The following multi-part (constructed response and fill-in-the-blank) question, explained here in hopes of helping algebra students in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2015 test in algebra 1, here:
A school is holding a raffle to earn money. The list shows all the prizes in the school’s raffle.
- A computer that costs $349
- A book collection that costs $42
- A gift certificate that costs $25
- A pair of movie tickets that costs $18
- A gift basket that costs $16
The raffle ticket price is set so that 75 raffle tickets will pay for all of the prizes.
Create a function that can be used to find the total amount of money the school earns by selling x tickets. Show your work used to create this function.
Enter your function and your work in the space provided.
The school’s goal is to raise at least $850 more than the total cost of the prizes. What is the minimum number of raffle tickets that have to be sold in order for the school to reach its goal?
Enter your answer in the box.
Resources for further study
The Minnesota Department of Education has a page entitled “Modeling Word Problems” in the Minnesota STEM Teacher Center, here. The page quotes from the book Step-by-step Model Drawing: Solving Math Problems the Singapore Way: “Word problems require that students have the skills to read, understand, strategize, compute, and check their work. That’s a lot of skills! Following a consistent step-by-step approach—and providing explicit, guided instruction in the beginning—can help students organize their thoughts and make the problem-solving task manageable.”
That’s what you need to do! Complete reference: Forsten, C. Step-by-step Model Drawing: Solving Math Problems the Singapore Way. Peterborough, N.H.: Crystal Spring Books, 2009. The Singapore math curriculum has been used in many US schools and incorporated into the curriculum used by many school districts across the country.
Analysis of this question and online accessibility
The question measures knowledge of the Common Core standard it purports to measure and tests students’ ability to build a function that models a real-world situation involving a linear relationship between two quantities. It is considered to have a median cognitive demand.
The question can be tested online and should yield results that are as valid and reliable as those obtained on paper. Students online may experience difficulties with the equation editor, as the use of this online tool is required to receive full credit for Part A.
If students are unfamiliar with the tool—which requires them to enter math work in paragraph form by selecting math symbols from a series of drop-down palettes and does not in any way resemble the way they would do the work if given a pencil and paper—their score will be in jeopardy. Typos are not forgiven in the PARCC scoring rubrics, and students are advised to take a little extra time when using the equation editor tool to make sure they have
- Entered all the work or logic necessary
- Transferred all work from scratch paper to the computer
(I realize using the equation editor is difficult, but you’re not alone. And while people at PARCC are trying to figure out how to make this tool usable for an online test, that’s not going to happen anytime soon. If PARCC people were here, they would be apologizing profusely for this poorly conceived online monstrosity. But they’re not; you’re here, and you have to do this test if you live in a PARCC state.)
No special accommodation challenges can be identified with this question, so the question is considered fair.
Jennie wants to buy tickets to Beyonce’s “Formation World Tour” in Miami, and each ticket costs $58. If she makes $8 an hour and usually has 28 percent income tax withheld, how many hours will she have to work to earn enough to buy tickets for herself and three friends?
Purpose of this series of posts
Voxitatis is developing blog posts that address every algebra 1 question released to the public by the Partnership for Assessment of Readiness for College and Careers, or PARCC, in order to help students prepare to take the test this spring.
Our total release will run from February 27 through March 15, with one or two questions discussed per day. Then we’ll move to geometry at the end of March, algebra 2 during the first half of April, and eighth grade during the last half of April.