Topic: Expressions |
Mathematics |
| Standard 3. Uses basic and advanced procedures while performing the processes of computation |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Adds, subtracts, multiplies, divides, and simplifies rational expressions |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a rational expressions |
| | | | | 2. | Adds rational expressions |
| | | | | 3. | Subtracts rational expressions |
| | | | | 4. | Multiplies rational expressions |
| | | | | 5. | Divides rational expressions |
| | | | | 6. | Simplifies rational expressions |
| | | Benchmark 2. | Adds, subtracts, multiplies, divides, and simplifies radical expressions containing positive rational numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Divides radical expressions with positive rational numbers |
| | | | | 2. | Adds radical expressions with positive rational numbers |
| | | | | 3. | Understands concept of radical expression with positive rational numbers |
| | | | | 4. | Subtracts radical expressions with positive rational numbers |
| | | | | 5. | Multiplies radical expressions with positive rational numbers |
| | | Benchmark 4. | Uses a variety of operations (e.g., finding a reciprocal, raising to a power, taking a root, taking a logarithm) on expressions containing real numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of raising real numbers to powers |
| | | | | 2. | Determines the logarithms of real numbers |
| | | | | 3. | Understands the concept of logarithm of real number |
| | | | | 4. | Computes the reciprocals of real numbers |
| | | | | 5. | Understands the concept of the reciprocal of a real numbers |
| | | | | 6. | Takes the roots of real numbers |
| | | | | 7. | Raises real numbers to powers |
| | | | | 8. | Understand the concept of taking roots of real numbers |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | 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 3. | Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands how algebraic expressions can represent functions |
| | | | | 2. | Represents functions using algebraic expressions |
| | | | | 3. | Understands how verbal descriptions can represent functions |
| | | | | 4. | Represents functions using tables |
| | | | | 5. | Understands how tables can represent functions |
| | | | | 6. | Understands how graphs can represent functions |
| | | | | 7. | Represents functions using graphs |
| | | | | 8. | Represents functions using verbal descriptions |
| | | | | 9. | Understands the concept of a Venn diagram |
| | | | | 10. | Represents patterns using Venn diagrams |
| | | | | 11. | Understands how Venn diagrams can represent patterns |
| | | | | 12. | Understands how algebraic expressions can represent patterns |
| | | | | 13. | Represents patterns using algebraic expressions |
| | | | | 14. | Understands how verbal descriptions can represent patterns |
| | | | | 15. | Represents patterns using tables |
| | | | | 16. | Understands how tables can represent patterns |
| | | | | 17. | Understands how graphs can represent patterns |
| | | | | 18. | Represents patterns using graphs |
| | | | | 19. | Represents patterns using verbal descriptions |
| | | | | 20. | Understands the relationship between tables and graphs |
| | | | | 21. | Understands the relationship between tables and verbal descriptions |
| | | | | 22. | Understands the relationship between tables and algebraic expressions |
| | | | | 23. | Understands the relationship between tables and Venn diagrams |
| | | | | 24. | Understands the relationship between graphs and verbal descriptions |
| | | | | 25. | Understands the relationship between graphs and algebraic expressions |
| | | | | 26. | Understands the relationship between graphs and Venn diagrams |
| | | | | 27. | Understands the relationship between verbal descriptions and algebraic expressions |
| | | | | 28. | Understands the relationship between verbal descriptions and Venn diagrams |
| | | Benchmark 8. | Understands basic operations (e.g., combining like terms, expanding, substituting for unknowns) on algebraic expressions |
| | | | Knowledge/skill statements |
| | | | | 1. | Combines like terms of an algebraic expression |
| | | | | 2. | Understands combining like terms of an algebraic expression |
| | | | | 3. | Expands algebraic expressions |
| | | | | 4. | Understands substituting for unknowns in an algebraic expression |
| | | | | 5. | Understands expanding algebraic expressions |
| | | | | 6. | Substitutes for unknowns in an algebraic expression |
| | | | | 7. | Understands operations on algebraic expressions |
| | 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 14. | Understands the meaning of and writes equivalent forms of expressions, equations, inequalities, and relations, including all of their parts(e.g., terms, factors, coefficients). |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the meaning of expressions. |
| | | | | 2. | Understands the meaning of equations. |
| | | | | 3. | Understands the meaning of inequalities. |
| | | | | 4. | Understands the meaning of relations. |
| | | | | 5. | Writes expressions in equivalent forms. |
| | | | | 6. | Writes equations in equivalent forms. |
| | | | | 7. | Writes inequalities in equivalent forms. |
| | | | | 8. | Writes relations in equivalent forms. |
| | | | | 9. | Understands the meanings of terms of an equation. |
| | | | | 10. | Understands the meanings of terms of an expression. |
| | | | | 11. | Understands the meanings of terms of an inequality. |
| | | | | 12. | Understands the meanings of terms of a relation. |
| | | | | 13. | Understands the meanings of factors of an equation. |
| | | | | 14. | Understands the meanings of factors of an expression. |
| | | | | 15. | Understands the meanings of factors of an inequality. |
| | | | | 16. | Understands the meanings of factors of a relation. |
| | | | | 17. | Understands the meanings of coefficient of an equation. |
| | | | | 18. | Understands the meanings of coefficient of an expression. |
| | | | | 19. | Understands the meanings of coefficient of an inequality. |
| | | | | 20. | Understands the meanings of coefficient of a relation. |