#### The following two-part computation-based question, explained here in hopes of helping seventh-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 “EOY” (end-of-year) test for grade 7 math:

**A furniture store had the following sale:**

**Buy one item at the regular price,**

**get the second item of equal or**

**lesser value for**

## Part A

Mr. Davis bought 2 chairs during the sale. The regular price of each chair was $168.

What was the total price, in dollars, for both chairs during the sale, not incluidng tax?

## Part B

Ms. Wilcox bought a sofa and a chair during the sale. The regular price of the sofa was $875 and the regular price of the chair was $250. After the discount was applied, a sales tax of 6.25% was charged on the total purchase.

How much did Ms. Wilcox pay, in dollars, for the sofa and chair, including tax, during the sale?

## Resources for further study

The **Khan Academy**, developed by Sal Khan, an engineer who has created thousands of video tutorials for students of all ages, has an entire series devoted to solving word problems that involve “discount, tax, and tips.” **Purple Math**, developed by Elizabeth Stapel, a math teacher from the St Louis area, has several pages on “percent of” word problems, such as discounts, markups, and sales tax.

In addition to the tutorials, several authors have produced worksheets loaded with practice problems that involve discounts, tips, sales tax, and markups:

- Western Reserve (Ohio)
- A sales tax game (free) from Math-Play.com
- Generate your own worksheets using Worksheet Works.com

## 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, or perhaps more valid, than those obtained from paper-and-pencil test-takers. The reason for this is that converting this question to a paper-and-pencil question would mean coming up with plausible incorrect answers to make at least four options for multiple choice. This format encourages guessing, which reduces the quality of performance statistics to a certain extent.

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

I would be remiss not to note the missing comma in between two independent clauses in Part B, here: “… sofa was $875 and the regular price …” There should be a comma before the “and,” but the error doesn’t affect readability at all. Some people might even say a comma isn’t necessary in this instance, since both clauses are short and have the same structure. In addition to the missing comma in Part B, the advertisement sign also features a comma splice error in which two imperative sentences are joined with only a comma (and no conjunction) between them.

## In a real classroom

Chelsea Katz writes in the *Kilgore News Herald* in Texas that seventh-grade students of Delina Chitwood set up a supermarket in the library of Kilgore Middle School, with the help of a local grocery store and a little math. “They have to mark up their product, and they are going to resell it to their classmates,” Ms Chitwood was quoted as saying.

Half the class became the “owners” of the store and had to purchase goods from “manufacturers” (the teachers). Each student had $100 with which to fill their shelves. Then the customers (the other half of the class) got $20 to spend in the store.

They are going to do the business part of it first, figure out the profit and the percent increase, and then we’re going to come back and they’ll be the customer. … We’re going to record what items sell and then give them that information, so they can know how much money they’ve made—the profit they’ve made.

We want them to be able to understand tax is an additional amount and as far as the teaching part of the seventh grade part they have to be able to calculate that as far as a percent proportion. We are also looking at constant rate of change that if you buy one of something, two of something, three of something, that that pattern—that constant rate—stays the same for items, for hourly wages.