Here are the first two pictures in a growth pattern.

(needs image)

1. Show two different ways to extend this tile pattern. Draw the third and fourth tile designs on grid paper.

2. Explain how you would extend your pattern in order to create or draw the sixth tile design in the pattern.

3. Choose any of the tile pictures. Using that picture, describe a rule for determining the number of square tiles needed to make any tile design in the sequence.

Part II (not shown while working on Part I)

1. Using the three pictures of the tile pattern, describe at least two different rules for determining the number of tiles needed to make any figure in the sequence.

2. Esther, Pam, and Steve each found a different rule for generalizing the number of square tiles neede to build the nth picture. Explain how each student divided the picture in order to come up with this rule. Feel free to use a diagram to help explain their rules.

Esther’s Rule: (2n – 1)(2n + 1) + 4 = # of tiles needed for the nth figure where n is the picture number.

Pam’s Rule: 3 + 4(n/2)(2n) = # of tiles needed for the nth figure where n is the picture number.

Steve’s Rule: [(2n + 1)(2n + 3)] – (2n x 4) = # of tiles needed for the nth figure where n is the picture number.

# Formative Assessment 115

Assessment Problem:

Domain:

Patterns & Functions

Theme:

Patterns

Common Core Standards:

F.BF.1