PERFORMANCE TASK
There are three health clubs in a city. Club A has a $150 initial fee and charges $45 per month. Club B has an initial fee of $250 and charges $35 per month. Club C has no initial fee but charges $60 per month. Which table (shown on worksheet) represents which club? Explain how you know.
Three friends are interested in joining a health club for different lengths of time.
- D’juan wants to join for just 6 months before he leaves for college.
- Cho wants to join a club for the length of the school year — 10 months.
- Lina wants to commit to a health club for an entire year.
Which health clubs should each friend join so that they spend the least amount of money on their health club membership as possible? Explain your reasoning.
ANNOTATION
The student’s strategy allows the student to easily come to the correct conclusion of which club is the best deal at varying amounts of time.
The student generated linear functions representing the cost of membership for each club at varying durations, which is an appropriate strategy for the task and grade level.
The student indicates through writing that the coefficient of the independent variable represents the slope and interprets it in the context of the problem correctly by relating it to the price per month. The students falls slightly short in explicitly articulating the meaning of slope by saying that it represents the price in dollars per month. Units are not mentioned in the formulas.
The student also indicates through writing that the constant represents the y-intercept and interprets it in the context of the problem correctly by relating it to the initial fee. The students falls slightly short in explicitly articulating the meaning of slope by saying that it represents the initial fee in dollars. Units are not mentioned in the formulas.
The strategy is easy to understand as it includes labels, clear layout, and organization. The work also includes evidence of the student writing notes (page 3, the equations for cost for all the clubs, and at the top of page 2, indicating what each part of the cost equation corresponds to) as reminders to develop his strategy. The work is organized and easily readable. Student computations are also accurate.
The student can move to the advanced category if:
–they possibly extended the table in addition to all the work theyʻve already produced.
–they generated a graph of the data.
–an organic / deductive explanation for Lina who was enrolling for 12 months, since they already determined that the price is equivalent under all plans at 10 months. (So the student could have related it to slope steepness / price per month to determine which plan would be less / more expensive after 10 months.)
–a student could have utilized a system of equations (substitution / graphing / elimination) to determine the intersection point of 10 months.