**Grades 9 - 12**

**1. Effectively uses a variety of strategies in the
problem-solving process**

- Classifies problem-solving strategies or problem types by underlying general characteristics
- Constructs and describes simple algorithms for solving problems that take several steps
- Constructs direct mathematical proofs when solving problems

**2. Understands and applies basic and advanced properties of the
concepts of numbers**

- Understands the basic characteristics of the real-number system and its subsystems
- Understands the basic characteristics of roots and exponents
- Demonstrates and understanding of relative magnitude by expressing numbers in scientific notation
- Has a basic understanding of the concept of inequalities

**3. Uses basic and advance procedures while performing the
process of computation**

- Solves real-world problems involving decimals
- Adds and subtracts algebraic expressions
- Solves real-world problems involving roots and exponents

4. Understands and applies basic and advance properties of the concept of measurement

- Applies measurement formulas and solves problems involving units of measurement
- Uses scale drawings in solving problems

5. Understands and applies basic and advanced properties of the concepts of geometry

- Uses the properties of lines to describe figures algebraically
- Knows the characteristics and properties of conic sections
- Solves real-world problems using Pythagorean relationships

6. Understands and applies basic and advanced concepts of data analysis and distributions

- Understands the basic features of data sets (matrices)
- Represents data sets in a variety of ways
- Solves real-world problems involving data matrices

7. Understands and applies basic and advanced concepts of probability and statistics

- Determines probabilities using a variety of techniques
- Understands that a mathematical mode can be used to predict real-world outcomes
- Compare experimental results with mathematical expectations

8. Understands and applies basic and advanced properties of functions and algebra

- Simplifies algebraic expressions involving numbers and variables
- Solves systems of equations and inequalities graphically, algebraically, and using matrices
- Represents real-world problems using algebraically functions and graphs of those functions (both linear and nonlinear)

9. Understands the general nature and uses of mathematics

- Understands the relationship of development of mathematics to real-world
- Understands that mathematical theories often have highly practical applications in the real-world
- Understands that technological innovations continue to lead to new mathematics and uses of currently developed theories