The following multiple-select 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:
Which of these represent a linear function?
- (3, 6), (0, 2), (3, 5)
- For each square whose sides have length s, the perimeter is 4s.
Resources for further study
Purple Math, developed by Elizabeth Stapel, a math teacher from the St Louis area, has a series of four webpages that deal with linear functions and how they are represented, here. She describes how they can be represented in tables, graphs, equations, and word problems, as shown here.
The Khan Academy, developed by Sal Khan, an engineer who has created a library of thousands of video lessons, has a series of tutorial videos, here, that explain how to recognize linear functions and distinguish them from nonlinear functions.
Chapter 3 of Paul A Foerster’s book Algebra and Trigonometry deals with linear functions. He comes right out and says: A linear function is a function specified by an equation of the form
Complete reference: Foerster, Paul A. Algebra and Trigonometry: Functions and Applications, revised edition. Addison-Wesley, 1980, 1984. The book is used in several algebra classes taught in middle and high schools in both Illinois and Maryland.
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 analyze different situations by stripping away the context, whether it be a word problem, a graph, a table of values, or whatever, in order to get at the underlying mathematics involving linear functions. It is considered to have a low cognitive demand.
The question can be tested online and should yield results that are as valid and reliable as those obtained on paper. The question is best tested online, since erasures of multiple answers may be interpreted by document scanners as marks rather than erasures if the student erases them incompletely.
No special accommodation challenges can be identified with this question, so the question is considered fair.
Helmut Landsberg developed a report he entitled “Weather and Health” using data from soldiers during World War II. Many documents and papers he produced can be found in the archives of the University of Maryland, here. He showed that people burn about 30 calories per day more for every drop of 1°C in the air temperature.
If you normally burn about 2,000 calories a day at room temperature (22°C), how hot would it have to be for you to burn, according to his predictions, zero calories? Does the relationship between air temperature and calories burned in a day represent a linear function? Do you think it’ll ever get that hot?
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.