Topic: Whole numbers/place value/numeration |
Mathematics |
| Standard 2. Understands and applies basic and advanced properties of the concepts of numbers |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 1. | Understands that numbers represent the quantity of objects |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a number |
| | | | | 2. | Understands the concept of how many |
| | | Benchmark 2. | Counts by ones to ten or higher |
| | | | Knowledge/skill statements |
| | | | | 1. | Counts to ten |
| | | | | 2. | Counts past ten |
| | | Benchmark 3. | Counts objects |
| | | | Knowledge/skill statements |
| | | | | 1. | Knows that a number can be assigned to an object |
| | | | | 2. | Knows that numbers increase by one for each new object that is counted |
| | | Benchmark 4. | Understands one-to-one correspondence |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that objects in a set can correspond with objects in another set |
| | | Benchmark 5. | Understands the concept of position in a sequence (e.g., first, last) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that in a sequence, an object has a position |
| | | | | 2. | Understands the concept of first |
| | | | | 3. | Understands the concept of last |
| | | Benchmark 6. | Knows the written numerals 0-9 |
| | | | Knowledge/skill statements |
| | | | | 1. | Knows that numbers have a written form |
| | | Benchmark 9. | Knows that numbers are used in real-world situations |
| | | | Knowledge/skill statements |
| | | | | 1. | Knows how numbers are used in daily life |
| | Level I (Grade K-2) |
| | | Benchmark 1. | Understands that numerals are symbols used to represent quantities or attributes of real-world objects |
| | | | Knowledge/skill statements |
| | | | | 1. | Knows that a number represents how many of something there is |
| | | Benchmark 2. | Counts whole numbers (i.e., both cardinal and ordinal numbers) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands concept of cardinal number |
| | | | | 2. | Understands concept of ordinal number |
| | | | | 3. | Counts ordinal numbers |
| | | | | 4. | Counts cardinal numbers |
| | | Benchmark 3. | Understands symbolic, concrete, and pictorial representations of numbers (e.g., written numerals, objects in sets, number lines) |
| | | | Knowledge/skill statements |
| | | | | 1. | Represents numbers in concrete fashion |
| | | | | 2. | Represents numbers in pictorial fashion |
| | | | | 3. | Represents numbers in symbolic fashion |
| | | | | 4. | Organizes objects into sets |
| | | | | 5. | Recognizes written numerals |
| | | | | 6. | Understands the concept of a number line |
| | | | | 7. | Knows that numbers are represented symbolically by numerals |
| | | | | 8. | Knows that numbers can be represented concretely in sets |
| | | | | 9. | Knows that numbers can be represented pictorially on a number line |
| | | Benchmark 4. | Uses base ten concepts to compare whole number relationships (e.g., 4 is less than 10, 30 is 3 tens) and represent them in flexible ways (e.g., expanded form, decomposing numbers) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the whole number relationship of "less than" |
| | | | | 2. | Understands the whole number relationship of "greater than" |
| | | | | 3. | Uses base ten concepts to compare whole number relationships |
| | | | | 4. | Uses base ten concepts to represent whole numbers in expanded form |
| | | | | 5. | Uses base ten concepts to represent decomposed whole numbers |
| | Level II (Grade 3-5) |
| | | Benchmark 3. | Understands the basic difference between odd and even numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Recognizes numbers as odd or even |
| | | Benchmark 4. | Understands the basic meaning of place value |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of place value |
| | | 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 6. | Uses models (e.g., number lines, two-dimensional and three-dimensional regions) to identify, order, and compare numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of ordered triplets |
| | | | | 2. | Understands the concept of ordered pairs |
| | | | | 3. | Uses two-dimensional space to represent ordered pairs |
| | | | | 4. | Uses number line to represent numbers |
| | | | | 5. | Uses three-dimensional space to represent ordered triplets |
| | | | | 6. | Uses models to identify numbers |
| | | | | 7. | Uses models to order numbers |
| | | | | 8. | Uses models to compare 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 I (Grade K-2) |
| | | Benchmark 1. | Adds and subtracts whole numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of addition |
| | | | | 2. | Adds whole numbers |
| | | | | 3. | Subtracts whole numbers |
| | | | | 4. | Understands the concept of subtraction |
| | | Benchmark 2. | Solves real-world problems involving addition and subtraction of whole numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Determines whether a problem can be solved by subtracting whole numbers |
| | | | | 2. | Determines whether a problem can be solved by adding whole numbers |
| | Level II (Grade 3-5) |
| | | Benchmark 1. | Multiplies and divides whole numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of multiplication |
| | | | | 2. | Multiplies whole numbers |
| | | | | 3. | Understands the concept of division |
| | | | | 4. | Divides whole numbers |
| | | Benchmark 5. | Performs basic mental computations (e.g., addition and subtraction of whole numbers) |
| | | | Knowledge/skill statements |
| | | | | 1. | Mentally adds whole numbers |
| | | | | 2. | Mentally subtracts whole numbers |
| | | | | 3. | Mentally multiplies whole numbers |
| | | | | 4. | Mentally divides whole numbers |
| | Level III (Grade 6-8) |
| | | Benchmark 1. | Adds, subtracts, multiplies, and divides integers, and rational numbers |
| | | | Knowledge/skill statements |
| | | | | 1. | Adds rational numbers |
| | | | | 2. | Subtracts rational numbers |
| | | | | 3. | Multiplies rational numbers |
| | | | | 4. | Divides rational numbers |
| | | | | 5. | Adds integers |
| | | | | 6. | Subtracts integers |
| | | | | 7. | Multiplies integers |
| | | | | 8. | Divides integers |
| | | | | 9. | Understands the concept of integer addition |
| | | | | 10. | Understands the concept of integer subtraction |
| | | | | 11. | Understands the concept of integer multiplication |
| | | | | 12. | Understands the concept of integer division |