The base ten standards at the second grade level center around the understanding that three-digit numbers include values of hundreds, tens and ones. Skills using base ten comprehension also include counting to 1000 by 5s, 10s and 100s. Students read and write numbers to 1000 and learn addition and subtraction of numbers up to 100 and 1000. Mentally adding 10 and 100 to other numbers is also a second grade base ten mathematics standard.
The standards for operations and algebraic thinking at the second grade level include fluency in addition and subtraction. Students learn and develop the skills for adding and subtracting numbers up to 100 and practice solving one- and two-step word problems. Addition and subtraction through the number 20 is performed mentally, and all sums of one-digit numbers are learned and committed to memory. Fluency in addition includes learning addition of identical numbers as the foundation for developing understanding of multiplication.
Second grade students learn how to measure objects of different sizes using tools such as rulers and yardsticks. Students also learn to estimate lengths in units of inches, feet, centimeters and meters. Principles of length are combined with addition and subtraction skills through the number 100. Students learn to measure time using both digital and analog clocks. The values of currency and how to represent money using numerals and symbols is learned as well as how to represent data derived from measurement in tables and graphs.
During the second grade year, students are introduced to principles of geometry and characteristics of shapes. They learn to recognize and draw shapes given specific characteristics such as number of sides or angles. Students learn to identify triangles, quadrilaterals, pentagons, hexagons and cubes. Second graders also learn to divide rectangles into equal-sized squares, to divide other shapes into even portions and develop vocabulary representing these divisions, such as halves, thirds and quarters.