Topic: Patterns |
Mathematics |
| Standard 1. Uses a variety of strategies in the problem-solving process |
| | Level III (Grade 6-8) |
| | | Benchmark 3. | Understands that there is no one right way to solve mathematical problems but that different methods (e.g., working backward from a solution, using a similar problem type, identifying a pattern) have different advantages and disadvantages |
| | | | Knowledge/skill statements |
| | | | | 1. | Works backward from a solution |
| | | | | 2. | Identifies a similar problem type |
| | | Benchmark 6. | Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning) |
| | | | Knowledge/skill statements |
| | | | | 1. | Provides supportive arguments for conjectures |
| | | | | 2. | Generalizes from a pattern of observations |
| | | | | 3. | Makes conjectures from generalizations |
| | Level IV (Grade 9-12) |
| | | Benchmark 1. | Uses a variety of strategies (e.g., identify a pattern, use equivalent representations) to understand new mathematical content and to develop more efficient solution methods or problem extensions |
| | | | Knowledge/skill statements |
| | | | | 1. | Uses strategies to understand new mathematical content |
| | | | | 2. | Uses strategies to develop more efficient solution methods |
| | | | | 3. | Uses strategies to extend solution methods to other problems |
| Standard 5. Understands and applies basic and advanced properties of the concepts of geometry |
| | Level I (Grade K-2) |
| | | Benchmark 4. | Understands that patterns can be made by putting different shapes together or taking them apart |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that patterns can be made by putting shapes together |
| | | | | 2. | Understands that patterns can be made by taking shapes apart |
| Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 3. | Identifies patterns in graphical displays of data |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands graphical displays of data |
| | | | | 2. | Identifies trends in graphical displays of data |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | Level Pre-K (Grade Pre-K) |
| | | Benchmark 1. | Understands simple patterns (e.g., boy-girl-boy-girl) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands boy-girl-boy-girl patterns |
| | | | | 2. | Understands the basic concept of a pattern |
| | | Benchmark 2. | Repeats simple patterns |
| | | | Knowledge/skill statements |
| | | | | 1. | Repeats simple patterns |
| | Level I (Grade K-2) |
| | | Benchmark 1. | Recognizes regularities in a variety of contexts (e.g., events, designs, shapes, sets of numbers) |
| | | | Knowledge/skill statements |
| | | | | 1. | Recognizes patterns in events |
| | | | | 2. | Understands the concept of a pattern |
| | | | | 3. | Recognizes patterns in designs |
| | | | | 4. | Recognizes patterns in shapes |
| | | | | 5. | Recognizes patterns in sets of numbers |
| | | Benchmark 2. | Extends simple patterns (e.g., of numbers, physical objects, geometric shapes) |
| | | | Knowledge/skill statements |
| | | | | 1. | Extends simple patterns in numbers |
| | | | | 2. | Extends simple patterns in geometric shapes |
| | | | | 3. | Extends simple patterns in objects |
| | Level II (Grade 3-5) |
| | | Benchmark 1. | Recognizes a wide variety of patterns (e.g., basic linear patterns such as [2, 4, 6, 8 . . .] ; simple repeating and growing patterns) and the rules that explain them |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a growing pattern |
| | | | | 2. | Understands the concept of a simple repeating pattern |
| | | | | 3. | Recognizes linear patterns |
| | | | | 4. | Recognizes increasing patterns |
| | | | | 5. | Recognizes decreasing patterns |
| | | | | 6. | Recognizes the rules that explain simple patterns |
| | | Benchmark 2. | Understands that the same pattern can be represented in different ways (e.g., geometrically or numerically; the pattern of numbers [7, 14, 21, 28 . . .] is equivalent to the mathematical relationship 7 × n) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that patterns can be represented numerically |
| | | | | 2. | Understands that patterns can be represented geometrically |
| | | | | 3. | Represents simple patterns geometrically |
| | | | | 4. | Represents simple patterns numerically |
| | Level III (Grade 6-8) |
| | | Benchmark 3. | Understands various representations (e.g., tables, graphs, verbal descriptions, algebraic expressions, Venn diagram) of patterns and functions and the relationships among them |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands how algebraic expressions can represent functions |
| | | | | 2. | Represents functions using algebraic expressions |
| | | | | 3. | Understands how verbal descriptions can represent functions |
| | | | | 4. | Represents functions using tables |
| | | | | 5. | Understands how tables can represent functions |
| | | | | 6. | Understands how graphs can represent functions |
| | | | | 7. | Represents functions using graphs |
| | | | | 8. | Represents functions using verbal descriptions |
| | | | | 9. | Understands the concept of a Venn diagram |
| | | | | 10. | Represents patterns using Venn diagrams |
| | | | | 11. | Understands how Venn diagrams can represent patterns |
| | | | | 12. | Understands how algebraic expressions can represent patterns |
| | | | | 13. | Represents patterns using algebraic expressions |
| | | | | 14. | Understands how verbal descriptions can represent patterns |
| | | | | 15. | Represents patterns using tables |
| | | | | 16. | Understands how tables can represent patterns |
| | | | | 17. | Understands how graphs can represent patterns |
| | | | | 18. | Represents patterns using graphs |
| | | | | 19. | Represents patterns using verbal descriptions |
| | | | | 20. | Understands the relationship between tables and graphs |
| | | | | 21. | Understands the relationship between tables and verbal descriptions |
| | | | | 22. | Understands the relationship between tables and algebraic expressions |
| | | | | 23. | Understands the relationship between tables and Venn diagrams |
| | | | | 24. | Understands the relationship between graphs and verbal descriptions |
| | | | | 25. | Understands the relationship between graphs and algebraic expressions |
| | | | | 26. | Understands the relationship between graphs and Venn diagrams |
| | | | | 27. | Understands the relationship between verbal descriptions and algebraic expressions |
| | | | | 28. | Understands the relationship between verbal descriptions and Venn diagrams |
| | | Benchmark 7. | Understands special values (e.g., minimum and maximum values, x- and y-intercepts, slope, constant ratio or difference) of patterns, relationships, and functions |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands x- and y-intercepts |
| | | | | 2. | Understands the concept of slope |
| | | | | 3. | Understands constant ratio or difference |
| | | | | 4. | Understands the concept of maximum |
| | | | | 5. | Understands the concept of minimum |
| | | Benchmark 11. | Understands the properties of arithmetic and geometric sequences (i.e., linear and exponential patterns) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the properties of geometric sequences |
| | | | | 2. | Understands the properties of arithmetic sequences |
| | | | | 3. | Understands the concept of a linear sequence |
| | | | | 4. | Understands the concept of an exponential sequence |
| | Level IV (Grade 9-12) |
| | | Benchmark 7. | Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships |
| | | | Knowledge/skill statements |
| | | | | 1. | Represents functions using graphs |
| | | | | 2. | Represents functions using table of input/output values |
| | | | | 3. | Represents functions using algebraic formula |
| | | | | 4. | Represents functions using written statements |
| | | | | 5. | Represents functions using models |
| | | | | 6. | Represents patterns using graphs |
| | | | | 7. | Represents patterns using table of input/output values |
| | | | | 8. | Represents patterns using algebraic formula |
| | | | | 9. | Represents patterns using written statements |
| | | | | 10. | Represents patterns using models |
| | | | | 11. | Represents relationships using graphs |
| | | | | 12. | Represents relationships using table of input/output values |
| | | | | 13. | Represents relationships using algebraic formula |
| | | | | 14. | Represents relationships using written statements |
| | | | | 15. | Represents relationships using models |