### M3.A: Algebra

#### M3.A.SSE: Seeing Structure in Expressions

M3.A.SSE.A: Interpret the structure of expressions.

M3.A.SSE.A.1: Use the structure of an expression to identify ways to rewrite it.

M3.A.SSE.B: Write expressions in equivalent forms to solve problems.

M3.A.SSE.B.2: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

M3.A.SSE.B.2.a: Use the properties of exponents to rewrite expressions for exponential functions.

#### M3.A.APR: Arithmetic with Polynomials and Rational Expressions

M3.A.APR.A: Understand the relationship between zeros and factors of polynomials.

M3.A.APR.A.1: 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).

M3.A.APR.A.2: 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.

M3.A.APR.B: Use polynomial identities to solve problems.

M3.A.APR.B.3: Know and use polynomial identities to describe numerical relationships.

#### M3.A.CED: Creating Equations

M3.A.CED.A: Create equations that describe numbers or relationships.

M3.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

M3.A.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.

M3.A.CED.A.3: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

#### M3.A.REI: Reasoning with Equations and Inequalities

M3.A.REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

M3.A.REI.A.1: Explain each step in solving an 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.

M3.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.

M3.A.REI.B: Represent and solve equations graphically.

M3.A.REI.B.3: 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 approximate solutions using technology.

### M3.F: Functions

#### M3.F.IF: Interpreting Functions

M3.F.IF.A: Interpret functions that arise in applications in terms of the context.

M3.F.IF.A.1: 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.

M3.F.IF.A.2: 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.

M3.F.IF.B: Analyze functions using different representations.

M3.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.

M3.F.IF.B.3.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

M3.F.IF.B.3.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

M3.F.IF.B.3.c: Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.

M3.F.IF.B.3.d: Graph exponential and logarithmic functions, showing intercepts and end behavior.

M3.F.IF.B.4: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### M3.F.BF: Building Functions

M3.F.BF.A: Build new functions from existing functions.

M3.F.BF.A.1: 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. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

M3.F.BF.A.2: Find inverse functions.

M3.F.BF.A.2.a: Find the inverse of a function when the given function is one-to-one.

#### M3.F.LE: Linear, Quadratic, and Exponential Models

M3.F.LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.

M3.F.LE.A.1: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

M3.F.LE.A.2: 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.

#### M3.F.TF: Trigonometric Functions

M3.F.TF.A: Extend the domain of trigonometric functions using the unit circle.

M3.F.TF.A.1: Understand and use radian measure of an angle.

M3.F.TF.A.1.a: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

M3.F.TF.A.1.b: Use the unit circle to find sin theta, cos theta, and tan theta when theta is a commonly recognized angle between 0 and 2pi.

M3.F.TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

M3.F.TF.B: Prove and apply trigonometric identities.

M3.F.TF.B.3: Know and use trigonometric identities to find values of trig functions.

M3.F.TF.B.3.b: Given the quadrant of the angle, use the identity sin² theta + cos² theta = 1 to find sin theta given cos theta, or vice versa.

### M3.G: Geometry

#### M3.G.CO: Congruence

M3.G.CO.A: Make geometric constructions.

M3.G.CO.A.1: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

#### M3.G.C: Circles

M3.G.C.A: Understand and apply theorems about circles.

M3.G.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.

M3.G.C.A.3: Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context.

M3.G.C.B: Find areas of sectors of circles.

M3.G.C.B.4: Know the formula and find the area of a sector of a circle in a real-world context.

#### M3.G.GPE: Expressing Geometric Properties with Equations

M3.G.GPE.A: Translate between the geometric description and the equation for a circle.

M3.G.GPE.A.1: Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

M3.G.GPE.B: Use coordinates to prove simple geometric theorems algebraically.

M3.G.GPE.B.5: Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

### M3.S: Statistics and Probability

#### M3.S.ID: Interpreting Categorical and Quantitative Data

M3.S.ID.A: Summarize, represent, and interpret data on a single count or measurement variable.

M3.S.ID.A.1: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.

M3.S.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

M3.S.ID.B.2: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

M3.S.ID.B.2.a: Fit a 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.

M3.S.ID.B.2.b: Fit a linear function for a scatter plot that suggests a linear association.

#### M3.S.IC: Making Inferences and Justifying Conclusions

M3.S.IC.A: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

M3.S.IC.A.1: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

M3.S.IC.A.2: Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.

Correlation last revised: 9/15/2020

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