Gizmos for Utah - Mathematics: Mathematics III (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.

SIII.MP: : Mathematical Practices

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

SIII.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.

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

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

SIII.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.

SIII.MP.4: : Model with mathematics.

SIII.MP.4.a: : Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret 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.

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

SIII.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.

SIII.MP.6: : Attend to precision.

SIII.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.

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

SIII.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.

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

SIII.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 Structures in Expressions

(Framing Text): : Interpret the structure of expressions. Extend to polynomial and rational expressions

A.SSE.1: : Interpret polynomial and rational expressions 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 complex expressions by viewing one or more of their parts as a single entity. For example, examine the behavior of P(1+r/n) to the nt power as n becomes large.

A.SSE.2: : Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ – y⁴ as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

A.APR: : Arithmetic With Polynomials and Rational Expressions

(Framing Text): : Perform arithmetic operations on polynomials, extending beyond the quadratic polynomials.

A.APR.1: : Understand that all 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.

(Framing Text): : Understand the relationship between zeros and factors of polynomials.

A.APR.2: : Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

A.APR.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.

(Framing Text): : Use polynomial identities to solve problems.

A.APR.5: : Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers.

A.CED: : Creating Equations

(Framing Text): : Create equations that describe numbers or relationships, using all available types of functions to create such equations.

A.CED.1: : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and 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.2: : Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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

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, for example, 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, polynomial, rational, absolute value, exponential, and logarithmic functions.

F: : Functions

F.IF: : Interpreting Functions

(Framing Text): : Interpret 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; end behavior; and periodicity.

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 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.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Compare and contrast square root, cubed root, and step functions with all other functions.

F.IF.7.c: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.7.d: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

F.IF.7.e: : Graph exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.

F.BF: : Building Functions

(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, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.

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

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

F.LE.3: : Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quanitity increasing linearly, quadratically, or (more generally) as a polynomial function.

F.LE.4: : For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Include the relationship between properties of logarithms and properties of exponents, such as the connection between the properties of exponents and the basic logarithm property that log xy = log x + log y.

(Framing Text): : Interpret expressions for functions in terms of the situation it models. Introduce f(x) = ex as a model for continuous growth

F.LE.5: : Interpret the parameters in a linear, quadratic, and exponential functions in terms of a context.

F.TF: : Trigonometric Functions

(Framing Text): : Extend the domain of trigonometric functions using the unit circle.

F.TF.3: : Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π6, and use the unit circle to express the values of sine, cosine, and tangent for π – x, π + x, and 2π – x in terms of their values for x, where x is any real number.

(Framing Text): : Model periodic phenomena with trigonometric functions.

F.TF.5: : Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

S: : Statistics

S.IC: : Making Inferences and Justifying Conclusions

(Framing Text): : Understand and evaluate random processes underlying statistical experiments.

S.IC.1: : Understand that statistics allow inferences to be made about population parameters based on a random sample from that population.

(Framing Text): : Draw and justify conclusions from sample surveys, experiments, and observational studies. In earlier grades, students are introduced to different ways of collecting data and use graphical displays and summary statistics to make comparisons. These ideas are revisited with a focus on how the way in which data is collected determines the scope and nature of the conclusions that can be drawn from that data. The concept of statistical significance is developed informally through simulation as meaning a result that is unlikely to have occurred solely as a result of random selection in sampling or random assignment in an experiment. For S.IC.4, focus on the variability of results from experiments—that is, focus on statistics as a way of dealing with, not eliminating, inherent randomness.

S.IC.4: : Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Correlation last revised: 9/16/2020

Utah - Mathematics: Mathematics III

UT--Core Standards | Adopted: 2016

SIII.MP: : Mathematical Practices

A: : Algebra

F: : Functions

S: : Statistics