N-Gen Math™ Algebra I Workbook

Standard Alignment

The N-Gen Math™ Algebra I workbook covers required topics aligned with the Next Generation Learning Standards (NGLS). Below are some of the key areas addressed in the workbook, though this is not a comprehensive list:

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
AI-A.SSE.: Algebra – Seeing Structure in Expression
AI-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it. (Shared standard with Algebra II)
AI-A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Shared standard with Algebra II)
AI-A.SSE.3.c: Use the properties of exponents to rewrite exponential expressions. (Shared standard with Algebra II)
AI-A.APR.1: Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial.
AI-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available. (Shared standard with Algebra II)
AI-A.CED.1: Create equations and inequalities in one variable to represent a real-world context. (Shared standard with Algebra II)
AI-A.CED.2: Create equations and linear inequalities in two variables to represent a real-world context.
AI-A.CED.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.
AI-A.CED.4: Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
AI-A.REI.1a: Explain each step when solving a linear or quadratic 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.
AI-A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
AI-A.SSE.1.a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
AI-F.IF.1: Understand that a function from one set (domain) to another set (range) assigns to each domain element exactly one range element. The graph of f is the graph of the equation y = f(x).
AI-F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements using function notation in context.
AI-F.IF.4: For a function modeling a relationship between two quantities: i) interpret key features of graphs/tables in terms of quantities; ii) sketch graphs showing key features from verbal descriptions. (Shared standard with Algebra II)
AI-F.IF.5: Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
AI-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval. (Shared standard with Algebra II)
AI-F.IF.7.a: Graph linear, quadratic, and exponential functions and show key features.
AI-F.IF.8.a: For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.
AI-F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, in tables, or by verbal descriptions). (Shared standard with Algebra II)
AI-F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context. (Shared standard with Algebra II)
AII-N.RN.2: Convert between radical expressions and expressions with rational exponents using the properties of exponents.
AII-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it. (Shared standard with Algebra I)
AII-A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Shared standard with Algebra I)
AII-A.SSE.3.c: Use the properties of exponents to rewrite exponential expressions. (Shared standard with Algebra I)
AII-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available. (Shared standard with Algebra I)
AII-A.CED.1: Create equations and inequalities in one variable to represent a real-world context. (Shared standard with Algebra I)
AII-A.REI.1b: Explain each step when solving rational or radical 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.
AII-F.IF.4: For a function modeling a relationship between two quantities: i) interpret key features of graphs/tables; ii) sketch graphs from verbal descriptions. (Shared standard with Algebra I)
AII-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval. (Shared standard with Algebra I)
AII-F.IF.9: Compare properties of two functions represented in different ways. (Shared standard with Algebra I)
AII-F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context. (Shared standard with Algebra I)
AII-S.IC.4: Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.

CCSS Equivalent Standards:

CSSHSA-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
CCSSHSA-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
CCSSHSA-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.
CCSSHSF-IF.A.1: Understand that a function from one set to another set assigns to each element of the domain exactly one element of the range.
CCSSHSF-IF.B.4: Form 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.
CCSSHSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
CCSSHSF-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.
CCSSHSF-IF.C.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
CCSSHSF-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
CCSSMP1: Make sense of problems and persevere in solving them.
CCSSMP4: Model with mathematics.
CCSSMP6: Attend to precision.
CCSSMP7: Look for and make use of structure.