# Mathematics

## What Do Students Learn in 5th Grade Math?

5th Grade Math focuses on three key advancements from previous years: (1) developing fluency with addition and subtraction of fractions, and developing understanding of multiplication and division of fractions in certain cases; (2) integrating decimal fractions into the place value system and developing fluency with operations with whole numbers and decimals to hundredths; and (3) developing understanding of volume.

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## Units

Unit 1

13 Lessons

### Place Value with Decimals

Students build upon their understanding of the place value system by extending its patterns to decimals, and continue to read, write, compare, and round numbers, including decimals, in various forms.

Unit 2

20 Lessons

### Multiplication and Division of Whole Numbers

Students continue their work with multi-digit multiplication and division and the base-ten system in order to finalize fluency with multi-digit multiplication and extend division to two-digit divisors.

Unit 3

16 Lessons

### Shapes and Volume

Students explore the volume of three-dimensional shapes, connecting it to the operations of multiplication and addition, as well as classify two-dimensional shapes hierarchically.

Unit 4

15 Lessons

### Addition and Subtraction of Fractions/Decimals

Students extend their computational work to include fractions and decimals, adding and subtracting numbers in those forms in this unit before moving to multiplication and division in subsequent units.

Unit 5

25 Lessons

### Multiplication and Division of Fractions

Students deepen their understanding of fraction multiplication and begin to explore to fraction division (and fractions as division), as well as apply this new understanding to the context of line plots.

Unit 6

24 Lessons

### Multiplication and Division of Decimals

Students use their knowledge of multiplication and division with whole numbers and with fractions to multiply and divide with decimals, and apply this understanding to the context of measurement conversion.

Unit 7

14 Lessons

### Patterns and the Coordinate Plane

Students are introduced to the coordinate plane and use it to represent the location of objects in space, as well as to represent patterns and real-world situations.

## How Do Students Build 5th Grade Math Skills Across Units?

In 4th grade, students learned that in whole numbers a digit in one place represents ten times what is represented in the place to its right. In 5th Grade Unit 1, Place Value with Decimals, students extend this understanding in two ways. First, they see that a similar pattern emerges with place values to the left of a digit; namely, that a digit in one place represents 1/10 of what it represents in the place to its left. Secondly, students extend these understandings of a digit and the places to the left and to the right to decimal numbers.

In Unit 2, Multiplication and Division of Whole Numbers, students build on their work in 4th grade to establish fluency with up to four-digit by two-digit and three-digit by three-digit multiplication, as well as extend their understanding of division from one-digit divisors in 4th grade to two-digit divisors in 5th grade.

In Unit 3, Shapes and Volume, students explore two-dimensional shapes by classifying them in a hierarchy according to their properties. Students also explore three-dimensional shapes, filling rectangular prisms with unit cubes to find their volume. Then, seeing the layered nature of volume and its relationship to the formula for the area of a rectangle, students apply their recently acquired fluency with multi-digit multiplication to calculate the volume of a rectangular prism, and they use their 4th grade fluency with addition to find the area of composite three-dimensional shapes.

In Unit 4, Addition and Subtraction of Fractions and Decimals, students generalize their understanding of addition and subtraction only being possible when operating with like units to the context of fractions and decimals. Because one must add like units, students see that before they can compute, they may need to find equivalent fractions or be careful to align units (which in turn means aligning the decimal point).

In Units 5, Multiplication and Division of Fractions, students develop a more nuanced idea of what multiplication and division mean in the context of fractions, and they apply that understanding to new cases of those operations, including multiplication of a fraction by a fraction, dividing two whole numbers to acquire a fraction as an answer, and dividing a unit fraction by a whole number and vice versa. With a deep understanding of these operations with fractions, students perform them with decimals in Unit 6, Multiplication and Division of Decimals, making sense of their answers in the context of their place value understanding.

The course ends with Unit 7, Patterns and the Coordinate Plane, in which students explore two numerical patterns and their relationship to one another. The coordinate plane helps to visualize those patterns, as well as other mathematical contexts. This provides a nice culmination to the year, hinting at some concepts that will be further developed in the middle grades, such as bivariate data and ratios and proportions.

### What math skills do students learn in 5th grade?

Students in fifth grade focus on 3 key math skills: Developing fluency with fraction addition and subtraction, integrating decimal fractions into the place value system, and developing an understanding of volume.

### What Common Core Math Standards do students focus on in 5th grade?

The major work of the course focuses on the following Common Core State Standards:

• 5.NBT.A Understand the place value system.
• 5.NBT.B Perform operations with multi-digit whole numbers and with decimals to hundredths.
• 5.NF.A Use equivalent fractions as a strategy to add and subtract fractions.
• 5.NF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
• 5.MD.C Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

### What are the expectations for 5th grade math fluency?

5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

Learn how to develop students' procedural skill and fluency within Fishtank Math curriculum with our Procedural Skill and Fluency Teacher Tool.

### What kind of word problems do students solve in 5th grade math?

Having learned all situation types of all four operations, 5th grade students extend this understanding to solve word problems involving all four operations with fractions and decimals with computations appropriate for the grade level.  Learn how to develop students' word problem solving skills in the Fishtank Math curriculum with our Word Problem Teacher Tool

Math Worksheets

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