The National Council for Teachers of Mathematics expects primary school students to have a basic understanding of the concepts that will later be explored in future geometry classes. By the end of the second grade, students should be able to recognize basic two-dimensional and three-dimensional shapes. Students should also be able to anticipate what the shapes might look like if combined.
By the end of the second grade, the NCTM recommends that students have learned to recognize length, volume, weight and area. In addition, students should be able to measure units of these attributes and know which unit goes with which attribute. Students should also be able to order groups of objects based on these measurements.
To lay the groundwork for algebra and other advanced mathematics, the NCTM recommends that students in primary school learn the basics of pattern recognition. By the second grade, students should be able to organize objects by size, number or other types of attributes. In addition, the students should be able to recognize basic patterns such as simple number patterns or series of sounds or colors. Finally, students should be able to reason how these patterns are created and the basic rules that govern the patterns.
Primary school students learn the basics of numbers during this period. Students should be able to basic counting using fingers and recognize the order of numbers in a base-10 system. Students should also be able to recognize numerals and the words for basic numbers. Students should have a general understanding of whole numbers as well as common fractions such as ½ or 1/4.