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Measuring a Flagpole by Its Shadow

6th grade nonfiction passage about proportions and shadows: 208 words, six questions, an answer key and vocabulary.

6th grade nonfiction proportions and shadows 208 words

Measuring a Flagpole by Its Shadow

How tall is the flagpole in front of your school? You cannot easily hold a tape measure up to the top. But with a stick, a tape measure, and a sunny afternoon, you can find the height without leaving the ground.

Stand a straight stick upright on flat ground. Say it is exactly 1 meter tall. Measure the shadow it casts, and suppose it is 1.5 meters long. Now measure the flagpole's shadow right away, before the sun moves. Suppose it is 12 meters long.

The sun's light reaches the stick and the pole at the same angle, so each one makes a triangle with its shadow, and the two triangles have the same shape. One is small and one is large. Shapes like these are called similar, and their matching sides are in proportion. For the stick, the shadow is 1.5 times as long as the height. The same has to be true for the flagpole. So divide 12 by 1.5, and you get 8. The flagpole is about 8 meters tall.

For good results, measure both shadows at about the same time of day, hold the stick straight up, and use level ground. People have used this idea for a very long time, because it turns a hard measurement into a few simple steps.

Questions

  1. What three things do you need to measure the pole's height this way? in the text

  2. How long was the stick's shadow in the example? in the text

  3. Why do the stick and the flagpole make triangles of the same shape? think about it

  4. How did the writer get the flagpole's height from its 12 meter shadow? in the text

  5. Why must both shadows be measured at about the same time? think about it

  6. What kind of ground should you use? in the text

Words to know

upright
standing straight up
casts
throws or makes, as in a shadow on the ground
similar
having the same shape but not always the same size
proportion
a fair comparison between two sets of numbers
level
flat, with no slope or hills
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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 · 167 words · Flesch-Kincaid grade 2

How tall is the flagpole at your school? You cannot hold a tape measure up to the top. But you can find the height from the ground. You need a stick, a tape measure, and a sunny afternoon.

Stand a straight stick up on flat ground. Say it is 1 meter tall. Measure its shadow. Say it is 1.5 meters long. Now measure the flagpole's shadow right away, before the sun moves. Say it is 12 meters long.

The sun's light hits the stick and the pole at the same angle. Each one makes a triangle with its shadow. The two triangles have the same shape. One is small and one is big. These are called similar shapes. Their sides are in proportion. For the stick, the shadow is 1.5 times its height. It must be the same for the flagpole. Divide 12 by 1.5 and you get 8. The flagpole is about 8 meters tall.

For good results, measure at about the same time of day. Hold the stick straight up. Use level ground.

▲ This passage · 208 words · Flesch-Kincaid grade 4.6

How tall is the flagpole in front of your school? You cannot easily hold a tape measure up to the top. But with a stick, a tape measure, and a sunny afternoon, you can find the height without leaving the ground.

Stand a straight stick upright on flat ground. Say it is exactly 1 meter tall. Measure the shadow it casts, and suppose it is 1.5 meters long. Now measure the flagpole's shadow right away, before the sun moves. Suppose it is 12 meters long.

The sun's light reaches the stick and the pole at the same angle, so each one makes a triangle with its shadow, and the two triangles have the same shape. One is small and one is large. Shapes like these are called similar, and their matching sides are in proportion. For the stick, the shadow is 1.5 times as long as the height. The same has to be true for the flagpole. So divide 12 by 1.5, and you get 8. The flagpole is about 8 meters tall.

For good results, measure both shadows at about the same time of day, hold the stick straight up, and use level ground. People have used this idea for a very long time, because it turns a hard measurement into a few simple steps.

■ Harder · 223 words · Flesch-Kincaid grade 8

How tall is the flagpole standing in front of your school? Because you cannot reach the top with a tape measure, the question seems difficult. Yet with a stick, a tape measure, and a sunny afternoon, you can determine the height without ever leaving the ground.

Stand a straight stick upright on level ground. Suppose it is exactly 1 meter tall, and suppose the shadow it casts measures 1.5 meters. Then, without delay and before the sun has had time to move, measure the shadow of the flagpole. Suppose that shadow is 12 meters long.

The sun's light strikes the stick and the pole at the very same angle, so each of them forms a triangle with its shadow, and the two triangles have the same shape even though one is small and the other is large. Shapes like these are called similar, and their matching sides are in proportion. For the stick, the shadow is 1.5 times as long as the height, and the same relationship must hold for the flagpole. Dividing 12 by 1.5 gives 8, so the flagpole is approximately 8 meters tall.

To obtain reliable results, measure both shadows at roughly the same time of day, keep the stick perfectly vertical, and choose level ground. People have relied on this idea for a very long time, because it converts a difficult measurement into a few simple steps.

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 upright, casts, similar, proportion and level 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 3 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 "Measuring a Flagpole by Its Shadow"?

It was written for 6th grade. It has 208 words and works out to a Flesch-Kincaid grade level of about 4.6. 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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