Square Tiles Task

Tiles are arranged to form pictures like the ones below. Find a formula that enables you to calculate the number of square tiles in Picture “n.” How did you obtain your formula?

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A. If the solution has been obtained numerically, respond to the following question: Is there a way to explain your formula from the figures?

B. How many square tiles will there be in Picture 75? Explain.

C. Can you think of another way of finding a direct formula?

D. Two sixth graders came up with the following two formulas:

Kevin’s direct formula is: T=(n x 2)+(n x 2)+ 1, where n means Picture number and T means total number of squares. Is his formula correct? Why or why not?

Melanie’s direct formula is: T=(n x 2)+ 1+(n x 2)+ 1-1, where n and T mean the same thing as in (D) above. Is her formula correct? Why or why not?

Which formula is correct: Kevin’s formula, Melanie’s formula, or your formula? Explain.

# Formative Assessment 119

Assessment Problem:

Domain:

Patterns & Functions

Theme:

Patterns

Common Core Standards:

F.BF.2

F.BF.1

Research References:

Becker, J., & Rivera, F. (2006). Establishing and justifying algebraic generalization at the sixth grade level. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N. (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 465-472. Prague: PME.