screte random variable. Lessons 7 and 8 introduce the concept of expected value, and students calculate and interpret the expected value of discrete random variables in context.

Once students have developed an understanding of what the probability distribution of a discrete random variable is and what information it provides, they see in Lessons 9 and 10 that probabilities associated with a discrete random variable can be calculated given a description of the random variable (S-MD.A.3). In the final lessons of this topic, students also see how empirical data can be used to approximate the probability distribution of a discrete random variable (S-MD.A.4).

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Extending their understanding of complex numbers to points in the complex plane, students come to understand that multiplying a given set of points by a complex number amounts to rotating and dilating those points in the complex plane about zero. Matrices are studied as tools for performing rotations and reflections of the coordinate plane, as well as for solving systems of linear equations. Inverse functions are explored as students study the relationship between exponential and logarithmic functions and restrict the domain of the trigonometric functions to allow for their inverses. The year concludes with a capstone module on modeling with probability and statistics. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

About Downloadable Resources

A Story of Functions Curriculum Map and Overview 9-12: provides teachers with a clear picture of the modules at each grade level from Grades 9 to 12.

Scaffolding Instruction for ELLs, Resource Guide for Mathematics: provide guidance to educators on how to take the curriculum materials on Engage

Module 5 - Probability and statistics