Topic: Addition/subtraction |
Mathematics |
| | Standard 3. Uses basic and advanced procedures while performing the processes of computation |
| | | Level Pre-K [Grade Pre-K] |
| | | | Benchmark 1. | Knows that the quantity of objects can change by adding or taking away objects |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Knows that the quantity of objects in a group can change by adding more objects
|
| | | | | | 2. | Knows that the quantity of objects in a group can change by taking away some objects |
| | | 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 |
| | | | Benchmark 4. | Understands the inverse relationship between addition and subtraction |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands that addition and subtraction are inverse relationships |
| | | Level II [Grade 3-5] |
| | | | Benchmark 2. | Adds, subtracts, multiplies, and divides decimals |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands the concept of decimal addition |
| | | | | | 2. | Adds decimals |
| | | | | | 3. | Understands the concept of decimal subtraction |
| | | | | | 4. | Subtracts decimals |
| | | | | | 5. | Understands the concept of decimal multiplication |
| | | | | | 6. | Multiplies decimals |
| | | | | | 7. | Understands the concept of decimal division |
| | | | | | 8. | Divides decimals |
| | | | Benchmark 3. | Adds and subtracts simple fractions |
| | | | | 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 |
| | | | 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 |
| | | | Benchmark 6. | Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Determines the effects of addition on the size and order of numbers |
| | | | | | 2. | Determines the effects of division on the size and order of numbers |
| | | | | | 3. | Determines the effects of subtraction on the size and order of numbers |
| | | | | | 4. | Determines the effects of multiplication on the size and order of numbers |
| | | | Benchmark 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) |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands that multiplication and division are inverse operations |
| | | | | | 2. | Understands multiplication as repeated addition |
| | | | | | 3. | Understands division as repeated subtraction |
| | | | | | 4. | Understands effects of reversing order of things added |
| | | | | | 5. | Understands effects of reversing order of things subtracted |
| | | | | | 6. | Understands effects of reversing order of things multiplied |
| | | | | | 7. | Understands effects of reversing order of things divided |
| | | | Benchmark 8. | Solves real-world problems involving number operations (e.g., computations with dollars and cents) |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Solves money-based problems using multiplication |
| | | | | | 2. | Solves money-based problems using division |
| | | | | | 3. | Solves money-based problems using addition |
| | | | | | 4. | Solves money-based problems using subtraction |
| | | | | | 5. | Determines whether a real-world problem can be solved with computation |
| | | | Benchmark 9. | Knows the language of basic operations (e.g., "products," "multiplication") |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands the term "addend" |
| | | | | | 2. | Understands the term "sum" |
| | | | | | 3. | Understands the term "minuend" |
| | | | | | 4. | Understands the term "subtrahend" |
| | | | | | 5. | Understands the term "difference" |
| | | | | | 6. | Understands the term "product" |
| | | | | | 7. | Understands the term "divisor" |
| | | | | | 8. | Understands the term "dividend" |
| | | | | | 9. | Understands the term "quotient" |
| | | 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 |
| | | | 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 4. | Selects and uses appropriate computational methods (e.g., mental, paper and pencil, calculator, computer) for a given situation |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Knows when paper/pencil is best method for computation |
| | | | | | 2. | Uses calculator for computations |
| | | | | | 3. | Knows when calculator is best method for computation |
| | | | | | 4. | Knows when mental computation is the best method |
| | | | | | 5. | Uses paper/pencil for computation |
| | | | | | 6. | Uses mental computation |
| | | | | | 7. | Knows when computer is best method for computation |
| | | | | | 8. | Uses a computer for computation |
| | | | Benchmark 5. | Understands the correct order of operations for performing arithmetic computations |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Knows the order of operations |
| | | | Benchmark 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) |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands the associative property of addition |
| | | | | | 2. | Understands the commutative property of multiplication |
| | | | | | 3. | Understands the commutative property of addition |
| | | | | | 4. | Understands the concept of multiplicative inverse |
| | | | | | 5. | Understands the distributive property of multiplication |
| | | | | | 6. | Understands the associative property of multiplication |
| | | | | | 7. | Understands the concept of additive inverse |
| | | | | | 8. | Understands how the properties of operations relate to rational numbers |
| | | | | | 9. | Understands the concept of additive identity |
| | | | | | 10. | Understands the concept of multiplicative identity |
| | | | Benchmark 9. | Understands how different algorithms work for arithmetic computations and operations |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands how different algorithms work for multiplication |
| | | | | | 2. | Understands how different algorithms work for division |
| | | | | | 3. | Understands how different algorithms work for subtraction |
| | | | | | 4. | Understands how different algorithms work for addition |
| | | Level IV [Grade 9-12] |
| | | | Benchmark 1. | Adds, subtracts, multiplies, divides, and simplifies rational expressions |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands the concept of a rational expressions |
| | | | | | 2. | Adds rational expressions |
| | | | | | 3. | Subtracts rational expressions |
| | | | | | 4. | Multiplies rational expressions |
| | | | | | 5. | Divides rational expressions |
| | | | | | 6. | Simplifies rational expressions |
| | | | Benchmark 2. | Adds, subtracts, multiplies, divides, and simplifies radical expressions containing positive rational numbers |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Divides radical expressions with positive rational numbers |
| | | | | | 2. | Adds radical expressions with positive rational numbers |
| | | | | | 3. | Understands concept of radical expression with positive rational numbers |
| | | | | | 4. | Subtracts radical expressions with positive rational numbers |
| | | | | | 5. | Multiplies radical expressions with positive rational numbers |
| | | Level V [Grade 13] |
| | | | Benchmark 1. | Knows properties (e.g., distributive, associative) of complex numbers |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Knows how the associative property relates to complex numbers |
| | | | | | 2. | Knows how the distributive property relates to complex numbers |
| | Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | | Level V [Grade 13] |
| | | | Benchmark 4. | Adds, subtracts, multiplies, and divides polynomials |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Adds polynomials |
| | | | | | 2. | Subtracts polynomials |
| | | | | | 3. | Multiplys polynomials |
| | | | | | 4. | Divides polynomials |
