Sunday, September 20, 2020

# Grade 8 Common Core math: Price per gallon

#### The following two-part computation-based question, explained here in hopes of helping eighth-grade students and their parents 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 “PBA” (performance-based assessment) test for grade 8 math:

The average price per gallon of gasoline in the state of California is given for 4 different dates.

### Gasoline Price Data

Date Average Price per Gallon (dollars)
January 1998 1.291
January 2000 1.354
March 2011 3.874
March 2013 4.069

## Part A

A student claims that the percent increase in the average price per gallon for the two-year period from 2011 to 2013 was about the same as the percent increase for the two-year period from 1998 to 2000. Provide work or an explanation to justify whether or not the student’s claim is correct.

## Part B

In March 2011, a California newspaper predicted that the price of gasoline in two years would be 4.10. The newspaper claimed that the prediction would be within 2% of the actual price of gasoline in March 2013. Given the data in the table, determine the percent error of the prediction. Was the newspaper’s claim correct or incorrect? Provide work or an explanation to justify your answer. Enter your answers and your work or explanation in the space provided. It can be expensive to drive because you have to fill your tank. Answer and references Correct answers: Part A: Both periods saw an increase of about 5 percent, so the claim can be supported. Part B: The prediction was off by less than 1 percent, which would probably be considered close enough for the purposes of a newspaper. PARCC evidence statement(s) tested: 8.C.6, according to the PARCC alignment document. Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. Content Scope: Knowledge and skills articulated in 7.RP.A, 7.NS.A, 7.EE.A. The evidence statement above references Math Practice 3 (construct viable arguments and critique the reasoning of others) and Math Practice 6 (attend to precision). The question involves computations in the seventh-grade math Common Core, including standard 7.RP.A.1, which says students should be able to “compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units,” and 7.NS.A.1, which says students should be able to “Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.” Example solution strategy (there are others) Both mathematical work and reasoning are required to receive full credit for this question. Be sure to type in all work and show your reasoning. What logic did you use to back up your statements. Part A: Compare the price increase from 1998 to 2000 with the price increase from 2011 to 2013. $\frac{1.354 - 1.291}{1.291} \approx 0.0488$ $\frac{4.069 - 3.874}{3.874} \approx 0.0503$ Both increases are about 5 percent, so the claim that they are “about the same” is supported. Part B: Compare the percent error of the claim with 2 percent. The newspaper predicted a price of4.10, and the actual price was \$4.069. The error of the prediction, expressed as a proportion, is the difference between those two divided by the actual price.

$\frac{4.10 - 4.069}{4.069} \approx 0.008$

Since 0.8 percent is less than 2 percent, the claim that “the prediction would be within 2% of the actual price” is supported.

## Resources for further study

For resources on the underlying computational skills, which are seventh-grade skills, see our page entitled “Grade 7 PARCC math: Furniture store sale.”

This problem relies on the fact that the seventh-grade knowledge is securely held in order to test students’ ability to reason with that knowledge. These are the skills described mainly in Math Practice 3, such as students’ ability to analyze and explain any flaws in an argument using mathematical reasoning.

## Analysis of this question and online accessibility

The question measures knowledge of the Common Core math standard I have listed above, in addition to assessing whether students are proficient in the math practice it purports to test.

The question can be delivered online and would yield performance statistics that are as valid than those obtained from paper-and-pencil test-takers. However, online test-takers may have difficulty with the equation editor, and if they have such difficulty, they may not be able to type in all the logic and reasoning needed to receive full credit (4 points) for this question.

I remind students, as I have in the past, when the equation editor pops up for a question, take a little extra time to make sure you:

• Type in all the logic and reasoning you used when solving the problem
• Transfer all your work from scratch paper to the computer

It has been argued that the imprecise nature of the Common Core standards themselves—that students can just as easily say .0488 doesn’t approximately equal .0503, for example, as long as they show reasoning to support their answer—flies in the face of logic and instead turns mathematical reasoning into a matter of opinion, which it isn’t.

It would be better to define the parameters of “about the same” than to force students to make up a definition for the approximation as they proceed with the problem. In that sense, the flaw in the claim is actually a flaw in the standards found in the Common Core.

That being said, I am obliged to point out that this test question is faithful to the flawed standard. Several years ago, I called for a revision of the Common Core, and this is one big area that needs to be revisited in any reworking or rewording of the standards.

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

## In the real world

Five years ago, Richard Newell, of the US Energy Information Administration, explained on C-SPAN what causes gas prices to fluctuate.

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

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