**Grade
7 Mathematics Module 1: Ratios and Proportional Relationship**

In this 30-day
Grade 7 module, students build upon sixth grade reasoning of ratios and rates
to formally define proportional relationships and the constant of
proportionality. Students explore multiple representations of
proportional relationships by looking at tables, graphs, equations, and verbal
descriptions. Students extend their understanding about ratios and
proportional relationships to compute unit rates for ratios and rates specified
by rational numbers. The module concludes with students applying proportional
reasoning to identify scale factor and create a scale drawing.

**Grade
7 Module 2: Rational Numbers**

In Grade 6,
students formed a conceptual understanding of integers through the use of the
number line, absolute value, and opposites and extended their understanding to
include the ordering and comparing of rational numbers. This module uses
the Integer Game: a card game that creates a conceptual understanding of
integer operations and serves as a powerful mental model students can rely on
during the module. Students build on their understanding of rational
numbers to add, subtract, multiply, and divide signed numbers. Previous work in
computing the sums, differences, products, and quotients of fractions serves as
a significant foundation.

**Grade
7 Module 3: Expressions and Equations**

This module
consolidates and expands upon students’ understanding of equivalent expressions
as they apply the properties of operations to write expressions in both
standard form and in factored form. They use linear equations to solve
unknown angle problems and other problems presented within context to
understand that solving algebraic equations is all about the numbers.
Students use the number line to understand the properties of inequality and
recognize when to preserve the inequality and when to reverse the inequality
when solving problems leading to inequalities. They interpret solutions
within the context of problems. Students extend their sixth-grade study
of geometric figures and the relationships between them as they apply their
work with expressions and equations to solve problems involving area of a
circle and composite area in the plane, as well as volume and surface area of
right prisms.

**Grade
7 Module 4: Percent and Proportional Relationships**

In Module 4,
students deepen their understanding of ratios and proportional relationships
from Module 1 by solving a variety of percent problems. They convert between
fractions, decimals, and percents to further develop a conceptual understanding
of percent and use algebraic expressions and equations to solve multi-step
percent problems. An initial focus on relating 100% to “the whole” serves as a
foundation for students. Students begin the module by solving problems
without using a calculator to develop an understanding of the reasoning
underlying the calculations. Material in early lessons is designed to
reinforce students’ understanding by having them use mental math and basic
computational skills. To develop a conceptual understanding, students use
visual models and equations, building on their earlier work with these.
As the lessons and topics progress and students solve multi-step percent
problems algebraically with numbers that are not as compatible, teachers may
let students use calculators so that their computational work does not become a
distraction.

**Grade 7
Module 5: Statistics and Probability**

In this
module, students begin their study of probability, learning how to interpret
probabilities and how to compute probabilities in simple settings. They
also learn how to estimate probabilities empirically. Probability
provides a foundation for the inferential reasoning developed in the second
half of this module. Additionally, students build on their knowledge of
data distributions that they studied in Grade 6, compare data distributions of
two or more populations, and are introduced to the idea of drawing informal
inferences based on data from random samples.

**Grade 7
Module 6: Geometry**

In Module 6,
students delve further into several geometry topics they have been developing
over the years. Grade 7 presents some of these topics, (e.g., angles,
area, surface area, and volume) in the most challenging form students have
experienced yet. Module 6 assumes students understand the basics.
The goal is to build a fluency in these difficult problems. The remaining
topics, (i.e., working on constructing triangles and taking slices (or
cross-sections) of three-dimensional figures) are new to students.