STEM Innovation Academy of the Oranges
445 Scotland Road South Orange, NJ 07079
 STEM Innovation Academy of the Oranges
 Mathematics Offerings

MATHEMATICS
Integrated Mathematics I Honors (5 credits)
Prerequisites: STEM Academy Acceptance
The Integrated Mathematics I curriculum is designed to promote depth of knowledge and conceptual understanding in 6 critical areas organized into units designed to deepen and extend students’ understanding of linear relationships; done in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Topics studied in the regular Integrated Mathematics I curriculum are taught at an accelerated pace, and are extended and explored in greater depth using real life projects incorporated into each marking cycle.
Critical Area 1: Students work with expressions and creating equations; using quantities to model and analyze situations, to interpret expressions, and by creating equations to describe situations.
Critical Area 2: Students model relationships between quantities; using function notation and develop the concepts of domain and range; exploring examples of functions, including sequences; interpreting functions given graphically, numerically, symbolically, and verbally, and translating between representations, and understand the limitations of various representations. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
Critical Area 3: Students analyze and explain the process of solving an equation and to justify the process used in solving a system of equations.
Critical Area 4: Students use more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities and graphical representations and knowledge of the context to make judgments about the appropriateness of linear models.
Critical Area 5: Students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
Critical Area 6: Students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines.
The Mathematical Practice Standards apply throughout each unit together with the content standards and prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
Integrated Mathematics II Honors (5 credits)
Prerequisites: STEM Academy Acceptance; District/Teacher recommendation
The Integrated Mathematics II curriculum is designed to promote depth of knowledge and conceptual understanding in 6 critical areas organized into units designed to deepen and extend students’ mathematical understanding. The focus of Mathematics II is on quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships. The need for extending the set of rational numbers arises and real and complex numbers are introduced so that all quadratic equations can be solved. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. Circles, with their quadratic algebraic representations, round out the course. 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. Topics studied in the regular Integrated Mathematics II curriculum are taught at an accelerated pace, and are extended and explored in greater depth using real life projects incorporated into each marking cycle.
Critical Area 1: Students extend the laws of exponents to rational exponents and explore distinctions between rational and irrational numbers and explore relationships between number systems: whole numbers, integers, rational numbers, real numbers, and complex numbers.
Critical Area 2: Students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They expand their experience with functions to include more specialized functions  absolute value, step, and those that are piecewisedefined.
Critical Area 3: Students create and solve equations, inequalities, and systems of equations involving exponential and quadratic expressions.
Critical Area 4: Students expand their ability to compute and interpret theoretical and experimental probabilities for compound events and make use of geometric probability models wherever possible.
Critical Area 5: Students build a formal understanding of similarity and congruence and apply similarity in right triangles to understand right triangle trigonometry and develop facility with geometric proof.
Critical Area 6: Students prove basic theorems about circles and use the Cartesian coordinate system to write the equation of a circle, graph in the coordinate plane, and apply geometric techniques for solving quadratic equations.
Integrated Mathematics III Honors (5 credits)
Prerequisites: STEM Academy Acceptance; District/Teacher recommendation; Integrated Mathematics II
Integrated Mathematics III aims to apply and extend what students have learned in previous courses by focusing on finding connections between multiple representations of functions, transformations of different function families, finding zeros of polynomials and connecting them to graphs and equations of polynomials, modeling periodic phenomena with trigonometry, and understanding the role of randomness and the normal distribution in making statistical conclusions. Read More...
Students use problemsolving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas.
Key concepts addressed in this course include students’ ability to:
 Visualize, express, interpret and describe, and graph functions (and their inverses, in many cases).
 Use of variables and functions to represent relationships given in tables, graphs, situations, and geometric diagrams, and recognize the connections among these multiple representations.
 Apply multiple algebraic representations to model and solve problems presented as real world situations or simulations.
 Performa operations with complex numbers, and solving quadratics with complex solutions.
 Apply the Law of Sines and Law of Cosines.
 Model with periodic phenomena with trigonometric functions.
 Calculate the sums of arithmetic and geometric series, including infinite geometric series.
 Apply concepts of randomness and bias in survey design and interpretation of the results.
 Use of a normal distribution to model outcomes and to make inferences as appropriate.
 Use of computers to simulate and determine complex probabilities.
 Use of margin of error and sampletosample variability to evaluate statistical decisions.
 Solving trigonometric equations and proving trigonometric identities
 Apply concepts associated with Precalculus.
NJIT MATH111 Calculus I (5 credits; 4 NJIT credits)
Prerequisite: Successful completion of Algebra I, Algebra II, and Geometry
In this dual enrollment course (w/NJIT), students will learn about limits and their central role in calculus, derivatives and their relationship to instantaneous rates of change, understand many practical applications of derivatives, gain experience in the use of approximation in studying mathematical and scientific problems, and learn about integrals: their origin in the area problem and their relationship to derivatives. Students will gain an appreciation for the importance of calculus in scientific, engineering, computer, and other applications. Students will also gain experience in the use of technology to facilitate visualization and problem solving.
Course Outcomes
 Students will have improved logical thinking and problemsolving skills.
 Students will have a greater understanding of the importance of calculus in science and technology.
 Students will be prepared for further study in mathematics as well as science, engineering, computing, and other areas.