Utah Major Works: Secondary Math I
Skills available for Utah Integrated 1 math standards
Major Work
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Solve Algebraic Equations
A.SSE.1 Interpret linear expressions and exponential expressions with integer exponents that represent a quantity in terms of its context.
A.SSE.1 Interpret linear expressions and exponential expressions with integer exponents that represent a quantity in terms of its context.
A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
A.SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and simple exponential functions.
Linear equations
Inequalities
Exponential equations
A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and simple exponential functions.
Linear equations
Inequalities
Exponential equations
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Direct variation
Slope-intercept form
Standard form
Point-slope form
Exponential equations
Linear and exponential equations
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Direct variation
Slope-intercept form
Standard form
Point-slope form
Exponential equations
Linear and exponential equations
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.
Linear equations
Linear inequalities
Systems of equations
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.
Linear equations
Linear inequalities
Systems of equations
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A.REI.3 Solve equations and inequalities in one variable.
A.REI.3 Solve equations and inequalities in one variable.
A.REI.3.a: Solve one-variable equations and literal equations to highlight a variable of interest.
Multi-variable equations
Equations with models
Linear equations
A.REI.3.a: Solve one-variable equations and literal equations to highlight a variable of interest.
Multi-variable equations
Equations with models
Linear equations
A.REI.3.b: Solve compound inequalities in one variable, including absolute value inequalities.
A.REI.3.b: Solve compound inequalities in one variable, including absolute value inequalities.
A.REI.3.c: Solve simple exponential equations that rely only on application of the laws of exponents (limit solving exponential equations to those that can be solved without logarithms).
A.REI.3.c: Solve simple exponential equations that rely only on application of the laws of exponents (limit solving exponential equations to those that can be solved without logarithms).
A.REI.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.
A.REI.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.
A.REI.6 Solve systems of linear equations exactly and approximately (numerically, algebraically, graphically), focusing on pairs of linear equations in two variables.
Understand solutions
Graphing
Substitution
Elimination
Any method
A.REI.6 Solve systems of linear equations exactly and approximately (numerically, algebraically, graphically), focusing on pairs of linear equations in two variables.
Understand solutions
Graphing
Substitution
Elimination
Any method
Understand, Compare, and Represent Functions
F.BF.1 Write a function that describes a relationship between two quantities.
F.BF.1 Write a function that describes a relationship between two quantities.
F.BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences
Linear and exponential functions
F.BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences
Linear and exponential functions
F.BF.1.b: Combine standard function types using arithmetic operations.
F.BF.1.b: Combine standard function types using arithmetic operations.
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Limit F.BF.1a, 1b, and 2 to linear and exponential functions. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Limit F.BF.1a, 1b, and 2 to linear and exponential functions. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y-intercept. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y-intercept. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
F.LE.2 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).
Arithmetic and geometric sequences
Slope-intercept form
Point-slope form
Exponential functions
Linear and exponential functions
F.LE.2 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).
Arithmetic and geometric sequences
Slope-intercept form
Point-slope form
Exponential functions
Linear and exponential functions
F.IF.6 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.
F.IF.6 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.
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
F.IF.7 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.7 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.7.a: Graph linear functions and show intercepts.
F.IF.7.a: Graph linear functions and show intercepts.
F.IF.7.e: Graph exponential functions, showing intercepts and end behavior.
F.IF.7.e: Graph exponential functions, showing intercepts and end behavior.
F.IF.9 Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, compare the growth of two linear functions, or two exponential functions such as y=3n and y=100×2n.
F.IF.9 Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, compare the growth of two linear functions, or two exponential functions such as y=3n and y=100×2n.
A.REI.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).
A.REI.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).
A.REI.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. Include cases where f(x) and/or g(x) are linear and exponential functions.
Tables
Graphs
A.REI.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. Include cases where f(x) and/or g(x) are linear and exponential functions.
Tables
Graphs
A.REI.12 Graph the solutions to a linear inequality in two variables as a halfplane (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.
A.REI.12 Graph the solutions to a linear inequality in two variables as a halfplane (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.
F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
F.LE.1.a: Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
F.LE.1.a: Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
F.LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LE.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F.LE.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Describe Characteristics of Functions
F.IF.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).
Independent and dependent variables
Identify functions
Function tables and graphs
Domain and range
F.IF.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).
Independent and dependent variables
Identify functions
Function tables and graphs
Domain and range
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Evaluate a function
Interpret function notation
Tables and graphs
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Evaluate a function
Interpret function notation
Tables and graphs
F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Recognize arithmetic and geometric sequences as examples of linear and exponential functions.
Arithmetic sequences
Geometric sequences
Recursive formulas
Explicit and recursive sequences
Mixed sequences
F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Recognize arithmetic and geometric sequences as examples of linear and exponential functions.
Arithmetic sequences
Geometric sequences
Recursive formulas
Explicit and recursive sequences
Mixed sequences
F.IF.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. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.
Linear functions
Exponential functions
Linear and exponential functions
Word problems
F.IF.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. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.
Linear functions
Exponential functions
Linear and exponential functions
Word problems
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.
F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Limit exponential functions to those of the form f(x) = bx + k.
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Limit exponential functions to those of the form f(x) = bx + k.
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S.ID.6.a: Fit a linear function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions, or choose a function suggested by the context. Emphasize linear and exponential models.
S.ID.6.a: Fit a linear function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions, or choose a function suggested by the context. Emphasize linear and exponential models.
S.ID.6.b: Informally assess the fit of a function by plotting and analyzing residuals. Focus on situations for which linear models are appropriate.
S.ID.6.b: Informally assess the fit of a function by plotting and analyzing residuals. Focus on situations for which linear models are appropriate.
S.ID.6.c: Fit a linear function for scatter plots that suggest a linear association.
S.ID.6.c: Fit a linear function for scatter plots that suggest a linear association.
Understand and Apply Congruence as Defined in terms of Geometric Transformations
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide whether they are congruent.
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide whether they are congruent.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.2 Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Translations
Reflections
Rotations
Dilations
Classify and compare transformations
G.CO.2 Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Translations
Reflections
Rotations
Dilations
Classify and compare transformations
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Point out the basis of rigid motions in geometric concepts, for example, translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.
Graph an image
Sequences of transformations
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Point out the basis of rigid motions in geometric concepts, for example, translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.
Graph an image
Sequences of transformations
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; e.g., connect with The Pythagorean Theorem and the distance formula.
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; e.g., connect with The Pythagorean Theorem and the distance formula.