Alg1.M.A.CED.A.01: The Highly Proficient student can create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Alg1.M.A.CED.A.02: The Highly Proficient student can compare and contrast equations and graphs that model linear and exponential relationships. Additionally, they can write or create a system of linear inequalities given a graph or a context, and they can identify the solution set as a region of the coordinate plane that satisfies all inequalities.
Alg1.M.A.REI.A.01: The Highly Proficient student can explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Alg1.M.A.REI.B.03: The Highly Proficient student can create, solve and graph linear equations and inequalities in one variable.
Alg1.M.A.S.ID.B.06c: The Highly Proficient student can compare the fit of functions (including exponential) to data and determine which function has the best fit.
Alg1.M.A.S.ID.C.08: The Highly Proficient student can calculate and interpret the correlation coefficient of a set of linear data and determine whether a correlation implies causation.
Alg1.M.A.SSE.A.01a: The Highly Proficient student can explain the context of different parts of a formula presented as a complicated expression.
Alg1.M.F.BF.A.01: The Highly Proficient student can write a function that describes a relationship between two quantities.
Alg1.M.F.IF.A.02: The Highly Proficient student can apply and extend knowledge of domain and range to real world contexts and situations. Additionally, they can create a function for a given context where the domain meets certain parameters.
Alg1.M.F.IF.B.04: The Highly Proficient student can create a story or context modeling key features of linear, quadratic, square root, cube root, piecewise, step, absolute value and exponential functions.
Alg1.M.F.IF.B.06: The Highly Proficient student can calculate and describe the rate of change of a graph or table given specific intervals.
Alg1.M.F.IF.C.09: The Highly Proficient student can compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Alg1.M.N.Q.A.03: The Highly Proficient student can choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Alg1.M.N.RN.B.03: The Highly Proficient student can explain why the sum or product of two rational numbers are rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Alg1.M.S.ID.B.05: The Highly Proficient student can summarize categorical data for two categories in two‐way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends.
Alg1.M.S.ID.B.06: The Highly Proficient student can represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or chooses a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals.
Alg1.M.S.ID.C.07: The Highly Proficient student can interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Alg1.M.S.ID.C.09: The Highly Proficient student can distinguish between correlation and causation.
Alg1.M.A.APR.A.01: The Highly Proficient student can use addition, subtraction, and multiplication to create equivalent polynomial expressions.
Alg1.M.A.CED.A.03: The Highly Proficient student can represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non‐viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Alg1.M.A.REI.C.05: The Highly Proficient student can prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Alg1.M.A.REI.C.06: The Highly Proficient student can analyze a system of equations and choose a method to solve exactly and approximately given a context or real-world situation.
Alg1.M.A.REI.D.10: The Highly Proficient student can understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Alg1.M.A.REI.D.11: The Highly Proficient student can explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Alg1.M.A.REI.D.12: The Highly Proficient student can create and graph up to three inequalities in two variables and find their solution set.
Alg1.M.F.BF.A.02: The Highly Proficient student can write recursive and explicit formulas for arithmetic and geometric sequences.
Alg1.M.F.IF.C.07a: The Highly Proficient student can graph and compare linear functions.
Alg1.M.F.LE.A.01: The Highly Proficient student can describe the rate of change of a function and can prove that over equal intervals, linear functions grow by equal differences and exponential functions grow by equal factors.
Alg1.M.F.LE.A.02: The Highly Proficient student can create both linear and exponential functions from graphs, patterns, tables, and descriptions of relationships.
Alg1.M.F.LE.A.03: The Highly Proficient student can observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Alg1.M.F.LE.B.05: The Highly Proficient student can interpret the parameters in a linear or exponential function in terms of a context.
Alg1.M.A.APR.B.03: The Highly Proficient student can identify the zeros of a quadratic function graph and use the zeros to construct the quadratic function.
Alg1.M.A.CED.A.04: The Highly Proficient student can rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Alg1.M.A.REI.B.04: The Highly Proficient student can determine the most efficient method for solving quadratic equations and justify their choice. The Highly Proficient student can recognize when quadratic equations have no real solutions.
Alg1.M.A.S.ID.A.01: The Highly Proficient student can determine and justify the most appropriate type of data plot for a set of data. The Highly Proficient student can identify advantages and disadvantages of different types of data plots.
Alg1.M.A.S.ID.A.02: The Highly Proficient student can plot multiple data sets and compare and discuss the data plots using measures of center and spread for the data. Additionally, they can explore and manipulate additional data sets and justify which measures are most appropriate for comparison. They will be able to identify advantages and disadvantages of using each type of measure of center and spread.
Alg1.M.A.SSE.A.02: The Highly Proficient student can use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
Alg1.M.A.SSE.B.03: The Highly Proficient student can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Alg1.M.A.SSE.B.04: The Highly Proficient student can derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
Alg1.M.F.IF.A.01: The Highly Proficient student can understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Alg1.M.F.IF.C.07b: The Highly Proficient student can graph and compare linear, quadratic, piecewise, step and absolute value functions in various forms.
Alg1.M.F.IF.C.09: The Highly Proficient student can construct linear, quadratic, piecewise, step, absolute value and exponential functions over integer domains given certain function characteristics or given values greater than or lesser than a given function.
Alg1.M.F.IF.C.08: The Highly Proficient student can write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Alg1.M.N.Q.A.02: The Highly Proficient student can define appropriate quantities for the purpose of descriptive modeling.
Alg1.M.F.IF.A.01: The Highly Proficient student can apply and extend knowledge of domain and range to real world situations and contexts.
Alg1.M.F.IF.A.02: The Highly Proficient student can use function notations, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Alg1.M.F.IF.B.04: The Highly Proficient student can for a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Alg1.M.F.IF.B.05: The Highly Proficient student can relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person‐hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Alg1.M.F.IF.C.07: The Highly Proficient student can graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Alg1.M.S.ID.A.03: The Highly Proficient student can interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).