Gizmos for Utah - Mathematics: Mathematics I (UT--Core Standards adopted 2016)

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

SI.MP: : Mathematical Practices

(Framing Text): : Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

SI.MP.1: : Make sense of problems and persevere in solving them.

SI.MP.1.a: : Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

SI.MP.2: : Reason abstractly and quantitatively.

SI.MP.3: : Construct viable arguments and critique the reasoning of others.

SI.MP.3.a: : Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

SI.MP.4: : Model with mathematics.

SI.MP.5: : Use appropriate tools strategically.

SI.MP.5.a: : Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

SI.MP.6: : Attend to precision.

SI.MP.6.a: : Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

SI.MP.7: : Look for and make use of structure.

SI.MP.7.a: : Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

SI.MP.8: : Look for and express regularity in repeated reasoning.

SI.MP.8.a: : Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

A: : Algebra

A.SSE: : Seeing Structure in Expressions

(Framing Text): : Interpret the structure of expressions.

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

A.CED: : Creating Equations

(Framing Text): : Create equations that describe numbers or relationships. Limit these to linear equations and inequalities, and exponential equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.

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.

A.CED.2: : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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.

A.CED.4: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.REI: : Reasoning With Equations and Inequalities

(Framing Text): : Understand solving equations as a process of reasoning and explain the reasoning.

A.REI.1: : Explain each step in solving a linear 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. Students will solve exponential equations with logarithms in Secondary Mathematics III.

(Framing Text): : 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.

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). For example, 5ˣ = 125 or 2ˣ = 1/16.

(Framing Text): : Solve systems of equations. Build on student experiences graphing and solving systems of linear equations from middle school. Include cases where the two equations describe the same line—yielding infinitely many solutions—and cases where two equations describe parallel lines—yielding no solution; connect to GPE.5, which requires students to prove the slope criteria for parallel lines.

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.

(Framing Text): : Represent and solve equations and inequalities graphically.

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.

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: : Functions

F.IF: : Interpreting Linear and Exponential Functions

(Framing Text): : Understand the concept of a linear or exponential function and use function notation. Recognize arithmetic and geometric sequences as examples of linear and exponential 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).

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.

(Framing Text): : Interpret linear or exponential functions that arise in applications in terms of a context.

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.

F.IF.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

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.

(Framing Text): : Analyze linear or exponential functions using different representations.

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.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 yϓⁿ and y𽄀×2ⁿ.

F.BF: : Building Linear or Exponential Functions

(Framing Text): : Build a linear or exponential function that models 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.

(Framing Text): : Build new functions from existing 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.LE: : Linear and Exponential

(Framing Text): : Construct and compare linear and exponential models and solve problems.

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.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.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).

F.LE.3: : Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

(Framing Text): : Interpret expressions for functions in terms of the situation they model.

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.

G: : Geometry

G.CO: : Congruence

(Framing Text): : Build on student experience with rigid motions from earlier grades.

G.CO.1: : Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

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).

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.

(Framing Text): : Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems.

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.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

(Framing Text): : Make geometric constructions.

G.CO.12: : Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Emphasize the ability to formalize and defend how these constructions result in the desired objects.

G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Emphasize the ability to formalize and defend how these constructions result in the desired objects.

G.GPE: : Expressing Geometric Properties With Equations

(Framing Text): : Use coordinates to prove simple geometric theorems algebraically.

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.

S: : Statistics and Probability

S.ID: : Interpreting Categorical and Quantitative Data

(Framing Text): : Summarize, represent, and interpret data on a single count or measurement variable.

S.ID.1: : Represent data with plots on the real number line (dot plots, histograms, and box plots).

S.ID.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.

S.ID.3: : Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Calculate the weighted average of a distribution and interpret it as a measure of center.

(Framing Text): : Summarize, represent, and interpret data on two categorical and quantitative variables.

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.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.

(Framing Text): : Interpret linear models building on students’ work with linear relationships, and introduce the correlation coefficient.

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.8: : Compute (using technology) and interpret the correlation coefficient of a linear fit.

Correlation last revised: 9/16/2020

Utah - Mathematics: Mathematics I

UT--Core Standards | Adopted: 2016

SI.MP: : Mathematical Practices

A: : Algebra

F: : Functions

G: : Geometry

S: : Statistics and Probability