Topic: Exponents/logarithms/roots |
Mathematics |
| Standard 2. Understands and applies basic and advanced properties of the concepts of numbers |
| | Level III (Grade 6-8) |
| | | Benchmark 1. | Understands the relationships among equivalent number representations (e.g., whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponentials) and the advantages and disadvantages of each type of representation |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the equivalence of decimals and percents |
| | | | | 2. | Understands the equivalence of whole numbers and fractions |
| | | | | 3. | Understands the equivalence of fractions and ratios |
| | | | | 4. | Understands the equivalence of whole numbers and ratios |
| | | | | 5. | Understands the equivalence of whole numbers and decimals |
| | | | | 6. | Understands the equivalence of whole numbers and percents |
| | | | | 7. | Understands the equivalence of whole numbers and scientific notation |
| | | | | 8. | Understands the equivalence of integers and fractions |
| | | | | 9. | Understands the equivalence of integers and ratios |
| | | | | 10. | Understands the equivalence of integers and decimals |
| | | | | 11. | Understands the equivalence of integers and percents |
| | | | | 12. | Understands the equivalence of integers and scientific notation |
| | | | | 13. | Understands the equivalence of integers and exponents |
| | | | | 14. | Understands the equivalence of fractions and decimals |
| | | | | 15. | Understands the equivalence of ratios and decimals |
| | | | | 16. | Understands the equivalence of ratios and percents |
| | | | | 17. | Understands the equivalence of decimals and scientific notation |
| | | | | 18. | Understands the equivalence of decimals and exponents |
| | | | | 19. | Understands the equivalence of scientific notation and exponents |
| | | | | 20. | Understands the advantages and disadvantages of different number representations |
| | | Benchmark 5. | Understands the characteristics and uses of exponents and scientific notation |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of exponents |
| | | | | 2. | Understands the concept of scientific notation |
| | Level IV (Grade 9-12) |
| | | Benchmark 2. | Understands the properties and basic theorems of roots, exponents (e.g., [bm][bn] = bm+n), and logarithms |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a theorem |
| | | | | 2. | Understands theorems of exponents |
| | | | | 3. | Understands basic theorems of roots |
| | | | | 4. | Understands basic theorems of logarithms |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 1. | Understands the properties of rational exponents |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of rational exponents |
| Standard 3. Uses basic and advanced procedures while performing the processes of computation |
| | Level III (Grade 6-8) |
| | | Benchmark 3. | Understands exponentiation of rational numbers and root-extraction (e.g., squares and square roots, cubes and cube roots) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of square roots |
| | | | | 2. | Understands the concept of roots |
| | | | | 3. | Understands the concept of cubes |
| | | | | 4. | Understands the concept of squares |
| | | | | 5. | Understands the concept of cube roots |
| | Level IV (Grade 9-12) |
| | | 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 IV (Grade 9-12) |
| | | Benchmark 5. | Solves polynomial equations (e.g., find the real or complex roots of a quadratic equation) using a variety of methods (e.g., symbolically, graphically, numerically). |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of polynomials |
| | | | | 2. | Understands the concept of roots |
| | | | | 3. | Solves polynomial equations symbolically. |
| | | | | 4. | Models real world problems using polynomial equations without the use of technology. |
| | | | | 5. | Solves real world problems using polynomial equations with the use of technology. |
| | | | | 6. | Solves polynomial equations by finding the real roots of a quadratic equation. |
| | | | | 7. | Solves polynomial equations by finding the complex roots of a quadratic equation. |