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?
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?
3. Which of the questions from #2 are good third grade questions?
4. How can you use repeating patterns to generate skip counting sequences?
The following questions refer to the pattern block fish pattern:
5. Which of the following questions would be appropriate to ask of kindergarten children?
a. Make a 4 week-old fish using pattern blocks
b. Tell how many pattern blocks you need for a 1 week old fish, a 2 week old fish and a 3 week old fish.
c. Tell how many pattern blocks you need for a 4 week old fish
d. Tell how many pattern blocks you need for a 5 week old fish
e. Tell how many pattern blocks you need for an 8 week old fish
f. Tell how many pattern blocks you need for a 10 week old fish
g. Tell how many pattern blocks you need for a 20 week old fish
h. Tell how many pattern blocks you need for a 100 week old fish.
6. Which of the above questions would be good for third graders?
7. Make a table showing the age of the fish and the total number of pattern blocks you need to make it. How does this table help you answer the questions in #5? What sort of reasoning does this table encourage?
8. Make a table showing the age of the fish, the number of pattern blocks of each type, and the total number of pattern blocks. How does the table help you answer the questions in #5? What sort of reasoning could you have from this table that would be different from the reasoning in #7?
9. Why do we call this kind of pattern a growing pattern rather than a repeating pattern?
10. How can you use multiplication to find out how many pattern blocks are in an N week old fish?