The following paragraphs provide an overview of the important concepts and skills students in this grade level will learn. More importantly, teachers are provided a cursory look at how instruction in prior grades has built the foundation for the material in the current grade level. It is imperative that teachers understand that the topics outlined in the paragraphs, as well as the Standards listed within each trimester of the Pacing View, are not exclusive to the trimesters in which they are listed; the Common Core State Standards are not a list of Standards that can be “checked off” once they have been taught. For students to truly master the rigorous concepts and skills of the Common Core State Standards, they will need to be exposed to the Standards in multiple settings and situations, making connections between and among the Standards from different Domains. This will obviously require the revisiting of Standards over the course of the entire year. Finally, to ensure that the Standards are taught to the depth of understanding required in the Common Core State Standards, teachers will need to be keenly aware of how their lessons today can and will be extended and expanded in future lessons that may occur in subsequent trimesters and grade levels.
In fifth grade, instructional time should be devoted to developing fluency with addition and subtraction of fractions, understanding of volume, and extending and developing understanding of operations with decimals.
Fifth grade students begin working more formally with expressions. They evaluate and interpret numerical expressions and analyze patterns and relationships. Fifth grade students extend their fourth grade pattern work by working with two numerical patterns that can be related and by examining these relationships within sequences of ordered pairs and on the coordinate plane (OA). They apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions. Students make sense of fractional quantities when solving word problems, estimating answers mentally to see if they make sense. They calculate sums and differences of fractions with like and unlike denominators (NF).
Fifth grade students extend their fourth grade work with decimals as they convert measurement within given measurement systems. They use measurements in fractions to make line plots. They solve problems involving operations with fractions by using information presented in line plots. Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and determining actual volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes for solving real-world problems (MD).
In fifth grade, students extend their understanding of the base-ten system to decimals to the thousandths place, building on their fourth grade work with tenths and hundredths. They also extend their understanding to relationships between adjacent places, how numbers compare, and how decimal numbers round to thousandths. They apply their understanding of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between decimals and whole numbers, to understand and explain why the procedures for multiplying and dividing decimals make sense. They efficiently and accurately compute products and quotients of decimals to hundredths. They develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. By the end of fifth grade, students fluently compute products of multi-digit whole numbers using only the standard multiplication algorithm. Underlying this algorithm are the properties of operations and the base-ten system. Students are not expected to fluently compute quotients using the standard division algorithm until the end of sixth grade.