The American Diploma Project (ADP) college and workplace readiness benchmarks for mathematics are organized into four strands. Select the strand name to see the benchmarks.

I. Number Sense and Numerical Operations

Number sense is the cornerstone for mathematics in everyday life. Comparing prices, deciding whether to buy or lease a car, balancing a checkbook, deciding where to invest savings and understanding much of what appears in a daily newspaper all require understanding of and facility with quantified information. Working with numbers requires an understanding of the relationships between numbers, the magnitude of numbers and when to use which operation, as well as the ability to make reasonable estimations and mental computations.

J. Algebra

Mathematicians regularly identify sources of change, distinguish patterns in that change and seek multiple representations - verbal, symbolic, numeric and graphic - to express what transpires. Algebra provides a means of operating with these concepts at an abstract level and extending specific examples to broad generalizations. Predicting savings based on a rate of interest, projecting business revenues and knowing how costs will increase as the square footage of a building increases are all possible once a pattern has been identified.

K. Geometry

Geometry is the study of points, lines, planes and other geometric figures, resulting in a logical system that offers students a way to formulate and test hypotheses and to justify arguments in formal and informal ways. Geometry also provides students with an understanding of the structure of space and spatial relations, such as resolving the best way to fit an oversized object through a door and comparing the amount of a product contained in packages of different shapes. Geometric measurement is the basis by which we quantify the world. Through measurement, students develop respect for precision and accuracy. They also learn to spot potential and actual errors in those measurements and learn how those errors may be compounded in computations.

L. Data Interpretation, Statistics and Probability

Statistical data from opinion polls and market research are integral to informing business decisions and governmental policies. Many jobs require workers who are able to analyze, interpret and describe data quickly and to create visual representations of data - charts, graphs, diagrams - to help get a point across succinctly and accurately. When students learn to make predictions and develop and evaluate inferences from data, they are able to answer such questions as "Will a college degree improve my earnings?" or "Which kinds of college degrees will give me access to the most opportunities and the highest pay?" The ability to apply basic concepts of probability also is connected to the ability to interpret data.

A Note about Mathematical Reasoning

The study of mathematics is an exercise in reasoning. Beyond acquiring procedural mathematical skills with their clear methods and boundaries, students need to master the more subjective skills of reading, interpreting, representing and "mathematicizing" a problem. As college students and employees, high school graduates will need to use mathematics in contexts quite different from the high school classroom. They will need to make judgments about what problem needs to be solved and, therefore, about which operations and procedures to apply. Woven throughout the four domains of mathematics — Number Sense and Numerical Operations; Algebra; Geometry; and Data Interpretation, Statistics and Probability — are the following mathematical reasoning skills:

• Using inductive and deductive reasoning to arrive at valid conclusions.
• Using multiple representations to represent problems and solutions.
• Understanding the role of definitions, proofs and counter-examples in mathematical reasoning; constructing simple proofs.
• Using the special symbols of mathematics correctly and precisely.
• Recognizing when an estimate or approximation is more appropriate than an exact answer.
• Distinguishing relevant from irrelevant information, identifying missing information, and either finding what is needed or making appropriate estimates.
• Recognizing and using the process of mathematical modeling when mathematical structures are embedded in other contexts.
• When solving problems, thinking about strategy, testing ideas, trying different approaches, checking for errors and reasonableness of solutions, and devising ways to verify results.
• Shifting regularly between the specific and the general, using examples to understand general ideas, and extending specific results to more general cases to gain insight.