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 third grade, instructional time should be devoted to developing the understanding of multiplication, division, and fractions.
Third grade students develop the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models. They use properties of operations to calculate products of whole numbers, using strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. Mastering this material, and reaching fluency in single-digit multiplications and related divisions with understanding, may be quite time consuming because there are no general strategies for multiplying and dividing all single-digit numbers as there are for addition and subtraction. Instead, there are many patterns and strategies dependent upon specific numbers. Therefore, it is imperative that extra time and support be provided if needed. Students begin with modeling all the quantities involved, and then they work on strategies and finally progress into composing and decomposing using the associative or distributive property (OA).
Third grade students continue adding and subtracting within 1000. They use their place value understanding to round numbers to the nearest 10 or 100. The special role of 10 in the base-ten system is important in understanding multiplication of one-digit numbers with multiples of 10 (NBT).
In third grade, students develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. Students see unit fractions as the basic building blocks of fractions. They use fractions along with visual models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Number line diagrams are important representations for students as they develop an understanding of a fraction as a number, in the early stages they use other representations such as area models, tape diagrams, and strips of paper. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual models and strategies based on noticing equal numerators or denominators. As with equivalence of fractions, it is important in comparing fractions to make sure that each fraction refers to the same whole (NF). Students relate fraction work to geometry by expressing the area of a part of a shape as a unit fraction of the whole (G).
Third grade students use their developing knowledge of fractions and number lines to extend their work from the previous grade by working with measurement data involving fractional measurement. They measure lengths using rulers marked with halves and fourths of an inch. They recognize area as an attribute of two-dimensional regions. Students measure the area of a shape by covering the shape. They understand that rectangles can be decomposed into rectangular arrays of squares, connect area to multiplication, and justify using multiplication to determine the area of a rectangle (MD).
Second Grade Mathematics Progression