Topic: Variables |
Mathematics |
| Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis |
| | Level IV (Grade 9-12) |
| | | Benchmark 3. | Understands the concept of correlation (e.g., the difference between a "true" correlation and a "believable" correlation; when two variables are correlated) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the relationship between causality and correlation |
| | | | | 2. | Understands the concept of spurious correlation |
| | | | | 3. | Understands the concept of correlation |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | Level II (Grade 3-5) |
| | | Benchmark 3. | Knows that a variable is a letter or symbol that stands for one or more numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that a letter or symbol can stand for one or more numbers |
| | Level III (Grade 6-8) |
| | | Benchmark 1. | Knows that an expression is a mathematical statement using numbers and symbols to represent relationships and real-world situations (e.g., equations and inequalities with or without variables) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a mathematical expression |
| | | | | 2. | Understands the role of numbers in math expressions |
| | | | | 3. | Understands the role of variables in math expressions |
| | | | | 4. | Understands the concept of an inequality |
| | | | | 5. | Understands the role of symbols in math expressions |
| | | Benchmark 2. | Understands that a variable can be used in many ways (e.g., as a placeholder for a specific unknown, such as x + 8 = 13; as a representative of a range of values, such as 4t + 7) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that variables can be used in many ways |
| | | | | 2. | Understands variables can be placeholders for specific values |
| | | | | 3. | Understands variables can represent ranges of values |
| | | Benchmark 4. | Understands the basic concept of a function (i.e., functions describe how changes in one quantity or variable result in changes in another) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a function |
| | Level IV (Grade 9-12) |
| | | Benchmark 2. | Uses expressions, equations, inequalities, and matrices to represent situations that involve variable quantities and translates among these representations |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the relationship between inequalities and equations |
| | | | | 2. | Transforms inequalities to equations |
| | | | | 3. | Understands the relationship between equations and matrices |
| | | | | 4. | Represents equations in matrix form |
| | | | | 5. | Understands the relationship between expressions and equations |
| | | | | 6. | Understands the relationship between expressions and inequalities |
| | | | | 7. | Understands the relationship between expressions and matrices |
| | | | | 8. | Understands the relationship between inequalities and matrices |
| | | | | 9. | Understands the concept of an algebraic expressions |
| | | Benchmark 6. | Understands the concept of a function as the correspondences between the elements of two sets (e.g., in algebra, functions are relationships between variables that represent numbers; in geometry, functions relate sets of points to their images under motions such as flips, slides, and turns; in the "real-world," functions are mathematical representations of many input-output situations) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands functions as fixed relationships between elements of two sets |
| | | | | 2. | Understands that in the real world, functions relate inputs to outputs |
| | | | | 3. | Understands that in geometry, functions relate points to images in motion (e.g., flips, slides, turns) |
| | | | | 4. | Understands that in algebra, functions represent relationships between variables |