A1.A-SSE.A: Interpret the structure of expressions.
A1.A-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
A1.A-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
A1.A-SSE.A.1b: Interpret expressions by viewing one or more of their parts as a single entity.
A1.A-SSE.A.2: Use structure to identify ways to rewrite numerical and polynomial expressions. Focus on polynomial multiplication and factoring patterns.
A1.A-SSE.B: Write expressions in equivalent forms to solve problems.
A1.A-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A1.A-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
A1.A-SSE.B.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A1.A-APR.A: Perform arithmetic operations on polynomials.
A1.A-APR.A.1: 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.
A1.A-APR.B: Understand the relationship between zeros and factors of polynomials.
A1.A-APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Focus on quadratic and cubic polynomials in which linear and quadratic factors are available.
A1.A-CED.A: Create equations that describe numbers or relationships.
A1.A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A1.A-CED.A.3: 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.
A1.A-CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A1.A-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.
A1.A-REI.A.1: Explain each step in solving linear and quadratic equations 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.
A1.A-REI.B: Solve equations and inequalities in one variable.
A1.A-REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A1.A-REI.B.4: Solve quadratic equations in one variable.
A1.A-REI.B.4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - k)² = q that has the same solutions. Derive the quadratic formula from this form.
A1.A-REI.B.4b: Solve quadratic equations by inspection (e.g., x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Focus on solutions for quadratic equations that have real roots. Include cases that recognize when a quadratic equation has no real solutions.
A1.A-REI.C: Solve systems of equations.
A1.A-REI.C.5: 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.
A1.A-REI.C.6: Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Include problem solving opportunities utilizing real-world context.
A1.A-REI.D: Represent and solve equations and inequalities graphically.
A1.A-REI.D.10: 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.
A1.A-REI.D.11: 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). Focus on cases where f(x) and/or g(x) are linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.A-REI.D.12: 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.
A1.F-IF.A: Understand the concept of a function and use function notation.
A1.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).
A1.F-IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
A1.F-IF.B: Interpret functions that arise in applications in terms of the context.
A1.F-IF.B.4: 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. Include problem-solving opportunities utilizing real-world context. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.F-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
A1.F-IF.B.6: Calculate and interpret the average rate of change of a continuous function (presented symbolically or as a table) on a closed interval. Estimate the rate of change from a graph. Include problem-solving opportunities utilizing real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.F-IF.C: Analyze functions using different representations.
A1.F-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.F-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
A1.F-IF.C.8a: Use the process of factoring and completing the square of a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
A1.F-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.F-BF.A: Build a function that models a relationship between two quantities.
A1.F-BF.A.1: Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.F-BF.B: Build new functions from existing functions.
A1.F-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), 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. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).
A1.F-LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.
A1.F-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
A1.F-LE.A.1a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
A1.F-LE.A.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
A1.F-LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
A1.F-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or input/output pairs.
A1.F-LE.A.3: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
A1.F-LE.B: Interpret expressions for functions in terms of the situation they model.
A1.F-LE.B.5: Interpret the parameters in a linear or exponential function with integer exponents utilizing real world context.
A1.S-ID.A: Summarize, represent, and interpret data on a single count or measurement variable.
A1.S-ID.A.1: Represent real-value data with plots for the purpose of comparing two or more data sets.
A1.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.
A1.S-ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers if present.
A1.S-ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.
A1.S-ID.B.5: 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.
A1.S-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the quantities are related.
A1.S-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Focus on linear models.
A1.S-ID.B.6b: Informally assess the fit of a function by plotting and analyzing residuals.
A1.S-ID.C: Interpret linear models.
A1.S-ID.C.7: Interpret the slope as a rate of change and the constant term of a linear model in the context of the data.
A1.S-ID.C.8: Compute and interpret the correlation coefficient of a linear relationship.
A1.S-ID.C.9: Distinguish between correlation and causation.
A1.S-CP.A: Understand independence and conditional probability and use them to interpret data.
A1.S-CP.A.1: Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events.
A1.S-CP.A.2: Use the Multiplication Rule for independent events to 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.
5.1.1: Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?' to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others.
5.2.1: Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context.
5.3.1: Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.
5.4.1: Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
5.6.1: Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.
5.7.1: Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.
5.8.1: Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency.
Correlation last revised: 4/4/2018