The following questions refer to this pattern block fish pattern:
1. 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.
2. Which of the above questions would be good for third graders?
3. 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?
4. 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?
5. Why do we call this kind of pattern a growing pattern rather than a repeating pattern?
6. How can you use multiplication to find out how many pattern blocks are in an N week old fish?