## Algebra II

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###### Module 1:

###### Polynomial, Rational, and Radical Relationships

45-ish days

N-Q.2, N-CN.1, N-CN.2, N-CN.7, A-SSE.2, A-APR.2, A-APR.3, A-APR.4, A-APR.6, A-REI.1, A-REI.2, A-REI.4, A-REI.6, A-REI.7, F-IF-7, G-GPE.2

In this module, students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect the structure inherent in multi-digit whole number multiplication with multiplication of polynomials and similarly connect division of polynomials with long division of integers. Students identify zeros of polynomials, including complex zeros of quadratic polynomials. Through regularity in repeated reasoning, they make connections between zeros of polynomials and solutions of polynomial equations. Students analyze the key features of a graph or table of a polynomial function and relate those features back to the two quantities in the problem that the function is modeling. A theme of this module is that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.

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###### Module 2:

###### Trigonometric Functions

20-ish days

F-TF.1, F-TF.2, F-TF.5, F-TF.8, S-ID.6

Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students extend trigonometric functions to all (or most) real numbers. To reinforce their understanding of these functions, students begin building fluency with the values of sine, cosine, and tangent at π/6, π/4, π/3, π/2, etc. Students make sense of periodic phenomena as they model with trigonometric functions.

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EngageNY MATH MODULE

###### Module 3:

###### Functions

45-ish days

N-RN.1, N-RN.2, N-Q.2, A-SSE.3, A-SSE.4, A-CED.1, A-REI.11, F-IF.3, F-IF.4, F-IF.6, F-IF.7, F-IF.8, F-IF.9, F-BF.1, F-BF.2, F-BF.3, F-BF.4, F-LE.2, F-LE.4, F-LE.5

In this module, students synthesize and generalize what they have learned about a variety of function families. They extend their work with exponential functions to include solving exponential equations with logarithms. They explore (with appropriate tools) the effects of transformations on graphs of diverse functions, including functions arising in an application. They notice, by looking for general methods in repeated calculations, that the transformations on a graph always have the same effect regardless of the type of the underlying function. These observations lead to students to conjecture and construct general principles about how the graph of a function changes after applying a function transformation to that function. Students identify appropriate types of functions to model a situation, they adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module. In particular, through repeated opportunities in working through the modeling cycle, students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

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EngageNY MATH MODULE

###### Module 4:

###### Inferences and Conclusions from Data

40-ish days

S-ID.4, S-IC.1,, S-IC.2, S-IC.3, S-IC.4, S-IC.5, S-IC.6, S-CP.1, S-CP.2, S-CP.3, S-CP.4, S-CP.5, S-CP.6, S-CP.7

In this module, students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify different ways of collecting data, including sample surveys, experiments, and simulations, and the role that randomness and careful design play in the conclusions that can be drawn. Students create theoretical and experimental probability models following the modeling cycle (see page 61 of CCLS). They compute and interpret probabilities from those models for compound events, attending to mutually exclusive events, independent events, and conditional probability.