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The Nine-Inch Pan Problem

7th grade nonfiction passage about area of circles in baking: 246 words, six questions, an answer key and vocabulary.

7th grade nonfiction area of circles in baking 246 words

The Nine-Inch Pan Problem

A cake recipe calls for an 8-inch round pan, but the only round pan in the cupboard is 9 inches wide. One inch seems like a tiny difference, so a baker might just pour the batter in. The cake comes out flat and a little dry, and the math explains why.

The width of a circle, called its diameter, is only part of the story. What the batter covers is the area of the bottom, and the area of a circle depends on the square of its radius, which is half the diameter. The formula is pi times the radius times the radius. Pi is about 3.14.

For the 8-inch pan, the radius is 4 inches, and the area is about 3.14 times 16, or around 50 square inches. For the 9-inch pan, the radius is 4.5 inches, and the area is about 3.14 times 20.25, or around 64 square inches. The pan is only 12.5 percent wider, yet its bottom is more than 25 percent larger.

So the same amount of batter is spread over a bigger floor, making a thinner cake. A thinner layer heats through faster, so it often finishes baking sooner and can dry out if it is left in for the full time. A baker who knows this watches the oven earlier, perhaps testing the cake a few minutes ahead of schedule.

The same idea applies whenever a shape grows. When every length doubles, the area becomes four times as large, which is why pizza sizes are such good deals for bigger eaters.

Questions

  1. How wide is the pan the recipe calls for? in the text

  2. What is the formula for the area of a circle in the passage? in the text

  3. About how large is the bottom of the 9-inch pan? in the text

  4. What is a radius? in the text

  5. Why does the cake come out thinner in the larger pan? think about it

  6. Why might a baker check the cake earlier in the 9-inch pan? think about it

Words to know

diameter
the distance straight across a circle through its center
radius
the distance from the center of a circle to its edge
batter
a runny mix of flour and other foods used for baking
formula
a rule written with numbers or letters
layer
one flat level of something
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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 · 211 words · Flesch-Kincaid grade 3

A cake recipe needs an 8-inch round pan. The only round pan in the cupboard is 9 inches wide. One inch seems like a tiny difference. So a baker might just pour in the batter. The cake comes out flat and a bit dry. Math tells us why.

The width of a circle is called its diameter. But the batter covers the bottom of the pan. That is the area. The area of a circle depends on the radius times itself. The radius is half of the diameter. The formula is pi times the radius times the radius. Pi is about 3.14.

The 8-inch pan has a radius of 4 inches. Its area is about 3.14 times 16. That is around 50 square inches. The 9-inch pan has a radius of 4.5 inches. Its area is about 3.14 times 20.25. That is around 64 square inches. The pan is only 12.5 percent wider. But its bottom is more than 25 percent bigger.

So the same batter spreads over a bigger floor. The cake is thinner. A thin layer heats through fast. It may finish sooner. It can dry out if it stays in the full time. A baker who knows this checks the cake early.

The same idea works for any shape. When every length doubles, the area becomes four times as big.

▲ This passage · 246 words · Flesch-Kincaid grade 7.2

A cake recipe calls for an 8-inch round pan, but the only round pan in the cupboard is 9 inches wide. One inch seems like a tiny difference, so a baker might just pour the batter in. The cake comes out flat and a little dry, and the math explains why.

The width of a circle, called its diameter, is only part of the story. What the batter covers is the area of the bottom, and the area of a circle depends on the square of its radius, which is half the diameter. The formula is pi times the radius times the radius. Pi is about 3.14.

For the 8-inch pan, the radius is 4 inches, and the area is about 3.14 times 16, or around 50 square inches. For the 9-inch pan, the radius is 4.5 inches, and the area is about 3.14 times 20.25, or around 64 square inches. The pan is only 12.5 percent wider, yet its bottom is more than 25 percent larger.

So the same amount of batter is spread over a bigger floor, making a thinner cake. A thinner layer heats through faster, so it often finishes baking sooner and can dry out if it is left in for the full time. A baker who knows this watches the oven earlier, perhaps testing the cake a few minutes ahead of schedule.

The same idea applies whenever a shape grows. When every length doubles, the area becomes four times as large, which is why pizza sizes are such good deals for bigger eaters.

■ Harder · 270 words · Flesch-Kincaid grade 10.2

A cake recipe specifies an 8-inch round pan, but the only round pan available in the cupboard measures 9 inches across. A single inch appears to be a trivial difference, so a baker might simply pour the batter into the larger pan and proceed. The cake emerges flat and slightly dry, and the mathematics of circles explains the reason.

The width of a circle, known as its diameter, tells only part of the story. What the batter actually covers is the bottom of the pan, which is its area, and the area of a circle depends on the square of its radius, meaning half of the diameter. The formula is pi multiplied by the radius multiplied by the radius, where pi is approximately 3.14.

For the 8-inch pan, the radius is 4 inches, so the area is about 3.14 times 16, or roughly 50 square inches. For the 9-inch pan, the radius is 4.5 inches, so the area is about 3.14 times 20.25, or roughly 64 square inches. The larger pan is only 12.5 percent wider, yet its bottom is more than 25 percent larger.

Consequently, the same quantity of batter is spread across a much broader floor, producing a thinner cake. A thinner layer heats through more rapidly, so it frequently finishes baking sooner and can become dry if it is left in the oven for the full recommended time. A baker who understands this will check the oven earlier, perhaps testing the cake a few minutes ahead of schedule.

The identical principle applies whenever a shape grows. When every length doubles, the area becomes four times as large, which is why larger pizzas are such good bargains for hungry eaters.

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 diameter, radius, batter, formula and layer 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 "The Nine-Inch Pan Problem"?

It was written for 7th grade. It has 246 words and works out to a Flesch-Kincaid grade level of about 7.2. 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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