Class Descriptions

Scope and Sequence for Integrated Math 1

The course begins with students using a compass and a straightedge to improve their logical-reasoning skills in a

geometric setting. Students gradually build a toolkit of constructions that lead to rigid transformations and showing

congruence of figures. In particular, they examine conditions needed to guarantee triangle congruence.

Students describe the shape of data distributions, using measures of center and variability. This leads them to model

how multiple variables are related, using linear equations and systems of linear equations. Students write, evaluate,

graph, and solve equations, explaining and validating their reasoning with increased precision.

By examining how transformations affect graphs, students connect their geometric understanding of rigid

transformations to their understanding of linear equations on a coordinate plane. These insights lead into a unit on two-

variable statistics in which students examine relationships between variables, using two-way tables, scatter plots, and

linear models. Students continue their exploration of graphs by solving linear inequalities and systems of linear

inequalities to represent constraints in situations.

Shifting focus, students deepen their understanding of functions by representing, interpreting, and communicating

about them, using function notation, domain and range, average rate of change, and features of graphs. They also see

categories of functions, starting with linear functions (including their inverses) and piecewise-defined functions

(including absolute-value functions), followed by exponential functions. For each function type, students investigate real-

world contexts, look closely at the structural attributes of the function, and analyze how these attributes are expressed

in different representations.

Scope and Sequence for Integrated Math 2

Students begin the course making observations about triangles. Building from these observations, students gather

experimental information, develop conjectures, write informal justifications, and then progress to writing formal proofs

using definitions, assertions, and theorems developed in Math 1.

Using transformation-based definitions of congruence and similarity allows students to rigorously prove triangle

similarity theorems. Students apply theorems to prove results about quadrilaterals and other figures. Students extend

their understanding of similarity to right triangle trigonometry in this course and to periodic functions in future courses.

Students then begin their study of quadratic functions. Students investigate real-world contexts, look closely at the

structural attributes of a quadratic function, and analyze how these attributes are expressed in different

representations. The unit concludes with a study of the geometry of parabolas.

Next, students engage with quadratic equations. Through reasoning, writing equivalent equations, and applying the

quadratic formula, students extend their ability to use equations to model relationships and solve problems. Along the

way students encounter rational and irrational solutions, deepening their understanding of the real-number system.

This work leads to students developing an understanding of complex numbers and solving quadratic equations that

include non-real solutions. The idea of , a number whose square is -1, expands the number system to include complex

numbers.

Nearing the end of the course, students analyze relationships between segments and angles in circles and develop the

concept of radian measure for angles, which will be built upon in subsequent courses. Students close the year by

extending what they learned about probability in grade 7 to consider probabilities of combined events and to identify

when events are independent.

Scope and Sequence for Integrated Math 3

Students begin the course with a study of solid geometry. They examine cross-sections of solids and make connections

between cross-sections and dilations. Students also use square root and cube root graphs to illustrate the relationship

between scale factors and scaled area and volume. This work is an opportunity to revisit functions and how they can be

represented in a variety of ways.

This work leads students to analyze situations that are well modeled by polynomial functions before pivoting to study

the structure of polynomial graphs and equations. Students do arithmetic on polynomial and rational functions and use

different forms of the functions to identify asymptotes and end behavior. Students solve rational and radical equations

and learn to recognize when the steps used to solve these types of equations result in solutions that are not solutions to

the original equation. Students also study polynomial identities and use some key identities to establish the formula for

the sum of the first terms of a geometric sequence.

Students then return to their study of exponential functions and establish that the property of growth by equal factors

over equal intervals holds even when the interval has non-integer length. Students use logarithms to solve for unknown

exponents, and are introduced to the number and its use in modeling continuous growth. Logarithm functions and

some situations they model well are also briefly addressed.

Students learn to transform functions graphically and algebraically. In previous courses and units, students adjusted the

parameters of particular types of models to fit data. In this part of the course, students consolidate and generalize this

understanding. This work is useful in the study of periodic functions that comes next. Students work with the unit circle

to make sense of trigonometric functions, and then students use trigonometric functions to model periodic

relationships.

The last unit, on statistical inference, focuses on analyzing experimental data modeled by normal distributions. Students

learn to use sampling and simulations to account for variability in data and estimate population mean, margin of error,

and proportions. Students develop skepticism about news stories that summarize data inappropriately.