Here are the national standards. It doesn't list just 2nd grade but lumps it with pre-K through 2nd. I will list prek-2nd but if you would like to look at 3rd grade also it is at:
http://standards.nctm.org/
Number sense:
count with understanding and recognize "how many" in sets of objects; use multiple models to develop initial understandings of place value and the base-ten number system; develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections; develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers; connect number words and numerals to the quantities they represent, using various physical models and representations; understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.
Algebra:
sort, classify, and order objects by size, number, and other properties; recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another; analyze how both repeating and growing patterns are generated.
Geometry:
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes; describe attributes and parts of two- and three-dimensional shapes; investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
Measurement:
recognize the attributes of length, volume, weight, area, and time; compare and order objects according to these attributes; understand how to measure using nonstandard and standard units; select an appropriate unit and tool for the attribute being measured.
Data analysis and probability:
pose questions and gather data about themselves and their surroundings; sort and classify objects according to their attributes and organize data about the objects; represent data using concrete objects, pictures, and graphs.
Problem Solving
Instructional programs from prekindergarten through grade 12
should enable all students to
Build new mathematical knowledge through problem solving
Solve problems that arise in mathematics and in other contexts
Apply and adapt a variety of appropriate strategies to solve problems
Monitor and reflect on the process of mathematical problem solving
Reasoning and Proof
Instructional programs from prekindergarten through grade 12 should enable
all students to
Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Select and use various types of reasoning and methods of proof
Communication
Instructional programs from prekindergarten through grade 12 should enable
all students to
Organize and consolidate their mathematical thinking through communication
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Analyze and evaluate the mathematical thinking and strategies of others;
Use the language of mathematics to express mathematical ideas precisely.
Connections
Instructional programs from prekindergarten through grade 12 should enable
all students to
Recognize and use connections among mathematical ideas
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
Recognize and apply mathematics in contexts outside of mathematics
Representation
Instructional programs from prekindergarten through grade 12 should enable
all students to
Create and use representations to organize, record, and communicate mathematical ideas
Select, apply, and translate among mathematical representations to solve problems
Use representations to model and interpret physical, social, and mathematical phenomena
Now if most of this is clear as mud (it made my eyes glaze over and I'm a teacher.) Go here for examples to see if you child can do some or most of this. It has E-examples: http://standards.nctm.org/document/eexamples/index.htm#Pre-K-2