MTTC Lower Elementary Education (PK-3) Math Subtest [Subarea Two Objective #6-D]
Explicit Method
A method for generating patterns where each element can be directly calculated using a formula or rule. Example: The numerical pattern 2, 4, 8, 16, ... can be generated explicitly using the formula 2^n, where n is the position of the element.
Recursive Method
A method for generating patterns where each element is derived from the preceding element(s) in the sequence. Example: The numerical pattern 1, 3, 6, 10, ... is generated recursively by adding consecutive natural numbers: 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, and so on.
Methods of Generation
Different approaches or rules used to create new elements in a pattern based on the existing elements. Example: Two methods of generation for the numerical pattern 3, 6, 9, 12, ... could be "add 3 to the previous number" or "multiply each number by 3."
Pattern Completion
Extending a given pattern by predicting or finding missing elements based on the identified rule. Example: Completing the pattern 3, 6, 9, ___, ___ by applying the rule "add 3 to the previous number."
Geometric Patterns
Patterns that involve the arrangement of shapes or objects in a specific order, with each shape or object following a consistent rule. Example: A geometric pattern might involve arranging squares in an alternating black-white-black-white sequence.
Justification of Patterns
Providing reasoning and evidence to support the identified rule or method used to generate a pattern. Example: Justifying the numerical pattern 1, 4, 9, 16, ... as "square numbers," where each element is the square of a natural number.
Regular and Irregular Patterns
Regular patterns follow a predictable rule, while irregular patterns may not have a clear rule or may include variations. Example: The pattern 2, 4, 6, 10, 12 is regular, while 1, 3, 8, 18, 35 is irregular.
Rule Identification
The process of identifying the underlying rule or formula that generates the elements in a pattern. Example: Identifying the rule "multiply each number by 2" for the pattern 2, 4, 8, 16, ...
