Students in Kindergarten develop an understanding between numbers and quantities, and count to answer “How many?” They begin to develop an understanding of single-digit addition and subtraction based on subitizing. Students develop meanings for addition and subtraction as they encounter problem situations in Kindergarten, and they extend these meanings as they encounter increasingly difficult problem situations subsequent grades.
In grades 3-5, students focus on understanding the meaning and properties of multiplication and division, and they extend these meanings as they encounter increasingly difficult problem situations. Developing an understanding of the properties of place value and the base ten number system is fundamental in elementary school. Students begin to develop an understanding of addition and subtraction using place value properties.
As students progress they begin to use place value understanding to develop fluency with procedures and to solve problems by selecting and applying appropriate methods. Students also begin building a foundational understanding of fractions by partitioning circles and rectangles into equal shares which builds to an understanding of fractions as numbers. They develop an understanding of equivalence and begin to apply this understanding to compare quantities. Using models, student develop an understanding of the algorithms for adding, subtracting and multiplying fractions. Students learn to describe and compare measureable attributes, as well as estimating and measuring in length units and comparing lengths.
Students start to solve real-world problems using customary and metric units of measurement finding the areas, perimeter and volume of geometric shapes. In elementary school, students work with categorical and numerical data, answering simple questions regarding the data in graphs. Students pose questions, collect and analyze data, generate appropriate mathematical representations, and interpret the data to answer questions. In geometry, students begin to identify and compose shapes. They develop an understanding of measureable attributes to describes shapes. Students understand that geometric figures can be described, analyzed, compared, and classified based on their properties, such as the presence or absence of parallel or perpendicular sides, angle measures, and symmetry.
Students also begin to graph points in the first quadrant of a coordinate plane, and identify and interpret the x- and y-coordinates to solve problems. The concepts that students engage in during elementary school are fundamental to the work they will do in subsequent grades.