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Grade 5 · Algebra · Patterns and Equations

Find the Rule and the Unknown

Patterns help us predict values we have not built yet. Variables let one rule work for every term.

The big idea

A rule connects the term number to the term value

If a design begins with 2 tiles and gains 3 tiles each term, its values are 5, 8, 11, 14. The rule 3n + 2 describes every term.

Work it through

Find term 10 for the rule 3n + 2

  1. 1. Replace n with the term number: 3(10) + 2.
  2. 2. Multiply first: 30 + 2.
  3. 3. Add: term 10 has 32 tiles.
  4. 4. Verify that moving from term 9 to term 10 adds 3.