Patterns with Words, Numbers, Symbols, and Variables

Grade 5 introduces variables: the symbol n standing for any term number. A pattern rule like term value = 4n + 1 is a formula that works for every term simultaneously: it produces 5, 9, 13, 17 when n = 1, 2, 3, 4. This is the beginning of algebra. The table of values shows the input-output structure that becomes the function in secondary mathematics. Students who can write a rule with a variable can find any term without listing all the previous ones.