# Mathematics (Grades 5–12) Subtest 1

## Subarea I.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