate quantities for modeling

Independently define appropriate quantities for the purpose of descriptive modeling. across representations and contexts.

Component progression

  1. 1I can identify the real-world attribute a descriptive model needs to represent, such as overall safety or affordability.
  2. 2I can propose a specific, measurable quantity (with units) that reasonably captures the attribute of interest.
  3. 3I can explain why a proposed quantity is an appropriate way to measure the attribute, and note its limitations.
Real Number System · CCSS.Math.Content.HS.N-Q.A.3

Choose an appropriate level of accuracy

Independently choose a level of accuracy appropriate to limitations on measurement when reporting quantities. across representations and contexts.

Component progression

  1. 1I can identify the level of precision of the measurements used as inputs to a calculation.
  2. 2I can explain why a calculated result cannot be more precise than the least precise measurement that produced it.
  3. 3I can report a calculated or measured quantity at a level of accuracy appropriate to the context and its measurement limitations.
Algebra · CCSS.Math.Content.HS.A-SSE.A.1

Interpret parts of an expression

Independently interpret expressions that represent a quantity in terms of its context, including interpreting individual terms, factors, and coefficients, and interpreting complicated expressions by viewing one or more of their parts as a single entity. across representations and contexts.

Component progression

  1. 1I can identify the terms, factors, and coefficients of an expression and name what each represents in a given context.
  2. 2I can explain what an expression, or a specific part of it, represents about the situation it models (e.g. a coefficient as a rate, a constant term as a starting value).
  3. 3I can view a repeated or grouped part of a complicated expression as one entity to interpret or manipulate the expression more easily.
Algebra · CCSS.Math.Content.HS.A-SSE.A.2

Use structure to rewrite expressions

Independently use the structure of an expression to identify ways to rewrite it, such as seeing x^4 - y^4 as (x^2)^2 - (y^2)^2 to factor it as a difference of squares. across representations and contexts.

Component progression

  1. 1I can recognize common algebraic structures (difference of squares, perfect square trinomials, common factors) hidden inside more complex expressions.
  2. 2I can rewrite an expression by treating a part of it as a single entity to reveal a known factoring pattern.
  3. 3I can confirm an expression's rewritten form is equivalent to the original, such as by expanding it back or testing values.
Algebra · CCSS.Math.Content.HS.A-SSE.B.3

Choose an equivalent form to reveal properties

Independently choose and produce an equivalent form of an expression to reveal and explain properties of the quantity it represents, including factoring to reveal zeros, completing the square to reveal a maximum or minimum, and using exponent properties to transform exponential expressions. across representations and contexts.

Component progression

  1. 1I can factor a quadratic expression to identify the values that make it zero, and explain what those zeros mean for the quantity modeled.
  2. 2I can complete the square to rewrite a quadratic expression in vertex form, and identify the maximum or minimum value it represents.
  3. 3I can rewrite an exponential expression using exponent properties to reveal a rate (e.g. rewriting to show an equivalent monthly rate from an annual one).
Algebra · CCSS.Math.Content.HS.A-APR.A.1

Operate on polynomials

Independently understand that polynomials form a system analogous to the integers, closed under addition, subtraction, and multiplication; add, subtract, and multiply polynomials. across representations and contexts.

Component progression

  1. 1I can add and subtract polynomials by combining like terms, including distributing a negative sign correctly during subtraction.
  2. 2I can multiply polynomials by distributing each term of one polynomial across every term of the other.
  3. 3I can explain why adding, subtracting, or multiplying two polynomials always produces another polynomial, drawing the parallel to closure of the integers.
Algebra · CCSS.Math.Content.HS.A-CED.A.1

Create equations and inequalities in one variable

Independently create equations and inequalities in one variable, including linear, quadratic, and simple rational and exponential relationships, and use them to solve problems. across representations and contexts.

Component progression

  1. 1I can translate a real-world relationship described in words into a linear, quadratic, rational, or exponential equation in one variable.
  2. 2I can translate a real-world constraint (a limit, minimum, or requirement) into an inequality in one variable.
  3. 3I can solve the equation or inequality and interpret the solution in terms of the original situation, checking that it makes sense.
Algebra · CCSS.Math.Content.HS.A-CED.A.2

Create equations in two or more variables

Independently create equations in two or more variables to represent relationships between quantities; graph the equations on coordinate axes with labels and scales. across representations and contexts.

Component progression

  1. 1I can write an equation in two variables that represents how one quantity in a situation depends on another.
  2. 2I can set up coordinate axes with variable labels and a scale appropriate to the situation being graphed.
  3. 3I can graph the two-variable equation and explain what the resulting graph shows about the relationship.
Algebra · CCSS.Math.Content.HS.A-CED.A.3

Represent and interpret constraints

Independently represent constraints by equations, inequalities, or systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. across representations and contexts.

Component progression

  1. 1I can write a system of equations and/or inequalities that represents every constraint described in a situation.
  2. 2I can identify the solution set of a system of constraints, such as a feasible region for a system of inequalities.
  3. 3I can evaluate whether a mathematical solution to the system is actually viable given real-world limits on the quantities involved.
Algebra · CCSS.Math.Content.HS.A-CED.A.4

Rearrange formulas for a quantity of interest

Independently rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations (literal equations). across representations and contexts.

Component progression

  1. 1I can apply the same inverse-operation steps used to solve a numeric equation to isolate a specified variable in a formula.
  2. 2I can rearrange a given formula (e.g. a geometry or science formula) to solve explicitly for a specified quantity.
  3. 3I can check a rearranged formula by substituting known values and confirming it produces the same result as the original formula.
Algebra · CCSS.Math.Content.HS.A-REI.A.1

Justify a solution method

Independently 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. across representations and contexts.

Component progression

  1. 1I can state the property of equality (addition, subtraction, multiplication, division property) that justifies each step of solving a specific equation.
  2. 2I can solve an equation while explicitly justifying every step as following from equality of the previous step.
  3. 3I can identify solving steps (such as squaring both sides) that can introduce extraneous solutions, and explain why checking the original equation matters.
Algebra · CCSS.Math.Content.HS.A-REI.B.3

Solve linear equations and inequalities

Independently solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. across representations and contexts.

Component progression

  1. 1I can solve linear equations in one variable that require multiple steps, including equations with variables on both sides.
  2. 2I can solve linear inequalities in one variable, correctly reversing the inequality symbol when multiplying or dividing by a negative number.
  3. 3I can solve a linear equation in one variable when some of the coefficients are represented by other letters instead of numbers.
Algebra · CCSS.Math.Content.HS.A-REI.C.5

Prove the elimination method preserves solutions

Independently prove that, given a system of two equations in two variables, replacing one equation with the sum of that equation and a multiple of the other produces a system with the same solutions. across representations and contexts.

Component progression

  1. 1I can show, for a specific system, that a solution to the original system still satisfies the equation produced by adding a multiple of one equation to another.
  2. 2I can construct a general argument (algebraically) for why replacing one equation with a linear combination of both equations does not change the system's solution set.
  3. 3I can explain how this result justifies solving systems of linear equations by the elimination method.
Algebra · CCSS.Math.Content.HS.A-REI.C.6

Solve systems of linear equations

Independently solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables — by graphing, substitution, and elimination. across representations and contexts.

Component progression

  1. 1I can explain that a solution to a system of two linear equations is an ordered pair satisfying both equations, corresponding to the point where their graphs intersect.
  2. 2I can solve a system of two linear equations by graphing both lines and identifying their point of intersection.
  3. 3I can solve a system of two linear equations using substitution and using elimination.
  4. 4I can choose an efficient method for a given system, solve it independently, and verify the solution satisfies both original equations.
Algebra · CCSS.Math.Content.HS.A-REI.D.10

Understand the graph of an equation

Independently 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). across representations and contexts.

Component progression

  1. 1I can determine whether a given point satisfies an equation in two variables by substitution.
  2. 2I can generate multiple solutions to an equation in two variables and plot them to form its graph.
  3. 3I can explain that every point on the graph is a solution to the equation, and every solution appears on the graph.
Algebra · CCSS.Math.Content.HS.A-REI.D.11

Find intersections as solutions to f(x) = g(x)

Independently explain why the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect are the solutions of f(x) = g(x), and find those solutions approximately, including cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, or logarithmic functions. across representations and contexts.

Component progression

  1. 1I can explain why a point where two graphs intersect represents an input where the two functions produce the same output.
  2. 2I can identify the approximate coordinates where two graphed functions intersect, using technology or careful reading of the graph.
  3. 3I can state the approximate solution(s) to f(x) = g(x) using the x-coordinates of the intersection points found.
Algebra · CCSS.Math.Content.HS.A-REI.D.12

Graph solutions to linear inequalities and systems

Independently graph the solution set of 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 of a system of linear inequalities in two variables as the intersection of the corresponding half-planes. across representations and contexts.

Component progression

  1. 1I can graph the boundary line of a linear inequality, using a solid line for ≤/≥ and a dashed line for < or >.
  2. 2I can use a test point to determine and shade the correct half-plane representing the solution set of a linear inequality.
  3. 3I can graph a system of linear inequalities and identify the region where all shaded half-planes overlap as the system's solution set.
Functions · CCSS.Math.Content.HS.F-IF.A.1

Understand the definition of a function

Independently understand that a function from one set (the domain) to another set (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, f(x) denotes the output of f corresponding to the input x, and the graph of f is the graph of the equation y = f(x). across representations and contexts.

Component progression

  1. 1I can determine whether a relation (given as a table, graph, mapping, or set of ordered pairs) assigns exactly one output to every input.
  2. 2I can identify the domain and range of a function from its representation.
  3. 3I can explain that f(x) represents the specific output value the function produces for the input x, not multiplication.
Functions · CCSS.Math.Content.HS.F-IF.A.2

Use function notation

Independently use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. across representations and contexts.

Component progression

  1. 1I can evaluate a function for a specific numeric input, including expressions like f(a+2), by substituting correctly into the function's rule.
  2. 2I can explain what a statement like f(3) = 12 means in terms of the real-world quantities the function models.
  3. 3I can given a function and a target output value, find the corresponding input(s).
Functions · CCSS.Math.Content.HS.F-IF.A.3

Recognize sequences as functions

Independently recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. across representations and contexts.

Component progression

  1. 1I can identify the domain of a sequence as a subset of the integers, and connect each term number to a function input.
  2. 2I can generate terms of a sequence given a recursive definition (each term based on the previous term).
  3. 3I can explain why a sequence can be treated as a function, identifying the input (term number) and output (term value).
Functions · CCSS.Math.Content.HS.F-IF.B.4

Interpret key features of functions

Independently for a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, including intercepts, intervals where the function is increasing, decreasing, positive, or negative, relative maximums and minimums, symmetries, and end behavior, and sketch graphs showing key features given a verbal description. across representations and contexts.

Component progression

  1. 1I can identify intercepts, intervals where a function is increasing, decreasing, positive, or negative, relative maxima/minima, symmetries, and end behavior from a graph or table.
  2. 2I can explain what each key feature of a graph or table means in terms of the situation the function models.
  3. 3I can sketch a graph showing key features (intercepts, increasing/decreasing behavior, extrema) described verbally, without needing an exact equation.
Functions · CCSS.Math.Content.HS.F-IF.B.5

Relate domain to a function's graph and context

Independently relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. across representations and contexts.

Component progression

  1. 1I can identify the domain of a function directly from its graph, including any breaks or endpoints.
  2. 2I can determine a realistic domain for a function modeling a real-world situation, based on what input values actually make sense.
  3. 3I can explain how a function's domain, whether restricted by its rule or by context, is reflected in its graph.
Functions · CCSS.Math.Content.HS.F-IF.B.6

Calculate and interpret average rate of change

Independently calculate and interpret the average rate of change of a function presented symbolically or as a table, over a specified interval, and estimate the rate of change from a graph. across representations and contexts.

Component progression

  1. 1I can compute the average rate of change of a function over a specified interval, given a table, graph, or equation, as the change in output divided by the change in input.
  2. 2I can interpret an average rate of change as the meaning of a rate in the situation the function models.
  3. 3I can estimate the average rate of change of a function over an interval directly from reading its graph.
Functions · CCSS.Math.Content.HS.F-IF.C.7

Graph functions and show key features

Independently graph functions expressed symbolically and show key features of the graph, including linear, quadratic, piecewise-defined (including step and absolute value), and exponential functions. across representations and contexts.

Component progression

  1. 1I can graph linear and quadratic functions from their equations, showing intercepts and, for quadratics, the vertex.
  2. 2I can graph piecewise-defined functions, including step and absolute value functions, correctly restricting each piece to its domain.
  3. 3I can graph exponential functions from their equations, showing intercepts and end behavior including the horizontal asymptote.
Functions · CCSS.Math.Content.HS.F-IF.C.8

Rewrite a function to reveal properties

Independently write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function, such as factoring a quadratic to reveal zeros or using exponent properties to show growth or decay rate. across representations and contexts.

Component progression

  1. 1I can factor the expression defining a quadratic function to identify its zeros, and explain what the zeros represent on the graph.
  2. 2I can use exponent properties to rewrite an exponential function's expression in a form that reveals a percent growth or decay rate.
  3. 3I can explain how a specific equivalent form of a function's expression makes a particular property (zeros, rate, extremum) easier to see.
Functions · CCSS.Math.Content.HS.F-IF.C.9

Compare functions in different representations

Independently compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). across representations and contexts.

Component progression

  1. 1I can determine a specific property (such as rate of change, intercept, or maximum) of a function regardless of whether it's given algebraically, graphically, numerically, or verbally.
  2. 2I can compare a specific property between two functions given in different representations.
  3. 3I can draw and justify a conclusion (e.g. which function grows faster, which has a greater maximum) based on the comparison.
Functions · CCSS.Math.Content.HS.F-BF.A.1

Write a function describing a relationship

Independently write a function that describes a relationship between two quantities, determining an explicit expression, a recursive process, or steps for calculation from a context, and combining standard function types using arithmetic operations. across representations and contexts.

Component progression

  1. 1I can write an explicit function rule that models a relationship described in a real-world context.
  2. 2I can describe a relationship in a context as a recursive process (each output built from the previous one).
  3. 3I can build a new function by combining two given functions with addition, subtraction, multiplication, or division to model a combined situation.
Functions · CCSS.Math.Content.HS.F-BF.A.2

Write and translate sequences

Independently write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. across representations and contexts.

Component progression

  1. 1I can write a recursive formula for an arithmetic or geometric sequence given its pattern or context.
  2. 2I can write an explicit formula for an arithmetic or geometric sequence given its pattern or context.
  3. 3I can convert a sequence between its recursive and explicit formula forms.
Functions · CCSS.Math.Content.HS.F-BF.B.3

Identify the effect of function transformations

Independently 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, experimenting with cases and describing the effects using technology, and including recognizing even and odd functions from their graphs and algebraic expressions. across representations and contexts.

Component progression

  1. 1I can identify the vertical shift and vertical stretch/compression caused by f(x)+k and k·f(x) for specific values of k.
  2. 2I can identify the horizontal shift and horizontal stretch/compression caused by f(x+k) and f(kx) for specific values of k, including the reversed direction of horizontal shifts.
  3. 3I can given the graphs of f(x) and a transformed version, determine the value of k and which transformation was applied.
  4. 4I can determine whether a function is even, odd, or neither from its graph (symmetry about the y-axis or the origin) or its algebraic expression (testing f(-x)).
Functions · CCSS.Math.Content.HS.F-LE.A.1

Distinguish linear from exponential growth

Independently distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions, recognizing that linear functions grow by equal differences over equal intervals and exponential functions grow by equal factors over equal intervals. across representations and contexts.

Component progression

  1. 1I can examine a table of values to determine whether consecutive outputs differ by a constant amount, indicating linear growth.
  2. 2I can examine a table of values to determine whether consecutive outputs share a constant ratio, indicating exponential growth.
  3. 3I can determine, from a verbal description, table, or graph, whether a situation is better modeled linearly or exponentially, and justify the choice.
Functions · CCSS.Math.Content.HS.F-LE.A.2

Construct linear and exponential functions

Independently construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). across representations and contexts.

Component progression

  1. 1I can construct a linear function from a graph, verbal description, or two points.
  2. 2I can construct an exponential function from a graph, verbal description, or two points, by finding the common ratio and initial value.
  3. 3I can check a constructed linear or exponential function by confirming it reproduces the original graph, description, or points.
Functions · CCSS.Math.Content.HS.F-LE.A.3

Compare exponential growth to linear and quadratic growth

Independently observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or as any polynomial function. across representations and contexts.

Component progression

  1. 1I can generate tables comparing an exponential function to a linear or quadratic function over an extended domain.
  2. 2I can identify, from a graph or table, the approximate point after which the exponential function's values permanently exceed the other function's values.
  3. 3I can explain, in terms of equal factors versus equal differences, why exponential growth eventually overtakes linear or polynomial growth no matter the starting values.
Functions · CCSS.Math.Content.HS.F-LE.B.5

Interpret parameters in a linear or exponential function

Independently interpret the parameters in a linear or exponential function in terms of the context it models. across representations and contexts.

Component progression

  1. 1I can interpret the slope and y-intercept of a linear function in terms of the rate and starting value of the situation it models.
  2. 2I can interpret the initial value and growth/decay factor of an exponential function in terms of the situation it models, converting a factor to a percent rate correctly.
  3. 3I can explain how a change in a specific parameter would change the situation being modeled.
Statistics Data · CCSS.Math.Content.HS.S-ID.A.1

Represent data with plots

Independently represent data with plots on the real number line, including dot plots, histograms, and box plots. across representations and contexts.

Component progression

  1. 1I can construct a dot plot to represent a small data set on the real number line.
  2. 2I can construct a histogram from a data set using consistent bin widths.
  3. 3I can construct a box plot from a data set, correctly identifying the minimum, quartiles, median, and maximum.
Statistics Data · CCSS.Math.Content.HS.S-ID.A.2

Compare data sets using center and spread

Independently use statistics appropriate to the shape of the data distribution to compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. across representations and contexts.

Component progression

  1. 1I can choose median and interquartile range for skewed distributions, and mean and standard deviation for roughly symmetric distributions.
  2. 2I can calculate the median, mean, interquartile range, and standard deviation of a data set.
  3. 3I can compare the center and spread of two or more data sets and describe what the comparison reveals.
Statistics Data · CCSS.Math.Content.HS.S-ID.A.3

Interpret shape, center, and spread; account for outliers

Independently interpret differences in shape, center, and spread in the context of data sets, accounting for possible effects of extreme data points (outliers). across representations and contexts.

Component progression

  1. 1I can identify outliers in a data set and determine how they affect the mean versus the median.
  2. 2I can explain what differences in shape, center, and spread between two data sets mean in the real-world context.
  3. 3I can justify a decision about whether an outlier should be included, investigated, or excluded when summarizing a data set.
Statistics Data · CCSS.Math.Content.HS.S-ID.A.4

Fit and use the normal distribution

Independently use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using appropriate tools, recognizing that there are data sets for which fitting a normal distribution is not appropriate. across representations and contexts.

Component progression

  1. 1I can examine a data set's shape to judge whether modeling it with a normal distribution is reasonable.
  2. 2I can use the mean, standard deviation, and the 68-95-99.7 empirical rule to estimate what percentage of data falls within given ranges.
  3. 3I can use a calculator, spreadsheet, or table to estimate population percentages for a normally distributed data set.
Statistics Data · CCSS.Math.Content.HS.S-ID.B.5

Summarize categorical data in two-way tables

Independently summarize categorical data for two categories in two-way frequency tables, interpret relative frequencies in the context of the data, and recognize possible associations and trends. across representations and contexts.

Component progression

  1. 1I can construct a two-way frequency table summarizing categorical data across two categories.
  2. 2I can calculate joint, marginal, and conditional relative frequencies from a two-way table.
  3. 3I can use relative frequencies from a two-way table to describe possible association or trends between the two categories.
Statistics Data · CCSS.Math.Content.HS.S-ID.B.6

Represent and describe bivariate quantitative data

Independently represent data on two quantitative variables on a scatter plot and describe how the variables are related, including fitting a function to the data, informally assessing the fit, and fitting a linear function for data that suggests a linear association. across representations and contexts.

Component progression

  1. 1I can construct a scatter plot to display the relationship between two quantitative variables.
  2. 2I can describe the form, direction, and strength of the association shown in a scatter plot.
  3. 3I can fit a linear function to data that shows a linear association, and informally assess how well the line fits the data.
Statistics Data · CCSS.Math.Content.HS.S-ID.C.7

Interpret slope and intercept of a linear model

Independently interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. across representations and contexts.

Component progression

  1. 1I can interpret the slope of a linear model as the rate of change of the response variable with respect to the explanatory variable, stated in context.
  2. 2I can interpret the y-intercept of a linear model in context, and judge whether the interpretation is meaningful for the data.
  3. 3I can use a linear model's equation to predict a value, and explain the prediction in terms of the slope and intercept.
Statistics Data · CCSS.Math.Content.HS.S-ID.C.8

Compute and interpret the correlation coefficient

Independently compute (using technology) and interpret the correlation coefficient of a linear fit. across representations and contexts.

Component progression

  1. 1I can use technology to compute the correlation coefficient for a linear fit to bivariate data.
  2. 2I can interpret the value of a correlation coefficient in terms of the strength and direction of the linear relationship.
  3. 3I can explain why a correlation coefficient near zero does not necessarily mean there is no relationship between the variables.
Statistics Data · CCSS.Math.Content.HS.S-ID.C.9

Distinguish correlation from causation

Independently distinguish between correlation and causation. across representations and contexts.

Component progression

  1. 1I can identify when two variables are correlated without concluding that one causes the other.
  2. 2I can propose a confounding variable or alternative explanation that could account for an observed correlation.
  3. 3I can evaluate a real or realistic claim that treats a correlation as proof of causation, explaining what additional evidence would be needed to support causation.
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