Topic: Fractions |
Mathematics |
| Standard 2. Understands and applies basic and advanced properties of the concepts of numbers |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 8. | Understands that a whole object can be separated into parts |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that a whole object is made up of parts |
| | Level I (Grade K-2) |
| | | Benchmark 5. | Understands the concept of a unit and its subdivision into equal parts (e.g., one object, such as a candy bar, and its division into equal parts to be shared among four people) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a unit |
| | | | | 2. | Understands that a unit can be subdivided |
| | | | | 3. | Understands the concept of equal parts |
| | Level II (Grade 3-5) |
| | | Benchmark 2. | Understands equivalent forms of basic percents, fractions, and decimals (e.g., 1/2 is equivalent to 50% is equivalent to .5) and when one form of a number might be more useful than another |
| | | | Knowledge/skill statements |
| | | | | 1. | Converts fractions to percents |
| | | | | 2. | Converts percents to decimals |
| | | | | 3. | Converts fractions to decimals |
| | | | | 4. | Knows the equivalence of common fractions and percents |
| | | | | 5. | Knows the equivalence of common fractions and decimals |
| | | | | 6. | Knows the equivalence of common percents and decimals |
| | | Benchmark 5. | Understands the concepts related to fractions (e.g., numerator and denominator, equivalence, relative magnitudes) and decimals (e.g.,relative magnitudes) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of numerator and denominator |
| | | | | 2. | Understands the concept of fractions |
| | | | | 3. | Understands the concept of decimals |
| | | | | 4. | Understands the concept of equivelant fractions |
| | | | | 5. | Understands the relative magnitude of fractions |
| | | | | 6. | Understands the relative magnitudes of decimals |
| | | Benchmark 7. | Uses base ten concepts to represent decimals and fractions in flexible ways (e.g., composing and decomposing numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Uses base ten concepts to represent decimals in flexible ways. |
| | | | | 2. | Uses base ten concepts to represent fractions in flexible ways. |
| | | | | 3. | Uses base ten concepts to compose decimal numbers. |
| | | | | 4. | Uses base ten concepts to decompose decimal 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 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 |
| Standard 3. Uses basic and advanced procedures while performing the processes of computation |
| | Level II (Grade 3-5) |
| | | Benchmark 3. | Adds and subtracts simple fractions (i.e., commonly used fractions, fractions with common denominators) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of addition of fractions |
| | | | | 2. | Adds simple fractions |
| | | | | 3. | Understands the concept of subtraction of fractions |
| | | | | 4. | Subtracts simple fractions |
| | Level III (Grade 6-8) |
| | | Benchmark 2. | Adds and subtracts fractions with unlike denominators; multiples and divides fractions |
| | | | Knowledge/skill statements |
| | | | | 1. | Adds fractions with unlike denominators |
| | | | | 2. | Subtracts fractions with unlike denominators |
| | | | | 3. | Multiplies fractions |
| | | | | 4. | Divides fractions |
| | | Benchmark 6. | Uses proportional reasoning to solve mathematical and real-world problems (e.g., involving equivalent fractions, equal ratios, constant rate of change, proportions, percents) |
| | | | Knowledge/skill statements |
| | | | | 1. | Determines whether a problem can be solved by calculating percents |
| | | | | 2. | Understands the concept of a constant rate of change |
| | | | | 3. | Determines whether a problem can be solved using the concept of a constant rate of change |
| | | | | 4. | Determines whether a problem can be solved using the concept of proportions |
| | | | | 5. | Determines whether a problem can be solved using the concept of equivalent fractions |
| | | | | 6. | Understands the concept of equivalent fractions |
| | | | | 7. | Understands the concept of equal ratios |
| | | | | 8. | Understands the concept of mathematical proportion |
| | | | | 9. | Determines whether a problem can be solved using the concept of equal ratios |
| | | | | 10. | Uses proportional reasoning to solve mathematical problems involving percents |
| | | | | 11. | Uses proportional reasoning to solve mathematical problems involving equivalent fractions |
| | | | | 12. | Uses proportional reasoning to solve mathematical problems involving equal ratios |
| | | | | 13. | Uses proportional reasoning to solve mathematical problems involving a constant rate of change |
| | | | | 14. | Uses proportional reasoning to solve mathematical problems involving proportions |