Students in the second grade are introduced to fractions, learn new math vocabulary terms, build on their knowledge of addition and subtraction to include adding and subtracting 2 and 3 digit numbers and work with the metric system as well as the American system of weights and measures. Students are taught scientific methodology such as collecting and analyzing data to prove their answers.
Grade two students are expected to understand the baseten system of numeration and build on their first grade introduction to place values and zero as a place holder. They are expected to recognize and understand the numbers up to 1000 and identify the place values. Students should be familiar with estimating, renaming and comparisons of numbers. In second grade a child should be able to take any number under 1000 and expand it with numbers or words. For instance, 79 = 7 tens + 9 ones or 532 is 5 sets of 100, 3 sets of 10 and 2 units. Students are expected to have competency using the greater than, less than or equal to symbols. They should also recognize odd and even numbers and should be able to skip count by 2's, 3's, 5's, 10's, 25's, 50's and 100's to 1000. Counting forward or backward by 1's or 10's with any starting point less than 1000 is another second grade accomplishment.
In addition and subtraction, students are expected to have the inverse property rule memorized and should be able to predict that adding results in a larger sum and subtraction reduces the result. They should be able to prove their answers using the inverse relationship between addition and subtraction. They should be able to recognize multiple strategies for equations such an s modeling, doubling and separation of units. They learn to choose appropriate strategies to be able to do the calculations in their heads, if the numbers allow.

Part/whole relationships are explored further with the introduction of fractions. Halves, quarters, thirds and other fractions are recognized as parts of a set and as such, make up the whole. Students should be able to represent fractions, compare them, make different representations of the same fraction, and combine different fractions to make a whole. Second grade students should also be able to model and solve problems that use addition, subtraction and the use of recording in fraction form.
The multiplication tables are introduced and the students are expected to learn the 2's, 5's and 10's up to "times 10." Multiplication is presented as repeated addition. This readies the student for the challenges of grade three.
The foundations of measurement introduced in the first grade are expanded to include the metric system and when to use it versus the American system. Second graders learn how to mentally divide an object into equal parts and they also learn if part A is longer than part B, and part B is longer than part C, then part A is longer than part C. These more advanced mathematical measuring concepts and terminology, partitioning and transitivity, and the use of standard units of measure and the understanding that students develop which lets them see that the smaller the unit, the more of them they will need to make up the whole are all lessons in most second grade math classes. Lessons in measuring time and the ability to tell time at 5minute intervals are part of the curriculum competency goals. Students are also given lessons on counting various coin denominations to add up to a dollar or more and practice making change.
In geometry, students are using simple figures to create a given shape, can describe symmetry and congruency and can explain what happens to two and three dimensional figures when they are cut an rearranged. The children use these concepts to prepare themselves for understanding area, proportions and more advanced spatial reasoning.