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 fourth grade, instructional time should be devoted to developing student understanding of multi-digit multiplication and division, fraction equivalence, addition and subtraction of fractions, and multiplication of fractions by whole numbers.
Students in fourth grade learn to interpret multiplication equations within comparison situations. They extend problem solving to multi-step word problems using the four operations posed with whole numbers. In these problem situations, students must interpret and use remainders with respect to context. Fourth graders extend the idea of decomposition to multiplication and gain familiarity with factors and multiples. They begin reasoning about number or shape patterns, connecting a rule for a given pattern with its sequence of numbers or shapes (OA). Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of two-dimensional objects and classify them by properties of their lines and angels (G).
Fourth grade students extend their work in the base-ten system to 1,000,000 and develop deeper understanding of the relative sizes of digits in each place. They apply their understanding of models for multiplication and division. Students develop strategies based on place value, properties of operations, and the relationship of division to multiplication. They develop, discuss, and use efficient, accurate, and generalizable methods to compute products and find quotients of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate and mentally calculate products, quotients, and interpret remainders based upon the context. Students develop fluency with efficient procedures for multiplying; they understand and explain why the procedures work based on place value and properties of operations. They use these strategies to solve real-world problems. By reasoning repeatedly about the connections between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities. They use standard algorithms to fluently add and subtract (NBT).
Fourth grade students develop understanding of fraction equivalence and operations with fractions. They use benchmark fractions, area models, and number line diagrams to reason about fractions. Students recognize that two different fractions can represent equal amounts, and they develop methods for generating and recognizing equivalent fractions. Fourth grade students use understanding gained from work with whole numbers and the relationships between operations in their work with fractions. They extend previous understanding about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number. When solving word problems, students learn to attend carefully to underlying unit quantities. Students compare decimals up to the hundredths, using the meaning of a decimal as a fraction (NF). Fourth graders use measurements in fractions to make line plots. They also solve problems involving addition and subtraction of fractions by using information presented in line plots (MD).
Third Grade Mathematics Progression