In pre-kindergarten through 2nd grade, students are developing the foundation for future learning, so it's important to focus on the basics right away. Children should therefore understand whole numbers and commonly used fractions such as 1/4, 1/3 and 1/2. They should also recognize two-and-three dimensional shapes. By the second grade they should be able to classify objects by size, recognize two and three dimensional shapes, and understand the attributes of length, weight, volume, area and time.
From the 3rd to the 5th grade, students should develop a solid understanding of fractions, decimals and percents. They should also be able to compare whole numbers and decimals. They should be assembling the building blocks of algebra by analyzing patterns and functions, and be preparing for advanced geometry studies classifying two-and three-dimensional shapes according to their properties. They should also be exploring numbers less than 0 and be able to carry out conversions, such as from centimeters to meters.
During grades 6-through-8 students are developing firm conclusions about their abilities and limitations. Children who adopt the attitude that "I'm just not good at math" will find this to be a self-defeating prophecy while those who make steady progress develop the confidence that's vital for higher-level work. This means being able to use fundamental algebraic and geometric concepts to solve problems, understanding ratios, proportions, prime numbers, and exponents and - according to the NCTM - being able to "create and critique inductive and deductive arguments concerning congruence, similarity and the Pythagorean relationship."
By the 12th grade, a student must be able to solve problems using algebra, geometry, statistics, probability and discrete mathematics. This means understanding and using formulas to determine the area and volume of geometric figures, understanding the characteristics of well-designed studies such as those used in surveys and experiments, and understanding how to use Cartesian coordinates and other coordinate systems.
Keep in mind that doing well in mathematics - or most any subject - is a lot like building a house. Your child will need a solid foundation in basic computation skills and a basic understanding of numbers and shapes, followed by framework of skills and knowledge to support the challenging and rigorous work that will cap his or her high school career. With a positive outlook and a concerted focus on addressing problem areas, every child can find the winning formula for success.