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 In this module, students build on their understanding of probability developed in previous grades. In Topic A the multiplication rule for independent events introduced in Algebra II is generalized...

 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via highdimensional matrices. Matrix...

 Precalculus Module 1: Complex Numbers and Transformations Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the...

 Student Outcomes Students determine the values of the sine, cosine, and tangent functions for rotations of π/3, π/4, and π/6 radians. Students use the unit circle to express the values of the sine,...

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 Student Outcomes Students construct a tangent line from a point outside a given circle to the circle.

 Updated Modules and Curricular Resources The tables below reflect Mathematics and English Language Arts curricular materials and resources that have been updated. As additional materials are updated...

 Student Outcomes Students use expected pay off to compare strategies for a simple game of chance.

 Student Outcomes Students calculate expected values. Students make rational decisions based on calculated expected values.

 Student Outcomes Students use probabilities to make fair decisions (e.g., drawing by lots, using a randomnumber generator).

 Student Outcomes Students use probability to learn what it means for a game to be fair. Students determine whether or not a game is fair. Students determine what is needed to make fair an unfair game...

 Student Outcomes Students use probability concepts to make decisions in a variety of contexts.

 Student Outcomes Students use probability concepts to make decisions in a variety of contexts.

 Student Outcomes Given a description of a discrete random variable, students determine the probability distribution of that variable. Students interpret probabilities in context.

 Student Outcomes Students use empirical data to estimate probabilities associated with a discrete random variable. Students interpret probabilities in context.

 Student Outcomes Students use empirical data to estimate probabilities associated with a discrete random variable. Students interpret probabilities in context.

 Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts (S.MD.B....

 Student Outcomes Students analyze simple games of chance. Students calculate expected pay off for simple games of chance. Students interpret expected pay off in context.

 Student Outcomes Given the probability distribution of a discrete random variable in table or graphical form, students describe the longrun behavior of the random variable. Given a discrete...

 In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...

 Student Outcomes Students calculate the expected value of a discrete random variable.

 Student Outcomes Students interpret expected value in context.