Students continue to explore operations with fractions; develop understanding of operations containing whole numbers and decimals to hundredths; and familiarize themselves with volume.

**What’s 5th Grade Math all about? **

Grade 5 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.

**How did we order the units?**

In Grade 4, students learned that in whole numbers a digit in one place represents ten times what is represented in the place to its right. In Grade 5** 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, they are 1/10 of the value. 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 Grade 4 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 Grade 4 to two-digit divisors in Grade 5.

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 Grade 4 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 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 each operation 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.

This course follows the 2017 Massachusetts Curriculum Frameworks, which incorporate the 2010 Common Core State Standards. Further, we believe that daily fluency and application practice are an important part of elementary mathematics instruction but are not included in our mathematics units. All students in Grade 5 receive about 45 minutes of practice in those areas during other blocks.

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1

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.

2

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.

3

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.

4

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.

5

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.

6

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.

7

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.