### ICD: Inferences and Conclusions from Data

#### (Framing Text): Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

ICD.M.3HS.4: Recognize the purposes of and differences among sample surveys, experiments and observational studies; explain how randomization relates to each.

ICD.M.3HS.5: 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.

ICD.M.3HS.6: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

#### (Framing Text): Use probability to evaluate outcomes of decisions.

ICD.M.3HS.8: Use probabilities to make fair decisions (e.g., drawing by lots or using a random number generator).

ICD.M.3HS.9: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, and/or pulling a hockey goalie at the end of a game).

### PRR: Polynomials, Rational, and Radical Relationships

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

PRR.M.3HS.18: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x ²+ y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples.

PRR.M.3HS.19: 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, with coefficients determined for example by Pascal’s Triangle.

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

PRR.M.3HS.23: 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, polynomial, rational, absolute value, exponential and logarithmic functions.

#### (Framing Text): Analyze functions using different representations.

PRR.M.3HS.24: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.

### MM: Mathematical Modeling

#### (Framing Text): Create equations that describe numbers or relationships.

MM.M.3HS.31: 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.

MM.M.3HS.32: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

MM.M.3HS.33: 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.)

MM.M.3HS.34: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.)

#### (Framing Text): Analyze functions using different representations.

MM.M.3HS.38: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

MM.M.3HS.38.a: Graph square root, cube root and piecewise-defined functions, including step functions and absolute value functions.

MM.M.3HS.38.b: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline and amplitude.

MM.M.3HS.40: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.)

Correlation last revised: 9/24/2019

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