**Trading Stickers, Combining Coins: Addition, Subtraction, and the Number System (1)**

Students
solve addition problems with two and three-digit numbers, solve
subtraction problems involving two-digit numbers, find combinations of
numbers that add to 100, and work with coins and coin values. Their
understanding of place value develops as they add and subtract 10s to
and from three-digit numbers, break three-digit numbers into hundreds,
tens, and ones in different ways, and solve story problems involving
hundreds, tens, and ones.

**Collections and Travel Stories: Addition, Subtraction, and the Number System (2)**

Students
practice and refine their strategies for solving addition problems with
three-digit numbers and two- and three-digit numbers. In addition to
solving removal problems, they expand their understanding of subtraction
as they solve comparison problems and problems in which they find the
missing part of a whole. They increase their understanding of
place-value as they extend their work into three-digit numbers up to
1,000 and study the structure of 1,000.

**Perimeter, Angles, and Area: 2-D Geometry and Measurement**

This
unit develops ideas about the attributes of a 2-D objects and how they
are classified (the definition of a triangle, rectangle, and square),
linear measurement (which includes perimeter), area and the measurement
of angles. Using the context of perimeter, students continue to develop
their ability to use measurement tools as they work on accurate linear
measurement techniques. Students learn to identify angles by their
relationship to a right angle. They develop an understanding of area as
the amount of flat space an object covers and determine the area of 2-D
shapes in square units. LogoPaths, a Logo programming environment
designed for Investigations is introduced in this unit. It allows
students to explore geometrical relationships, especially focusing on
angle, length, and perimeter, patterns in sides and angles, and
characteristics of specific shapes.

**Equal Groups: Multiplication and Division**

In
this unit, students develop an understanding of multiplication as
combining a number of equal groups and division as splitting a quantity
into equal groups. This understanding is developed as students highlight
multiples on 100 charts, describe patterns in sets of multiples, and
compare set of multiples to each other. Students represent
multiplication and division situations with groups, rectangular arrays,
and by writing multiplication and division story problems. In this unit,
students achieve fluency with multiplication combinations with products
to 50 and consider the relationship between multiplication and
division.

**Finding Fair Shares: Fractions and Decimals**

Using
a variety of contexts (rectangles representing "brownies", pattern
block "cookies", and groups of objects), students develop their
understanding of fractions as representing equal parts of a whole. They
work with commonly used fractions and their equivalencies (e.g., 3/6 and
2/4 both equal on-half of the same whole) and use fractions and mixed
numbers as they solve sharing problems and build wholes from fractional
parts. They are introduced to decimal fractions in the context of money
and gain familiarity with decimal equivalents for one-fourth and
one-half.

**Surveys and Line Plots: Data Analysis**

Students
collect, represent, describe, categorize, and interpret both
categorical and numerical data. They begin the important work of seeing a
data set as a whole as they design and carry out their own data
investigations, create representations of the data collected, and
compare and discuss these representations. Students draw conclusions
about the data by identifying characteristics in their representations
(Where is most of the data clumped? Where is the mode?) Students'
collection of numerical data includes measuring length in inches and
feet. Students review the basic units of inches, feet, and yards and
their relationships (e.g., one foot is equivalent to 12 inches, one yard
is equivalent to 3 feet or 36 inches) by measuring lengths longer than
one foot.

**Perimeter, Angles, and Area**

during
this unit students work on identifying various attributes of shapes and
learn that the number of sides identifies a shape as a triangle or a
quadrilateral. Students will identify right angles as having a measure
of 90 degrees and learn that angle size is independent of figure size.

**How Many Hundreds? How Many Miles? Addition, Subtraction and the Number System (3)**

Students
further refine their addition strategies with problems involving any
three-digit numbers as they identify and name these strategies. They
continue to solve a variety of subtraction problems and examine their
strategies for subtracting any two- and three-digit number in greater
depth. Students extend their work with place value by estimating the sum
of three-digit numbers (will the sum be more of less than 400?) and
adding and subtracting multiples of 10 and 100 to and from three-digit
numbers. In this unit, students are assessed on fluency with subtraction
facts.