Topic: Communicating about mathematics |
Mathematics |
| Standard 1. Uses a variety of strategies in the problem-solving process |
| | Level I (Grade K-2) |
| | | Benchmark 2. | Uses discussions with teachers and other students to understand problems |
| | | | Knowledge/skill statements |
| | | | | 1. | Discusses with peers to understand a numerical problem |
| | | Benchmark 3. | Explains to others how she or he went about solving a numerical problem |
| | | | Knowledge/skill statements |
| | | | | 1. | Communicates the steps of a problem–solving process |
| | Level II (Grade 3-5) |
| | | Benchmark 6. | Understands the basic language of logic in mathematical situations (e.g., "and," "or," "not") |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands logic operator “and” |
| | | | | 2. | Understands logic operator “or” |
| | | | | 3. | Understands logic operator “not” |
| | Level III (Grade 6-8) |
| | | Benchmark 8. | Understands the role of written symbols in representing mathematical ideas and the use of precise language in conjunction with the special symbols of mathematics |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands how written symbols represent mathematical ideas |
| | Level IV (Grade 9-12) |
| | | Benchmark 5. | Uses formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations |
| | | | Knowledge/skill statements |
| | | | | 1. | Explains relationships among different representations of problems |
| | | | | 2. | Represents word problems using formal notation |
| Standard 2. Understands and applies basic and advanced properties of the concepts of numbers |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 7. | Knows the common language for comparing quantity of objects (e.g., "more than," "less than," "same as") |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the term "more than" for comparing quantity |
| | | | | 2. | Understands the term "less than" for comparing quantity |
| | | | | 3. | Understands the term "same as" for comparing quantity |
| Standard 3. Uses basic and advanced procedures while performing the processes of computation |
| | Level I (Grade K-2) |
| | | Benchmark 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") |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the term "about" |
| | | | | 2. | Understands the term "near" |
| | | | | 3. | Understands the term "closer to" |
| | | | | 4. | Understands the term "between" |
| | | | | 5. | Understands the term "a little less than" |
| | | | | 6. | Understands the concept of reference sets in estimation |
| | | | | 7. | Understands the concept of front-end estimation |
| | | | | 8. | Understands the concept of estimation as a strategy |
| | Level II (Grade 3-5) |
| | | 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" |
| Standard 5. Understands and applies basic and advanced properties of the concepts of geometry |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 2. | Understands the common language used to describe position and location (e.g., "up," "down," "below," "above," "beside," "inside," "outside") |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the common language used to describe position |
| | | | | 2. | Understands the common language used to describe location |
| | | | | 3. | Understands the term "up" |
| | | | | 4. | Understands the term "down" |
| | | | | 5. | Understands the term "below" |
| | | | | 6. | Understands the term "above" |
| | | | | 7. | Understands the term "beside" |
| | | | | 8. | Understands the term "inside" |
| | | | | 9. | Understands the term "outside" |
| | Level I (Grade K-2) |
| | | Benchmark 2. | Understands the common language of spatial sense (e.g., "left," "right," "horizontal," "in front of") |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of "left" |
| | | | | 2. | Understands the concept of "right" |
| | | | | 3. | Understands the concept of "horizontal" |
| | | | | 4. | Understands the concept of "in front of" |
| | Level II (Grade 3-5) |
| | | Benchmark 1. | Knows basic geometric language for describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a trapezoid |
| | | | | 2. | Understands the concept of a parallelogram |
| | | | | 3. | Understands the concept of a sphere |
| | | | | 4. | Understands the concept of a cube |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Understands appropriate terminology and notation used to define functions and their properties (e.g., domain, range, function composition, inverses) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of range as it relates to functions |
| | | | | 2. | Understands the notation used to represent functions |
| | | | | 3. | Understands the concept of inverse as it relates to functions |
| | | | | 4. | Understands the concept of function composition |
| | | | | 5. | Understands the concept of domain as it relates to functions |