**Module 1: Place Value and Decimal Fractions**

In Module 1,
students’ understanding of the patterns in the base ten system are extended
from Grade 4’s work with place value of multi-digit whole numbers and decimals
to hundredths to the thousandths place. In Grade 5, students deepen their
knowledge through a more generalized understanding of the relationships between
and among adjacent places on the place value chart, e.g., 1 tenth times any
digit on the place value chart moves it one place value to the right.
Toward the module’s end students apply these new understandings as they reason
about and perform decimal operations through the hundredths place.

**Module 2: Multi-Digit Whole Number and Decimal Fraction Operations**

In Module 2
students apply patterns of the base ten system to mental strategies and a
sequential study of multiplication via area diagrams and the distributive
property leading to fluency with the standard algorithm. Students move
from whole numbers to multiplication with decimals, again using place value as
a guide to reason and make estimations about products. Multiplication is explored
as a method for expressing equivalent measures in both whole number and decimal
forms. A similar sequence for division begins concretely with number
disks as an introduction to division with multi-digit divisors and leads
student to divide multi-digit whole number and decimal dividends by two-digit
divisors using a vertical written method. In addition, students evaluate
and write expressions, recording their calculations using the associative
property and parentheses. Students apply the work of the module to solve
multi-step word problems using multi-digit multiplication and division with
unknowns representing either the group size or number of groups. An
emphasis on the reasonableness of both products and quotients, interpretation
of remainders and reasoning about the placement of decimals draws on skills
learned throughout the module, including refining knowledge of place value,
rounding, and estimation.

**Module 3: Addition and Subtraction of Fractions**

In Module 3,
students' understanding of addition and subtraction of fractions extends from
earlier work with fraction equivalence and decimals. This module marks a
significant shift away from the elementary grades' centrality of base ten units
to the study and use of the full set of fractional units from Grade 5 forward,
especially as applied to algebra.

**Module 4: Multiplication and Division of Fractions and
Decimal Fractions**

Grade 5’s Module 4 extends student understanding of fraction operations
to multiplication and division of both fractions and decimal fractions.
Work proceeds from interpretation of line plots which include fractional
measurements to interpreting fractions as division and reasoning about finding
fractions of sets through fraction by whole number multiplication. The
module proceeds to fraction by fraction multiplication in both fraction and
decimal forms. An understanding of multiplication as scaling and multiplication
by n/n as multiplication by 1 allows students to reason about products and
convert fractions to decimals and vice versa. Students are introduced to
the work of division with fractions and decimal fractions. Division cases
are limited to division of whole numbers by unit fractions and unit fractions
by whole numbers. Decimal fraction divisors are introduced and equivalent
fraction and place value thinking allow student to reason about the size of
quotients, calculate quotients and sensibly place decimals in quotients.
Throughout the module students are asked to reason about these important
concepts by interpreting numerical expressions which include fraction and
decimal operations and by persevering in solving real-world, multistep problems
which include all fraction operations supported by the use of tape diagrams.

**Module 5: Addition and Multiplication with Volume and Area**

In this 25-day module, students work with two- and three-dimensional
figures. Volume is introduced to students through concrete exploration of
cubic units and culminates with the development of the volume formula for right
rectangular prisms. The second half of the module turns to extending
students’ understanding of two-dimensional figures. Students combine prior
knowledge of area with newly acquired knowledge of fraction multiplication to
determine the area of rectangular figures with fractional side lengths.
They then engage in hands-on construction of two-dimensional shapes, developing
a foundation for classifying the shapes by reasoning about their
attributes. This module fills a gap between Grade 4’s work with
two-dimensional figures and Grade 6’s work with volume and area.

**Module 6: Problem Solving with the Coordinate Plane**

In this 40-day module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiar number line as an introduction to the idea of a coordinate, and they construct two perpendicular number lines to create a coordinate system on the plane. Students see that just as points on the line can be located by their distance from 0, the plane’s coordinate system can be used to locate and plot points using two coordinates. They then use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the rules that generate them. This study culminates in an exploration of the coordinate plane in real world applications.