**Module 1: Ratios and Unit
Rates **

Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.

** Module 2: Arithmetic Operations Including Division of Fractions**

In Module 1,
students used their existing understanding of multiplication and division as
they began their study of ratios and rates. In Module 2, students
complete their understanding of the four operations as they study division of
whole numbers, division by a fraction and operations on multi-digit decimals.
This expanded understanding serves to complete their study of the four
operations with positive rational numbers, thereby preparing students for
understanding, locating, and ordering negative rational numbers (Module 3) and
algebraic expressions (Module 4).

**Module 3: Rational Numbers**

Students are
familiar with the number line and determining the location of positive
fractions, decimals, and whole numbers from previous grades. Students extend
the number line (both horizontally and vertically) in Module 3 to include the
opposites of whole numbers. The number line serves as a model to relate
integers and other rational numbers to statements of order in real-world
contexts. In this module's final topic, the number line model is extended to
two-dimensions, as students use the coordinate plane to model and solve
real-world problems involving rational numbers.

**Module 4: Expressions and Equations**

In Module 4,
Expressions and Equations, students extend their arithmetic work to include
using letters to represent numbers in order to understand that letters are
simply "stand-ins" for numbers and that arithmetic is carried out
exactly as it is with numbers. Students explore operations in terms of verbal
expressions and determine that arithmetic properties hold true with expressions
because nothing has changed—they are still doing arithmetic with numbers.
Students determine that letters are used to represent specific but unknown
numbers and are used to make statements or identities that are true for all
numbers or a range of numbers. They understand the relationships of operations
and use them to generate equivalent expressions, ultimately extending
arithmetic properties from manipulating numbers to manipulating expressions.
Students read, write and evaluate expressions in order to develop and evaluate
formulas. From there, they move to the study of true and false number
sentences, where students conclude that solving an equation is the process of
determining the number(s) that, when substituted for the variable, result in a
true sentence. They conclude the module using arithmetic properties,
identities, bar models, and finally algebra to solve one-step, two-step, and
multi-step equations.

**Module 5: Area, Surface Area, and Volume Problems**

In this module,
students utilize their previous experiences in order to understand and develop
formulas for area, volume, and surface area. Students use composition and
decomposition to determine the area of triangles, quadrilaterals, and other
polygons. Extending skills from Module 3 where they used coordinates and
absolute value to find distances between points on a coordinate plane, students
determine distance, perimeter, and area on the coordinate plane in real-world
contexts. Next in the module comes real-life application of the volume
formula where students extend the notion that volume is additive and find the volume
of composite solid figures. They apply volume formulas and use their
previous experience with solving equations to find missing volumes and missing
dimensions. The final topic includes deconstructing the faces of solid
figures to determine surface area. To wrap up the module, students apply
the surface area formula to real-life contexts and distinguish between the need
to find surface area or volume within contextual situations.

** Module 6: Statistics**

In this module,
students move from simply representing data into analysis of data.
Students begin to think and reason statistically, first by recognizing a
statistical question as one that can be answered by collecting data.
Students learn that the data collected to answer a statistical question has a distribution
that is often summarized in terms of center, variability, and shape.
Throughout the module, students see and represent data distributions using dot
plots and histograms. They study quantitative ways to summarize numerical
data sets in relation to their context and to the shape of the
distribution. As the module ends, students synthesize what they have
learned as they connect the graphical, verbal, and numerical summaries to each
other within situational contexts, culminating with a major project.

Important Vocabulary for 6th Grade Math

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