Gizmos for Tennessee - Mathematics: Algebra I (Academic Standards adopted 2021)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

2: : Algebra

A1.A.SSE: : Seeing Structure in Expressions

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 complicated expressions by viewing one or more of their parts as a single entity.

A1.A.APR: : Arithmetic with Polynomials and Rational Expressions

A1.A.APR.A: : Perform arithmetic operations on polynomials.

A1.A.APR.A.1: : Add, subtract, and multiply polynomials. Use these operations to demonstrate that polynomials form a closed system that adhere to the same properties of operations as the integers.

A1.A.CED: : Creating Equations

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 in a real-world context.

A1.A.CED.A.2: : Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

A1.A.CED.A.3: : Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.

A1.A.CED.A.4: : Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

A1.A.REI: : Reasoning with Equations and Inequalities

A1.A.REI.A: : Understand solving equations as a process of reasoning and explain the reasoning.

A1.A.REI.A.1: : Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

A1.A.REI.B: : Solve equations and inequalities in one variable.

A1.A.REI.B.2: : Solve linear and absolute value equations and inequalities in one variable.

A1.A.REI.B.2a: : Solve linear equations and inequalities, including compound inequalities, in one variable. Represent solutions algebraically and graphically.

A1.A.REI.B.2b: : Solve absolute value equations and inequalities in one variable. Represent solutions algebraically and graphically.

A1.A.REI.B.3: : Solve quadratic equations and inequalities in one variable.

A1.A.REI.B.3a: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has solutions that are not real numbers.

A1.A.REI.B.3b: : Solve quadratic inequalities using the graph of the related quadratic equation.

A1.A.REI.C: : Solve systems of equations.

A1.A.REI.C.4: : Write and solve a system of linear equations in real-world context.

A1.A.REI.D: : Represent and solve equations and inequalities graphically.

A1.A.REI.D.5: : 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.6: : 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 approximate solutions by graphing the functions or making a table of values, using technology when appropriate.

A1.A.REI.D.7: : Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

3: : Functions

A1.F.IF: : Interpreting Functions

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.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.

A1.F.IF.B.5: : Relate the domain of a function to its graph and, where applicable, to the context of the function it models.

A1.F.IF.B.6: : Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.

A1.F.IF.C: : Analyze functions using different representations.

A1.F.IF.C.7: : Graph functions expressed algebraically and show key features of the graph by hand and using technology.

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: : Rewrite quadratic functions to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a real-world context.

A1.F.BF: : Building Functions

A1.F.BF.A: : Build a function that models a relationship between two quantities.

A1.F.BF.A.1: : Build a function that describes a relationship between two quantities.

A1.F.BF.A.1a: : Determine steps for calculation, a recursive process, or an explicit expression from a context.

A1.F.BF.B: : Build new functions from existing functions.

A1.F.BF.B.2: : 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 graphs.

A1.F.LE: : Linear, Quadratic, and Exponential Models

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: : Know 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 factor 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 table, a description of a relationship, or input-output pairs.

A1.F.LE.B: : Interpret expressions for functions in terms of the situation they model.

A1.F.LE.B.3: : Interpret the parameters in a linear or exponential function in terms of a context.

4: : Statistics and Probability

A1.S.ID: : Interpreting Categorical and Quantitative Data

A1.S.ID.A: : Summarize, represent, and interpret data on a single count or measurement variable.

A1.S.ID.A.1: : Use measures of center to solve real-world and mathematical problems.

A1.S.ID.A.2: : Use statistics appropriate to the shape of the data distribution to compare center (mean, median, and/or mode) and spread (range, interquartile range) 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 extreme data points.

A1.S.ID.B: : Summarize, represent, and interpret data on two categorical and quantitative variables.

A1.S.ID.B.4: : Represent data from two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

A1.S.ID.C: : Interpret linear models.

A1.S.ID.C.5: : Interpret the rate of change and the constant term of a linear model in the context of data.

A1.S.ID.C.6: : Use technology to compute the correlation coefficient of a linear model; interpret the correlation coefficient in the context of the data.

A1.S.ID.C.7: : Explain the differences between correlation and causation. Recognize situations where an additional factor may be affecting correlated data.

Correlation last revised: 4/17/2023

Tennessee - Mathematics: Algebra I

Academic Standards | Adopted: 2021

2: : Algebra

3: : Functions

4: : Statistics and Probability