Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Patterns such as add 3 or multiply by 6. Also, patterns involving remainders. For example, the first day of the year was on Tuesday. What was the 43rd day of the year? Students will also learn how to compute terms of arithmetic series by making tables. Students will not be introduced to the term arithmetic series, nor will they be expected to find or use a formula, as that would require an understanding of variables. Next, give your students this challenge. Finally, give them this one.