Formative Assessment 44

Assessment Problem: 

Concert Hall Problem (arithmetic sequence)
The first row of a concert hall has 10 seats. Each row thereafter has 2 more seats than the row in front of it.
a) How many seats are in Row 10? (If student had difficulty, ask how many seats in Rows 2, 3, and 4.)
b) The ticket manager needs to know how many seats are in each row. If she knows the number of the row, explain how she can figure out how many seats are in that row.
c) Let R represent the number of the row and let S represent the number of seats in that row. Can you give an equation for finding the number of seats?
d) How many seats are in Row 21? If the last row has 100 seats, how many rows are in the concert hall?

Common Responses: 

This problem was used in an interview with 10 six-grade students:
All 10 students were able to compute specific cases correctly.
2 students were able to describe the functional relation. 5 students described the relation recursively.
Only 2 students were able to represent the problem symbolically (writing an equation)

Mathematical Issues: 

Students can translate a word problem into an equation, but cannot use the equation to solve the problem.

Algebraic Relations
Common Core Standards: 
A-CED: Create equations that describe numbers or relationships
Research References: 
(Swafford &Langrall, 2000)