# Mathematics (Grades 5–12) Subtest 1

## Subarea I.1. Number Sense

0001
Understand numbers and number systems.

- demonstrating knowledge of magnitude, mental mathematics, place value, and the reasonableness of results
- demonstrating knowledge of the properties and relations of number systems (e.g., integer, rational, complex)
- translating between equivalent representations of algebraic and transcendental numbers
- translating between geometric and polar representations of complex numbers
- interpreting complex solutions to equations

0002
Understand number theory and operations on numbers.

- applying basic properties of number theory (e.g., LCM, GCF, divisibility, prime and composite numbers, Euclidean algorithm) to solve mathematical and real-world problems
- demonstrating knowledge of number operations, including alternative computational algorithms
- applying 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 the best problem-solving approach to apply in a particular situation
- solving problems using different strategies and representations (e.g., ratio and proportions, percents, scientific notation)