Topic: Number systems |
Mathematics |
| Standard 2. Understands and applies basic and advanced properties of the concepts of numbers |
| | Level II (Grade 3-5) |
| | | Benchmark 1. | Understands basic number theory concepts (e.g., prime and composite numbers, factors, multiples, odd and even numbers, divisibility) |
| | | | Knowledge/skill statements |
| | | | | 1. | Knows that numbers are odd or even |
| | | | | 2. | Knows what makes a number prime |
| | | | | 3. | Knows what makes a composite number |
| | | | | 4. | Understands the basic concept of a factor |
| | | | | 5. | Understands the concept of divisibility |
| | | | | 6. | Understands the concept of multiples |
| | Level III (Grade 6-8) |
| | | Benchmark 2. | Understands the characteristics and properties (e.g., order relations, relative magnitude, base-ten place values) of the set of rational numbers and its subsets (e.g., whole numbers, fractions, decimals, integers) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of "less than" with rational numbers |
| | | | | 2. | Understands the concept of "greater than" with rational numbers |
| | | | | 3. | Understands the concept of base 10 |
| | | | | 4. | Understands the concept of rational numbers |
| | | | | 5. | Understands the concept of relative magnitude as it relates to rational numbers |
| | | | | 6. | Understands the concept of relative magnitude as it relates to integers |
| | | Benchmark 3. | Understands the role of positive and negative integers in the number system |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of positive integers |
| | | | | 2. | Understands the concept of negative integers |
| | | Benchmark 4. | Uses number theory concepts (e.g., divisibility and remainders, factors, multiples, prime, relatively prime) to solve problems |
| | | | Knowledge/skill statements |
| | | | | 1. | Determines whether a problem can be solved by using the concept of divisibility |
| | | | | 2. | Determines whether a problem can be solved by using the concept of multiples |
| | | | | 3. | Determines whether a problem can be solved by using the concept of factors |
| | | | | 4. | Determines whether a problem can be solved by using the concept of prime numbers |
| | | | | 5. | Understands the concept of relatively prime |
| | | | | 6. | Determines whether a problem can be solved by using the concept of relatively prime |
| | | Benchmark 6. | Understands the structure of numeration systems that are based on numbers other than 10 (e.g., base 60 for telling time and measuring angles, Roman numerals for dates and clock faces) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of base 60 and its relationship to time |
| | | | | 2. | Understands the concept of Roman numerals |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Understands the properties (e.g., relative magnitude, density, absolute value) of the real number system, its subsystems (e.g., irrational numbers, natural numbers, integers, rational numbers), and complex numbers (e.g., imaginary numbers, conjugate numbers) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of density as it relates to the real number system |
| | | | | 2. | Understands the concept of absolute value |
| | | | | 3. | Understands the concept of relative magnitude as it relates to real numbers |
| | | | | 4. | Understands the concept of real numbers |
| | | | | 5. | Understands the concept of relative magnitude as it relates to irrational numbers |
| | | | | 6. | Understands the concept of irrational numbers |
| | | | | 7. | Understands the concept of integers |
| | | | | 8. | Understands the concept of natural numbers |
| | | | | 9. | Understands the concept of complex numbers |
| | | | | 10. | Understands the concept of imaginary numbers |
| | | | | 11. | Understands the concept of conjugate numbers |
| | | | | 12. | Understands the concept of relative magnitude as it relates to complex numbers |