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Generate a pattern from a rule

A pattern is generated by applying a stated rule consistently to successive terms, producing an ordered sequence of whole numbers or shapes and explaining how each term relates to the previous one. The learner represents the resulting pattern in lists, tables, or diagrams and distinguishes the rule from incidental features, including patterns that increase, decrease, or repeat. This work does not include formal nth-term formulas or generalized functions.

Detailed Explanation: Generate a pattern from a rule

A pattern is made by following the same rule each time. Start with the given first term, then use the rule to find the next term.

Example: Start with 77. The rule is add 44 each time. Find the first five terms.

  1. Write the starting number: 77.
  2. Add 44 to get the next term:
7+4=11 7+4=11
  1. Add 44 again:
11+4=15 11+4=15
  1. Continue using the same rule:
15+4=19 15+4=19 19+4=23 19+4=23

You can show the pattern in a list:

7, 11, 15, 19, 237,\ 11,\ 15,\ 19,\ 23

Or in a table:

Term numberNumber
17
211
315
419
523

Check the pattern by comparing neighboring numbers:

7111519237\to11\to15\to19\to23

Each number is 44 more than the number before it. The important feature is the rule “add 44 each time,” not the appearance of the numbers.

Learn by doing: Generate a pattern from a rule

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Patterning - First Values from Rule for Geometric Pattern


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