Mathematics (Grades 5–12) Subtest 1

Subarea 1. Number Sense

0001

Understand numbers and number systems.

demonstrating knowledge of order, magnitude, mental mathematics, place value (e.g., bases other than base ten), and the reasonableness of results
demonstrating knowledge of the structure and properties of number systems and their subsets (e.g., integer, rational, complex)
translating between equivalent representations of algebraic and transcendental numbers
translating between geometric, rectangular, and polar representations of complex numbers
interpreting complex solutions to equations

0002

Understand number theory and number operations.

applying basic properties of number theory (e.g., least common multiples, greatest common factors, divisibility, prime and composite numbers, Euclidean algorithm) to solve mathematical and real-world problems
demonstrating knowledge of number operations and the relationships between them, including alternative computational algorithms
applying and justifying the properties (e.g., associative, distributive) of number operations

0003

Apply principles of problem solving.

analyzing methods of estimation and the reasonableness of estimates
selecting an appropriate problem-solving approach to apply in a particular situation
solving problems involving absolute value, integers, fractions, decimals, percents, integer and rational exponents, and scientific notation using different strategies and representations
solving and representing problems using ratios and proportional reasoning