# List of Benchmarks for Mathematics |

**Standard 3.** | Uses basic and advanced procedures while performing the processes of computation |

| ** Level Pre-K (Grade Pre-K)** |

| 1. | Knows that the quantity of objects can change by adding or taking away objects |

| ** Level I (Grade K-2)** |

| 1. | Adds and subtracts whole numbers A |

| 2. | Solves real-world problems involving addition and subtraction of whole numbers A |

| 3. | Understands basic estimation strategies (e.g., using reference sets, using front-end digits) and terms (e.g., "about," "near," "closer to," "between," "a little less than") |

| 4. | Understands the inverse relationship between addition and subtraction |

| 5. | Understands strategies for the addition and subtraction of whole numbers |

| ** Level II (Grade 3-5)** |

| 1. | Multiplies and divides whole numbers A |

| 2. | Adds, subtracts, multiplies, and divides decimals A |

| 3. | Adds and subtracts simple fractions (i.e., commonly used fractions, fractions with common denominators) A |

| 4. | Uses specific strategies (e.g., front-end estimation, rounding) to estimate computations and to check the reasonableness of computational results A |

| 5. | Performs basic mental computations (e.g., addition and subtraction of whole numbers) |

| 6. | Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers |

| 7. | Understands the properties of and the relationships among addition, subtraction, multiplication, and division (e.g., reversing the order of two addends does not change the sum; division is the inverse of multiplication) A |

| 8. | Solves word problems (e.g., problems that require students to put things into groups or combine things that come in groups)and real world problems involving number operations, including those that specify units (e.g., dollars and cents, hours and minutes, cubic units ) A |

| 9. | Knows the language of basic operations (e.g., "products," "multiplication") |

| 10. | Understand strategies for the multiplication of whole numbers (e.g., arrays, area models) and their division (e.g., creating equal shares, grouping) |

| ** Level III (Grade 6-8)** |

| 1. | Adds, subtracts, multiplies, and divides integers, and rational numbers A |

| 2. | Adds and subtracts fractions with unlike denominators; multiples and divides fractions A |

| 3. | Understands exponentiation of rational numbers and root-extraction (e.g., squares and square roots, cubes and cube roots) |

| 4. | Selects and uses appropriate computational methods (e.g., mental, paper and pencil, calculator, computer) for a given situation |

| 5. | Understands the correct order of operations for performing arithmetic computations A |

| 6. | Uses proportional reasoning to solve mathematical and real-world problems (e.g., involving equivalent fractions, equal ratios, constant rate of change, proportions, percents) A |

| 7. | Understands the properties of operations with rational numbers (e.g., distributive property, commutative and associative properties of addition and multiplication, inverse properties, identity properties) A |

| 8. | Knows when an estimate is more appropriate than an exact answer for a variety of problem situations A |

| 9. | Understands how different algorithms work for arithmetic computations and operations |

| ** Level IV (Grade 9-12)** |

| 1. | Adds, subtracts, multiplies, divides, and simplifies rational expressions A |

| 2. | Adds, subtracts, multiplies, divides, and simplifies radical expressions containing positive rational numbers |

| 3. | Understands various sources of discrepancy between an estimate and a calculated answer |

| 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 |

| 5. | Understands basic applications of and operations on matrices |

| 6. | Uses recurrence relations (i.e., formulas expressing each term as a function of one or more of the previous terms, such as the Fibonacci sequence or the compound interest equation) to model and to solve real-world problems (e.g., home mortgages, annuities) |

| 7. | Understands counting procedures and reasoning (e.g., use of the counting principles to find the number of ways of arranging objects in a set, the use of permutations and combinations to solve counting problems) |

| ** Level V (Grade (College Readiness))** |

| 1. | Knows properties (e.g., distributive, associative) of complex numbers |

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A = Assessment items available |