## Mathematics

#### An Overview of Grade 5: 2nd Edition1

The fifth grade curriculum is organized into 9 units that offer from 2½ to 4½ weeks of work, focused on the area(s) of mathematics identified in the unit’s subtitle. Because units build on each other, both within and across strands, they are designed for use in the sequence shown.

Unit Title and Number of Sessions

**Number Puzzles and Multiple Towers**

Multiplication and Division 1

**22 sessions**

**Prisms and Pyramids**

3-D Geometry and Measurement

**16 sessions**

**Thousands of Miles, Thousands of Seats**

Addition, Subtraction, and the Number System

**15 sessions**

**What's That Portion?**

Fractions and Percent 1

**21 sessions**

**Measuring Polygons**

2-D Geometry and Measurement

**18 sessions**

**Decimals on Grids and Number Lines**

Decimals, Fractions, and percent

**18 sessions**

**How Many People? How Many Teams?**

Multiplication and Division 2

**20 sessions**

**Growth Patterns**

Patterns, Functions, and Change

**13 sessions**

**How Long Can You Stand on One Foot?**

Data Analysis and Probability

**15 sessions**

Note that the Investigations curriculum assumes that each school day includes 70-75 minutes of math: one hour on the day’s Session, and 10-15 minutes on Ten-Minute Math. Designed to fit within the calendar of a typical school year, fifth grade includes a total of 158 sessions (or approximately 32 weeks of work). This provides some leeway for going further with particular ideas and/or accommodating local circumstances. Although pacing will vary somewhat in response to variations in school calendars, needs of students, your school's years of experience with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from the way mathematical ideas are introduced, developed, and revisited across the year.

#### An Overview of the Math in Fifth Grade*

**Number and Operations: Whole Numbers** Students practice and refine the strategies they know for addition, subtraction, multiplication, and division of whole numbers as they improve computational fluency and apply these strategies to solving problems with larger numbers. They expand their knowledge of the structure of place value and the base-ten number system as they work with numbers in the hundred thousand and beyond. By the end of the year, students are expected to know their division facts and to efficiently solve computation problems involving whole numbers for all operations.

**Number and Operations: Fractions, Decimals, and Percent** The major focus of the work with rational numbers is on understanding relationships among fractions, decimals, and percent. Students make comparisons and identify equivalent fractions, decimals and percent. They order fractions and decimals, and develop strategies for adding fractions and decimals to the thousandths.

**Geometry and Measurement** Students develop their understanding of the attributes of 2-D shapes; examine the characteristics of polygons, including a variety of triangles, quadrilaterals, and regular polygons. They also find the measure of angles of polygons. In measurement, students use standard units of measure to study area and perimeter and to determine the volume of prisms and other polyhedral.

**Patterns and Functions** Students examine, represent, and describe situations in which the rate of change is constant. They create tables and graphs to represent the relationship between two variables in a variety of contexts and articulate general rules using symbolic notation for each situation. Students create graphs for situations in which the rate of change is not constant and consider why the shape of the graph is not a straight line.

**Data Analysis and Probability** Work focuses on comparing two sets of data collected from experiments developed by the students. They represent, describe, and interpret this data. In their work with probability, students describe and predict the likelihood of events and compare theoretical probabilities with actual outcomes of many trials. They use fractions to express the probabilities of the possible outcomes.