Algebra 1 PARCC question: predict from data

The following multiple-droplist 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 quality-control technician at a candle factory tested eight 16-ounce candles, each 3 inches in diameter. These candles came from the same production run. The table shows the decrease in weight of each candle after burning for 3 hours. Candle makers believe that the rate at which the candles burn is constant.

Candle 1 2 3 4 5 6 7 8
Weight loss (ounces) 0.5 0.6 0.5 0.7 0.7 0.5 0.5 0.6

Write an equation that can be used to model the weight, w, of such a candle as a function of the number, h, of hours burning. Then, explain how the equation can be used to predict the weight of a candle that has burned for 5 hours.

Enter your equation and your explanation in the space provided.

Answer and references
Example of a solution strategy (there are others)

Resources for further study

Finding the average from a set of data is not a high school mathematics skill or an algebra 1 skill. But developing a mathematical model that requires you to use the mean of a set of data and interpret the investigation performed by the technician is. I therefore refer you to some discussion of selecting an appropriate modeling technique, which comes from an eighth-grade math class in the UK, developed by Australian author GS Rehill, here.

The Khan Academy, developed by Sal Khan, an engineer who has created a library of thousands of video lessons, has an entire series devoted to the basics of statistics and how to use them appropriately. For mean, median, and mode, see the video here, and use the navigation at the left to move around to different lessons in the series.

Analysis of this question and online accessibility

The question does not test students’ understanding of the Common Core standard it purports to measure; it tests students’ ability develop a model that may or may not be appropriate, given the insufficiency of information presented, to describe a real-world situation and to use that model in predicting future behavior. Students are required to do this, despite the fact that the context as explained in the text of the problem fails to warrant the use of the model that PARCC provides as the correct answer. The question is considered to have a median cognitive demand.

By leaving out important information about the investigation conducted by the technician and the actual source of the data collected and reported, it’s illogical to assume students can use any mathematical model at all to describe the data or to predict future behavior of the candles. The problem setup fails to align to the modeling standard in the Common Core.

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 using the equation editor to show their math in determining the slope. We have previously described problems with the user interface of the equation editor tool (see here), and we will not repeat that argument here. However, we will use the opportunity to remind those of you taking the PARCC math test to spend a little extra time on problems with the equation editor to:

  • Make sure you have typed in all the work necessary to make your case
  • Transfer all your work from scratch paper to the computer so you can receive credit for it

No special accommodation challenges can be identified with this question, so the question is considered fair.

Challenge

Nine geography students received the following scores on a test.

Student Number 1 2 3 4 5 6 7 8 9
Test Score (%) 47 35 67 32 38 39 36 34 35

It was a really hard test. Assuming all students have about the same level of understanding of geography, predict the score for the 10th student on the test, and explain why you chose to use the model you did.

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.

About the Author

Paul Katula

Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.