In pre-kindergarten through 2nd grade, children at this age should understand whole numbers and commonly used fractions such as 1/4, 1/3 and 1/2. They should also be able to recognize, name, build, draw, compare and sort two-and-three dimensional shapes. By the second grade they should also be able to sort and 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 represent and 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 by being able to classify 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 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 and understand ratios, proportions, prime numbers, and exponents.
By the 12th grade, a student must be able to solve problems using algebra, geometry, statistics, probability and discrete mathematics. This means being able to understand and use 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.
If your child is struggling to reach these basic levels, you need to get extra help right away. Begin by talking with your child's teachers and ask for an honest assessment of any obstacles that may be getting in the way of success. With a positive outlook and a concerted focus on problem areas, every child can find the winning formula for success.