By the end of Grade 5, competencies in shape composition and decomposition, and especially the special case of spatial structuring of rectangular arrays should be highly developed. Students need to develop these competencies because they form a foundation for understanding multiplication, area, volume, and the coordinate plane.

Students extend their spatial structuring in two ways. They learn to spatially structure in three dimensions; for example, they can decompose a right rectangular prism built from cubes into layers, seeing each layer as an array of cubes. They use this understanding to find the volumes of right rectangular prisms with edges whose lengths are whole numbers as the number of unit cubes that pack the prisms. Second, students extend their knowledge of the coordinate plane, understanding the continuous nature of two-dimensional space and the role of fractions in specifying locations in that space.

Students in Grade 5 learn to analyze and relate categories of two-dimensional and three-dimensional shapes explicitly based on their properties. Based on analysis of properties, they classify two-dimensional figures in hierarchies.

Students also solve mathematical and real-world problems using coordinates. They graph connect ordered pairs of (whole number) coordinates to points on a grid, so that these coordinate pairs constitute numerical objects. Students then interpret the results within the context of situation.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.