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Two Discounts Do Not Make Half Off

7th grade nonfiction passage about stacked percent discounts: 223 words, six questions, an answer key and vocabulary.

7th grade nonfiction stacked percent discounts 223 words

Two Discounts Do Not Make Half Off

A store hangs a sign over its jackets: 30 percent off. A second sign near the register says to take an extra 20 percent off any sale item. Many shoppers add the two together and expect half of the price to disappear. The math does not work that way.

Suppose a jacket costs $80. The first discount is 30 percent of $80, which is $24, so the sale price becomes $56. The extra 20 percent is taken from the new price, not from the old one. Twenty percent of $56 is $11.20, so the final price is $44.80. The shopper saved $35.20, which is 44 percent of the original price, not 50.

There is a quicker way to see this. Paying 70 percent of the price after the first discount means multiplying by 0.70. Paying 80 percent after the second discount means multiplying by 0.80. Multiply the two together and you get 0.56, so the shopper pays 56 percent of the starting price. That leaves a total discount of 44 percent.

The order of the discounts does not change the answer, since multiplication gives the same result either way. What matters is that each percent applies to a different amount, and a percent of a smaller number is a smaller piece. Knowing this helps a shopper compare deals fairly, such as one tag that says 40 percent off against two stacked discounts, and it keeps the final price from being a surprise at the register.

Questions

  1. What two discounts are used on the jacket in the example? in the text

  2. What is the sale price after the first discount? in the text

  3. What final price does the shopper pay for the jacket? in the text

  4. What share of the starting price does the shopper pay in the end? in the text

  5. Why is the second discount worth less than 20 percent of the original price? think about it

  6. Would the final price change if the 20 percent discount came first? Why or why not? think about it

Words to know

discount
an amount taken off the regular price
percent
a part out of every hundred
original
the first one, before anything was changed
multiplication
the math of repeated groups, used to find a product
compare
to look at two things to see how they are alike or different
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One passage, three levels

The same topic and facts written three ways, so a mixed class can read and talk about one text. Each group’s sheet shows only a shape; the key says which is which.

● Easier · 155 words · Flesch-Kincaid grade 2

A store has a sign over its jackets. It says 30 percent off. Near the register, another sign says to take 20 percent more off. Many shoppers think this means 50 percent off. It does not.

Say a jacket costs $80. First, take 30 percent off. That is $24. The sale price is now $56. Next, take 20 percent off the new price. Not the old price. Twenty percent of $56 is $11.20. The jacket costs $44.80. The shopper saved $35.20. That is 44 percent of $80, not 50 percent.

Here is a quick way to see it. After the first discount, you pay 70 percent. Think of that as 0.70. After the second, you pay 80 percent. Think of that as 0.80. Multiply them. You get 0.56. So you pay 56 percent of the first price. You save 44 percent.

The order does not matter. Multiplication gives the same answer either way. But each percent is taken from a different amount. A percent of a smaller number is a smaller piece. This helps you compare deals.

▲ This passage · 223 words · Flesch-Kincaid grade 5.9

A store hangs a sign over its jackets: 30 percent off. A second sign near the register says to take an extra 20 percent off any sale item. Many shoppers add the two together and expect half of the price to disappear. The math does not work that way.

Suppose a jacket costs $80. The first discount is 30 percent of $80, which is $24, so the sale price becomes $56. The extra 20 percent is taken from the new price, not from the old one. Twenty percent of $56 is $11.20, so the final price is $44.80. The shopper saved $35.20, which is 44 percent of the original price, not 50.

There is a quicker way to see this. Paying 70 percent of the price after the first discount means multiplying by 0.70. Paying 80 percent after the second discount means multiplying by 0.80. Multiply the two together and you get 0.56, so the shopper pays 56 percent of the starting price. That leaves a total discount of 44 percent.

The order of the discounts does not change the answer, since multiplication gives the same result either way. What matters is that each percent applies to a different amount, and a percent of a smaller number is a smaller piece. Knowing this helps a shopper compare deals fairly, such as one tag that says 40 percent off against two stacked discounts, and it keeps the final price from being a surprise at the register.

■ Harder · 265 words · Flesch-Kincaid grade 11.2

A department store displays a banner above its rack of winter jackets announcing a markdown of 30 percent. A second notice beside the register invites customers to take an additional 20 percent off any item that is already on sale. Many shoppers casually add the two figures together and expect half of the price to vanish, but the arithmetic does not cooperate with that assumption.

Consider a jacket that originally costs $80. The first discount removes 30 percent of $80, which is $24, so the sale price drops to $56. The additional 20 percent is calculated from this new price rather than from the original one. Twenty percent of $56 is $11.20, which leaves a final price of $44.80. The shopper has therefore saved $35.20, which amounts to 44 percent of the original price instead of the 50 percent that many people expect.

A faster route to the same conclusion uses multiplication. Paying 70 percent of the price after the first discount is equivalent to multiplying by 0.70, and paying 80 percent after the second is equivalent to multiplying by 0.80. The product of those two numbers is 0.56, which means the shopper ends up paying 56 percent of the starting price, and the combined discount is 44 percent.

Reversing the order of the discounts would not change the result, because multiplication produces the same product in either direction. The crucial point is that each percentage applies to a different base amount, and a percentage of a smaller number is always a smaller piece. Understanding this allows a shopper to compare offers fairly, for example one tag advertising 40 percent off against two stacked discounts, and it prevents unpleasant surprises when the total appears at the register.

Download as one PDF

How to use it

  1. Press Read it big (or B) to put the text on the projector, or Full screen (F) to fill the whole screen.
  2. Ask the questions one at a time and use Show answer when the class has decided. A shows or hides every answer.
  3. Print student copy for the class, or Print with answers for yourself.

Ideas for class

  • Before reading, put discount, percent, original, multiplication and compare on the board with their meanings from the Words to know section and have students predict what the text will be about.
  • Read it aloud once while students follow along, then have them reread it alone or with a partner. At a calm 100 words a minute it takes about 2 minutes to read aloud.
  • Use the Read it big button (or B) to put the text on the projector, and Show answer on one question at a time so the class commits to an answer first.
  • Question 5 asks the reader to infer. Ask students to point to the words in the passage that led them to their answer.
  • Ask students to write one question the passage did not answer, then look for the answer in a book or on a classroom screen.
  • Print the student copy for independent work and keep the answer-key copy for yourself.

Related

Questions

What reading level is "Two Discounts Do Not Make Half Off"?

It was written for 7th grade. It has 223 words and works out to a Flesch-Kincaid grade level of about 5.9. That is a formula's estimate from sentence length and syllables, and it is not a Lexile or a guided reading level, so check it against your students.

What do the questions ask?

There are six. 4 ask for something the text says directly and 2 ask the reader to work something out from clues. Each has an answer in the key, and the answers are written as a teacher would accept them, not as the only possible wording.

How long does it take to read?

About 2 minutes read aloud at 100 words a minute. For a one-minute fluency check, paste it into the fluency timer and use the word count.

Can I print it?

Yes. Print student copy gives the passage, the questions with lines to write on, and the word meanings. Print with answers gives the same page with the answers filled in. Both are made in your browser.

Is this passage from a published book?

No. It was written for Peabody Teach, so there is no book to buy and no login to read it.

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