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Patterns in Teaching - Coggle Diagram

- - - - Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use patterns in various contexts. 6.2.1.1
      - Represent the relationship from patterns between two varying quantities with function rules, graphs and tables; translate between any two of these representations. 6.2.1.2
  - - - Solve problems using the patterns between the angles formed by intersecting lines. 6.3.2.1
      - Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180 degrees. Use models of triangles to illustrate this fact. 6.3.2.2
  - - - Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions from patterns when actual probabilities are unknown. 6.4.1.4
- - - - Science and Engineering Practices (SEP): Scientific Knowledge is Based on Empirical Evidence- Science findings are based on recognizing patterns.
      - Crosscutting Concepts (CCC): Patterns- Similarities and differences in patterns can be
        used to sort and classify natural phenomena.
        Scientific Knowledge Assumes an Order and
        Consistency in Natural Systems- Science assumes consistent patterns in natural syste
      - Disciplinary Core Ideas (DCI): PS4.A: Wave Properties- Waves, which are regular patterns of motion, can be made in water by disturbing the surface. When waves move across the surface of deep water, the water goes up and down in place; there is no net motion in the direction of the wave ex dept when the water meets a beach.
    - - Crosscutting Concepts (CCC): Patterns-
        Similarities and differences in patterns can be
        used to sort and classify designed products.
  - - - Science and Engineering Practices (SEP): Use evidence (e.g., measurements, observations,
        patterns) to construct an explanation
  - - - Crosscutting Concepts (CCC): Patterns-Patterns can be used as evidence to support an explanation
      - Disciplinary Core Ideas (DCI) ESS2.B: Plate Tectonics and Large-Scale System Interactions- The locations of mountain ranges, deep ocean trenches, ocean floor structures, earthquakes, and volcanoes occur in patterns. Most earthquakes and volcanoes occur in bands that are often along the boundaries between continents and oceans. Major mountain chains form inside continents or near their edges. Maps can help locate the different land and water features areas of Earth
    - - Examples of evidence from patterns could include rock layers with shell fossils above rock layers with plant fossils and no shells, indicating a change from water to land over time; and, a canyon with different rock layers in the walls and a river in the bottom, indicating that over time a river cut through the rock
        
        Disciplinary Core Ideas (DCI): ESS1.C: The History of Planet Earth Local, regional, and global patterns of rock formations reveal changes over time due to earth forces, such as earthquakes. The presence and location of certain fossil types indicate the order in which rock layers were formed
- - - - Provide visual examples of patterns seen in items, shapes, etc. which have been introduced in previous grade levels
      - Students should be able to produce a definition of a pattern as it pertains to math instruction
      - Create numerical patterns based on one given rule (reach back skill)
        
        5.OA.B.3 Generate two numerical patters given two different rules
        
        Provided with scaffolded sequence of connected patterns, students should identify missing one digit numbers in the pattern
        
        Given modeled examples of connected patterns, utilize manipulatives to develop patterns (i.e. interlocking cubes, base ten blocks, colored chips, etc.)
        
        Use physical evidence (i.e. manipulatives to support determination of one digit pattern pair)
        
        Determine connection or relationship between the two rules in a given numerical pattern (scaffold as necessary utilizing picture representatives to support identification of relationship
        
        Graph ordered pairs on a coordinate plane (modifications including enlarging graph, reducing value of digits in pattern, labeling and identifying X vs Y on the plane, etc.)
        
        Given a specific rule (involving any of the four operations including one digit numbers and visual scaffolds (i.e. _, 3, __, 9...) with rule listed under each blank area, identify missing numbers in the numerical pattern
        
        Independently utilize math tools (i.e. calculator) to determine numerical pattern when given starting point (i.e. the starting point is 3 and the pattern rule is add 5) using all operations
  - - - Ensure the utilization of supportive math vocabulary sheet as it pertains to writing expressions, digits within expressions, and the four operations
        
        Identify patterns in definitions for math vocabulary
      - Define parentheses, brackets, and braces with corresponding visuals and define patterns seen within the definitions as it pertains to evaluation
        
        Allow for multisensory opportunities to create each symbol
      - Provide math manipulatives to represent given expression to solve with accuracy
        
        Model how to identify patterns between numerical expressions to solve various expressions using the different types of symbols
        
        Allow for independent creation of expression involving one or more of the listed symbols
        
        Share with partner(s) to practice evaluation using mathematical tools allowed through IEP accommodations
        
        Allow for group reflection of patterns seen within common factors used in partner's expressions and the patterns seen in evaluative situations