The following is many of the things second graders are expected to know and be able to do by the end of second grade.
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Represent and solve problems involving addition and subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain foundations for multiplication.
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Measure lengths indirectly and by iterating length units.
Relate addition and subtraction to length.
Work with time and money.
Represent and interpret data.
Reason with shapes and their attributes.