**Module
1: Integer Exponents and Scientific Notation**

In Grade 8 Module 1, students expand their basic knowledge of
positive integer exponents and prove the Laws of Exponents for any integer
exponent. Next, students work with numbers in the form of an integer
multiplied by a power of 10 to express how many times as much one is than the
other. This leads into an explanation of scientific notation and
continued work performing operations on numbers written in this form. '

**Module 2: The Concept of Congruence**

In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.

**Module 3: Similarity**

In Module 3, students learn about dilation and similarity and
apply that knowledge to a proof of the Pythagorean Theorem based on the
Angle-Angle criterion for similar triangles. The module begins with the
definition of dilation, properties of dilations, and compositions of
dilations. One overarching goal of this module is to replace the common
idea of “same shape, different sizes” with a definition of similarity that can
be applied to geometric shapes that are not polygons, such as ellipses and
circles.

**Module 4: Linear
Equations**

In Module 4, students extend what they already know about unit
rates and proportional relationships to linear equations and their
graphs. Students understand the connections between proportional
relationships, lines, and linear equations in this module. Students learn
to apply the skills they acquired in Grades 6 and 7, with respect to symbolic
notation and properties of equality to transcribe and solve equations in one
variable and then in two variables.

**Module 5: Examples
of Functions from Geometry**

In the first topic of this 15 day module, students learn the
concept of a function and why functions are necessary for describing geometric
concepts and occurrences in everyday life. Once a formal definition of a
function is provided, students then consider functions of discrete and
continuous rates and understand the difference between the two. Students
apply their knowledge of linear equations and their graphs from Module 4 to graphs
of linear functions. Students inspect the rate of change of linear
functions and conclude that the rate of change is the slope of the graph of a
line. They learn to interpret the equation y=mx+b as defining a linear
function whose graph is a line. Students compare linear functions and
their graphs and gain experience with non-linear functions as well. In
the second and final topic of this module, students extend what they learned in
Grade 7 about how to solve real-world and mathematical problems related to
volume from simple solids to include problems that require the formulas for
cones, cylinders, and spheres.

**Module 6: Linear
Functions**

In Grades 6 and 7, students worked with data involving a single
variable. Module 6 introduces students to bivariate data. Students
are introduced to a function as a rule that assigns exactly one value to each
input. In this module, students use their understanding of functions to
model the possible relationships of bivariate data. This module is
important in setting a foundation for students’ work in algebra in Grade 9.

**Module 7: Introduction
to Irrational Numbers Using Geometry**

Module 7 begins with work related to the Pythagorean Theorem and
right triangles. Before the lessons of this module are presented to
students, it is important that the lessons in Modules 2 and 3 related to the
Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons
13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to
determine the unknown length of a right triangle. In cases where the side
length was an integer, students computed the length. When the side length
was not an integer, students left the answer in the form of **x**^{2}**=*** c*, where