Course of Study
1.1.1: Extend the properties of exponents to rational exponents.
N-RN.1: Students will: 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.
N-RN.2: Students will: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
1.2.1: Reason quantitatively and use units to solve problems.
N-Q.4: Students will: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
N-Q.5: Students will: Define appropriate quantities for the purpose of descriptive modeling.
N-Q.6: Students will: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
2.1.1: Interpret the structure of expressions.
A-SSE.7: Students will: Interpret expressions that represent a quantity in terms of its context.
A-SSE.7.a: Interpret parts of an expression such as terms, factors, and coefficients.
A-SSE.7.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
A-SSE.8: Students will: Use the structure of an expression to identify ways to rewrite it.
2.1.2: Write expressions in equivalent forms to solve problems.
A-SSE.9: Students will: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.9.a: Factor a quadratic expression to reveal the zeros of the function it defines.
A-SSE.9.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A-SSE.9.c: Determine a quadratic equation when given its graph or roots.
A-SSE.9.d: Use the properties of exponents to transform expressions for exponential functions.
2.2.1: Perform arithmetic operations on polynomials.
A-APR.10: Students will: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
2.3.1: Create equations that describe numbers or relationships.
A-CED.12: Students will: Create equations and inequalities in one variable, and use them to solve problems.
A-CED.13: Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-CED.14: Students will: 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.
A-CED.15: Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
2.4.1: Understand solving equations as a process of reasoning and explain the reasoning.
A-REI.16: Students will: 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.
2.4.2: Solve equations and inequalities in one variable.
A-REI.17: Students will: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A-REI.18: Students will: Solve quadratic equations in one variable.
A-REI.18.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.
A-REI.18.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square and the quadratic formula, and factoring as appropriate to the initial form of the equation.
2.4.3: Solve systems of equations.
A-REI.19: Students will: 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.
A-REI.20: Students will: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
2.4.4: Represent and solve equations and inequalities graphically.
A-REI.22: Students will: 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).
A-REI.23: Students will: 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.
A-REI.24: Students will: 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.
3.1.1: Understand the concept of a function and use function notation.
F-IF.25: Students will: 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).
F-IF.26: Students will: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F-IF.27: Students will: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
3.1.2: Interpret functions that arise in applications in terms of the context.
F-IF.28: Students will: 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.
F-IF.29: Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F-IF.30: Students will: 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.
3.1.3: Analyze functions using different representations.
F-IF.31: Students will: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F-IF.31.a: Graph linear and quadratic functions, and show intercepts, maxima, and minima.
F-IF.31.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
F-IF.32: Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F-IF.32.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
F-IF.32.b: Use the properties of exponents to interpret expressions for exponential functions.
F-IF.33: Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
3.2.1: Build a function that models a relationship between two quantities.
F-BF.34: Students will: Write a function that describes a relationship between two quantities.
F-BF.34.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-BF.34.b: Combine standard function types using arithmetic operations.
F-BF.35: Students will: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
3.2.2: Build new functions from existing functions.
F-BF.36: Students will: 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.
3.3.1: Construct and compare linear, quadratic, and exponential models and solve problems.
F-LE.37: Students will: Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.37.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F-LE.37.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F-LE.37.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F-LE.38: Students will: 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).
F-LE.39: Students will: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
3.3.2: Interpret expressions for functions in terms of the situation they model.
F-LE.40: Students will: Interpret the parameters in a linear or exponential function in terms of a context.
4.1.1: Summarize, represent, and interpret data on a single count or measurement variable.
S-ID.41: Students will: Represent data with plots on the real number line (dot plots, histograms, and box plots).
S-ID.42: Students will: 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.
S-ID.43: Students will: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
4.1.2: Summarize, represent, and interpret data on two categorical and quantitative variables.
S-ID.44: Students will: 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.
S-ID.45: Students will: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S-ID.45.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
S-ID.45.b: Informally assess the fit of a function by plotting and analyzing residuals.
S-ID.45.c: Fit a linear function for a scatter plot that suggests a linear association.
4.1.3: Interpret linear models.
S-ID.46: Students will: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
4.2.1: Understand independence and conditional probability and use them to interpret data.
S-CP.47: Students will: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
Correlation last revised: 9/15/2020