• Integrated Math III

    Summary of Unit I: Click to access Unit Plan 1

    The purpose of this unit is to have a transition phase from Integrated Math II (geometry) course to Integrated Math III (Algebra II) course. The lessons and time will be planned based on procedural learning, and some conceptual learning of quadratic equations, graphing, and formulas that the students have encountered in Integrated Math I (Algebra I)course. There are three distinct related topics within this unit:

    1) Quadratic equations and complex numbers;
    2) Key characteristics of and sketching polynomials as well as solving Cubic equations;
    3) Remainder theorem and long division of polynomials


    Summary of Unit II: Click to access  Unit Plan 2

    In this unit, students will begin to explore radicals and rational functions. They will investigate the inverse relationship between radicals and exponential functions. In addition, students are going to explore polynomial functions with rational and integer exponents. They will be able to explore the features of radical and rational functions and compare their different functions by certain features such as end behavior, average rate of change, etc. Finally, students can determine the appropriate function to model a situation as well as investigate how transformations of functions relate to their parent function.


    Summary of Unit III: Click to access  Unit Plan 3

    The purpose of this unit is to have a full understanding of the differences between arithmetic and geometric sequences and the inverse relationship between exponential and logarithmic functions. The lessons and time will be a balance among conceptual understanding, procedural practice, and application of these functions



    NJIT’s MTH 111: Calculus I

    Summary of Unit I: Click to access  Unit Plan 1

    The idea of limits is essential in Calculus because it helps us develop definitions, formulas, and theorems. This unit will set us up for the study of derivatives.

    During this unit, students will...

    • compute various limits (regular limits, one-sided limits, limits as you approach infinity....)
    • be able to determine limits graphically, algebraically, numerically, and through tables
    • be able to apply limits to explain the behavior of functions near a given point.
    • be able to use limits to understand the concept of continuity.
    • use limits to talk about the asymptotic and unbounded behaviors of a function
    • use limits to talk about the types of discontinuity in given functions


    Summary of Unit II: Click to access  Unit Plan 2

    In Unit 1 students learned how to determine the slope of a curve at a point and how to measure the rate at which a function changes. Now they have studied limits, they can make these notions precise and see that both are interpretations of the derivative of a function at a point. They then extend this concept from a single point to the derivative function, and they develop rules for finding this derivative function easily, without having to calculate limits directly. These rules are used to find derivatives of most of the common functions reviewed in the last unit as well as combinations of them.

    The derivative is used to study a wide range of problems in mathematics, science, economics, and medicine. In this unit students will explore and solve these problems including finding solutions to very general equations, calculating the velocity and acceleration of a moving object, describing the path followed by a light ray going from a point in air to a point in water, finding the number of items a manufacturing company should produce in order to maximize its profits, studying the spread of an infectious disease within a given population, and calculating the amount of blood the heart pumps per minute based on how well the lungs are functioning.


    Summary of Unit III: Click to access  Unit Plan 3

    In this unit, students will apply derivatives to find extreme values of functions, to determine and analyze the shapes of graphs, and to solve equations numerically. We also introduce the idea of recovering a function from its derivative. The key to many of these applications is the Mean Value Theorem, which connects the derivative and the average change of a function.