1. If you have an ABC pattern, how many tiles (at least) should you show so that children can figure out and be confident they know what the pattern is?
6 tiles (show at least 2 full repetitions)
2. Which of these questions are appropriate for kindergarten children, when asked about an ABC pattern where 9 tiles are shown and the next 6 are hidden (and the visible and hidden tiles are numbered)?
a. What comes next in the pattern?
b. What are the next 5 tiles in the pattern?
c. What is the 14th tile?
d. What is the 20th tile?
e. What are the numbers of the first 8 "A" tiles?
f. What is the 100th tile?
a and b are good kindergarten questions, and probably c (14 isn't too far down from 9, and i'ts already there but hidden)
3. Which of the questions from #2 are good third grade questions?
c, d and e are really good third grade questions. Especially e, because it uses (and requires) skip counting. Some third graders could solve f, but it's more of a grade 4-6 problem.
4. How can you use repeating patterns to generate skip counting sequences?
Ask questions like 2e: asking the tile numbers for a particular tile in the pattern (the "A" tiles or "B" tiles etc.)