First grade marks a transition to a more academically oriented approach to learning. Children may now be in a full program after half-day kindergarten, and may now sit in rows instead of circles or in peer groups.

Math instruction becomes more academic, too. Lessons are more structured, and there are new facts to master. But unlike math classes of days past, when 1st graders were given rules and facts to memorize and then practiced endlessly on worksheets, today's best teachers emphasize experiences that deepen and strengthen kids' understanding of the ideas behind the computations.

**Focus on Sums**

First grade teachers may spend half the year or more on addition and subtraction. Most states have standards that aim for all 1st graders to know the addition facts, and corresponding subtraction facts, for sums to 20. But before kids can master these basics, they need to understand the nature of adding and taking away. Subtraction tends to be a concept that is especially difficult to comprehend. "There should be a lot of time spent on experiencing and understanding what the operations mean," says Cathy Seeley, President of the National Council of Teachers of Mathematics. "If you introduce the rules when a subject is only partially set in a child's mind, he'll become confused."

To that end, teachers use objects and games and challenge their first graders to think creatively about numbers. They may show children a group of objects and ask them, "How many ways can we make 6?" and together come up with 2 and 4, 3 and 3, 1 and 5, and 6 and 0. They will teach "fact families," a term for using the inverse relationship between addition and subtraction to solve problems. For example, 5, 4 and 9 is a fact family. If 5 plus 4 equals 9, then 9 take away 5 must equal 4.

**Shortcuts to Learning**

Most 1st grade teachers employ little tricks to help kids master addition and subtraction. They'll grab almost any object to show how to get 3 and 6 to make 9. They generally won't suggest counting on fingers, which can become a tough-to-break habit later. But they have other time-tested learning aids, such as making tally marks with pencil and paper (a series of parallel lines, with the fifth line in every "bundle" crossing the other lines diagonally), and counting forward for addition and backward for subtraction.

Knowing the sum of doubles, like 8 plus 8, and learning to skip-count (count every other number) is another shortcut. Many teachers encourage 1st graders to memorize their doubles up to 20, and to be able to count by 2's, 5's, and 10's to 100. For example, if your child knows instinctively that 8 plus 8 is 16, he simply has to add one to know the answer to 8 plus 9.

Once the concept of adding and subtracting has clicked, kids need to gain fluency. Teachers play fun games that take advantage of the growing importance of peers in first grade. My son's teacher plays a game called "four corners." Kids rotate through four different math centers in which they play different games. In the first, they take turns showing each other subtraction flash cards; in the second, they roll dice and add the two numbers that appear; in the third they use cards with fact families and try to create as many addition and subtraction facts as they can; in the fourth, they practice addition with flash cards. "Emotional and social interactions are so important to first graders," says Addie Fasulo, a 1st grade teacher at Brookdale Avenue School in Verona, New Jersey. "Pairing children together is a great way to motivate them to learn math."

**Money, Time, and More**

Word problems are a staple on standardized tests, and your child will get her first taste of them this year. She'll learn that word cues like "all together," "put together," and "in all" indicate that the numbers should be added, while phrases like "how many more," "compare," and "find the difference" suggest subtraction.

Your child will also learn about place value, which provides the foundation for learning to "carry over" or "regroup" when adding or subtracting multiple-digit numbers. To help kids understand the concept of the 1's, 10's and 100's place, a common strategy is to use a bundle of straws or Popsicle sticks to represent each place. For instance, to show 24 in Popsicle sticks, you'd put 4 sticks in the "ones" bundle and 2 in the "tens" bundle.

Money is also part of the 1st grade curriculum. A valuable skill in and of itself, it is also a hands-on way to practice adding and subtracting and understand place value. Your child will learn to exchange dimes for pennies and count and make change, perhaps in a pretend classroom store.

Other continuing math concepts include telling time to the nearest half-hour, recognizing shapes, reading thermometers, and using measuring tools, such as rulers. You can also expect your child to do elementary algebra with addition and subtraction problems that involve figuring out which part of the equation is missing, rather than the sum. (Eddie had 14 balloons. Some floated away. He had 5 left. How many did he lose?) He'll learn to organize and compare data, estimate, and continue patterns. Perhaps most vitally, he'll learn the "why" behind his answers, and get in the habit of explaining his reasoning. Even though some parents may be eager for their kids to push ahead to regrouping and other higher-level math skills, teachers realize that these concepts will come more easily when they're built on a solid understanding of the basics.