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

Welcome to algebra! In previous courses, you may have learned about relationships between two quantities that could be graphed with a straight line. In this unit, you will explore nonlinear functions and learn how to describe a function completely. You will see the shapes and behaviors of several different nonlinear functions. This unit also introduces you to sharing your mathematical knowledge with a study team as you work together to solve problems.

In this unit, we will focus on the starting value and growth of linear functions, how to multiply expressions, describing a dependent relationship, called the association, and using the association to make a prediction given realworld applications. You will explore the connections between the multiple representations of linear functions: tables, graphs, equations, and situations; and come to a deeper understanding of slope as a rate of change. You will solve equations that contain products and multivariables. This unit will also introduce how to utilize scatterplots of data to create lines and curves that model the data, and then use those models to make predictions.

Unit 3: Systems of Linear Equations & Inequalities; TwoVariable Statistics
In this unit, students expand and deepen their prior understanding of expressions, equations, and inequalities. Students reason about equations, inequalities, and systems of equations and inequalities as ways to represent constraints, and they reason about the process of solving equations and inequalities in terms of finding values that satisfy those constraints. The process of finding solutions may involve rewriting and manipulating equations. Students learn to explain and validate the steps to do so.
Students revisit twoway tables to find associations in categorical data using relative frequencies. The unit also builds on previous knowledge of scatter plots by assessing how well a linear model matches the data using residuals as well as the correlation coefficient for bestfit lines (found using technology). It closes with an exploration of the difference between correlation and causal relationships as well as an opportunity to apply this learning to anthropology and sports. Throughout the unit, students practice reasoning about situations and mathematical representations, interpreting expressions and numbers in context, and using mathematical tools to model quantities and relationships.

In this unit, you will study quadratic functions systematically. You will look at patterns which grow quadratically and contrast them with linear and exponential growth. You will then examine other quadratic relationships via tables, graphs, and equations, gaining appreciation for some of the special features of quadratic functions and the situations they represent. You will analyze equivalent quadratic expressions and how these expressions help to reveal important behavior of the associated quadratic function and its graph. You will also gain an appreciation for the factored, standard, and vertex forms of a quadratic function and use these forms, as well as your graphing calculator, to solve problems.

In this unit, students are introduced to exponential relationships. Students learn that exponential relationships are characterized by a constant quotient over equal intervals and compare them to linear relationships which are characterized by a constant difference over equal intervals. They encounter contexts with quantities that change exponentially. These contexts are presented verbally and with tables and graphs. They construct equations and use them to model situations and solve problems. They learn that the output of an increasing exponential function is eventually greater than the output of an increasing linear function for the same input.

Unit 6: OneVariable Statistics
In this unit, students are introduced to onevariable statistics. Students learn that. They encounter contexts with quantities that have varying means, medians, Interquartile Ranges (IQR), Mean Absolute Deviations (MAD), standard deviations, and outliers. These contexts are presented verbally and with box and whisker plots, dot plots and histograms. They construct spreadsheets and use them to obtain the information of varying situations and to solve problems.