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 first grade, instructional time should be devoted to developing students’ understanding of addition and subtraction and whole number relationships. Students develop strategies for adding and subtracting based on prior work with small numbers in kindergarten; knowing combinations of ten and decomposing numbers 11–19. Students begin with using a variety of models as they work through contextual situations and begin to understand connections between counting and addition and subtraction. As they progress with modeling, they begin to develop strategies based on properties of addition. Children build their understanding of the relationships of addition and subtraction by comparing a variety of solution strategies. Using direct modeling and counting strategies, first graders extend addition and subtraction beyond 10 to within 20 (OA).
As first grade students develop a solid understanding for the meaning of addition and subtraction, they begin to extend their understanding of the base-ten system (NBT). Students learn to view ten ones as a unit called “ten.” They compose and decompose this unit and see a two-digit numeral as representing some tens and ones. First graders use their base-ten work to develop, discuss, and use methods to add within 100 and subtract with multiples of 10. They will also compare and solve problems with whole numbers up to 100. Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
Measurement and Data (MD) and Geometry (G) work in first grade have important connections to addition, subtraction, and comparing amounts. First graders must develop an understanding of the meaning and process of measurement. They measure lengths indirectly and by iterating unit lengths (i.e., using non-standard units). Students also begin to represent and interpret data, comparing up to three categories. They build off their prior knowledge of composing and decomposing to understand part-whole relationships with plane and solid figures. As they combine shapes, they describe and compare attributes to develop a background for measurement and an initial understanding of properties such as congruence and symmetry.