### Course Summary

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 represents 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 with 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 & 6, Multiplication and Division of Fractions and Decimals, 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, 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 scholars in Grade 5 receive about 45 minutes of practice in those areas during other blocks.

### Standards Overview

How this course covers the Common Core standards for 5th Grade Math