Here is a table summarizing the key math skills that students may be expected to develop in each of four precollege grade groupings. It is based on United States national content guidelines. For more detail, see the Mathematics Standards and Benchmarks.
This table is provided by the Midcontinent Regional Educational Laboratory (McREL), and is used here with their permission.
Download as a PDF (40 K)
Primary 
Upper Elementary 
Middle School 
High School 

ProblemSolving 
represents problems with physical objects or pictures 
trial and error; process of elimination 
proportional thinking 
proofs; algorithms 
Numbers 
whole numbers 
decimals, fractions, odd & even numbers, mixed numbers; place value 
rational & irrational numbers; exponents; scientific notation; ratios, proportions, percents 
realnumber system; inequalities 
Computation 
adds & subtracts whole numbers 
adds, subtracts, multiplies, & divides whole numbers, and decimals; uses calculator 
adds, subtracts, multiplies, & divides mixed numbers & fractions; estimation techniques 
adds and subtracts algebraic expressions; performs basic operations involving roots and exponents 
Measurement 
length, width, height, weight, time, temperature 
area, mass, volume, circumference, perimeter, capacity 
rate; standard & metric systems; scale drawings; indirect measurements; surface area 
velocity; acceleration; precision, accuracy, & tolerance in measurements 
Geometry 
circles, squares, triangles 
angles, similarity, symmetry, congruence 
slope; 3dimensions; parallel, perpendicular; Pythagorean theorem; motion geometry; geometric models 
Pythagorean relationships; vectors; transformations of geometric shapes 
Data Analysis 
simple graphs 
organizes simple data sets; constructs & reads simple graphs & charts 
central tendency (mean, median, mode); dispersion of data 
data matrices 
Probability & Statistics 
likelihood of events 
predictions; data sampling 
estimates probabilities 
random variables; statistical measures; determines probabilities; normal curve 
Algebra & Functions 
recognizes basic patterns 
constructs patterns 
variables; coordinates; solves simple systems of equations 
functions; algebraic modeling; systems of equations & inequalities; basic trigonometric methods 