Second grade math skills are very important because they build on what was learned in first grade and prepare students for learning multiplication in third grade. While second graders already know how to count, they learn counting in a variety of ways. To do this, they must have a firm grasp of the order of numbers and how to add and subtract them. Second graders explore how numbers are used in everyday life by comparing them, manipulating them and representing them through many different methods.

### Counting and Place Value

Second grade students count by 1s up to 1,000 and understand that they could continue counting into infinity. They count by 2s, 3s, 4s, 5s, 10s, 25s and 100s out loud and explore number patterns by filling in the blanks of missing numbers. Comparing numbers is an important skill, and the concepts of "greater than," "less than" and whether a number is odd or even are introduced. By learning place value, knowing that a three-digit number tells you how many hundreds, tens and ones there are, second graders prepare to add and subtract larger numbers.

### Addition and Subtraction

Early in second grade students master basic addition facts for numbers one through 10 and the corresponding subtraction facts. By the end of second grade, students should be able to add and subtract two- and three-digit numbers. They know how to "regroup" numbers -- formerly called "carrying" and "borrowing" -- to complete more complex problems. Practice in estimating the addition and subtraction of whole numbers by rounding helps in understanding what the correct answer should be. Second graders also practice equations like 3+3+3+3=12 in preparation for multiplication.

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### Measurement and Money

Second graders practice measuring everything from their desks to each other in inches, feet and yards as well as centimeters, millimeters and meters, and learn the abbreviations and notations for each. They compare lengths and add and subtract them. Second graders learn to identify and count coin money and bills, and enjoy pretending to buy things from each other and give change. They can write $1.50 and know it means one dollar and fifty cents and how to represent it with a dollar bill, quarters, dimes, nickels and pennies.

### Shapes

Second graders probably already know the basic shapes of circle, square, rectangle and triangle, but now they add cylinder, octagon and more to their repertoire and learn to describe them, such as "a rectangle has two sides that are the same length and two sides that are a different length but equal to each other." They learn that a square is a flat shape while a pyramid is a solid.

### Telling Time

Even though clocks, phones and watches most likely have digital displays, learning to tell time helps explain the concept of time to second grade students. It's more than knowing what the hands on the clock face indicate; it's knowing that 2:15 means fifteen minutes past two o'clock, that one-quarter of an hour has passed and that in 45 minutes the time will be three o'clock.

### Interpreting Graphs

Students in second grade learn how to use pictographs as another way to represent numbers, including very large numbers. They learn to interpret basic pictographs that use a variety of symbols and to create the graphs themselves. By understanding that one-half or one-fourth of a symbol stands for one-half or one-fourth of the number that symbol represents, they begin to understand fractions.

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