Table of Math Skills by Grade Group

Here is a table summarizing the key math skills that students may be expected to develop in each of four pre-college 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 Mid-continent Regional Educational Laboratory (McREL), and is used here with their permission.

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Upper Elementary

Middle School

High School


represents problems with physical objects or pictures

trial and error; process of elimination

proportional thinking

proofs; algorithms


whole numbers

decimals, fractions, odd & even numbers, mixed numbers; place value

rational & irrational numbers; exponents; scientific notation; ratios, proportions, percents

real-number system; inequalities


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


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


circles, squares, triangles

angles, similarity, symmetry, congruence

slope; 3-dimensions; 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