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Why Quilters Cut Squares in Half

7th grade nonfiction passage about triangles and area in quilting: 245 words, six questions, an answer key and vocabulary.

7th grade nonfiction triangles and area in quilting 245 words

Why Quilters Cut Squares in Half

Look closely at a patchwork quilt and you will often find small squares that are split corner to corner into two colors. These patches are called half-square triangles, and they hide a lot of geometry. A quilter can make one by cutting a square of fabric along its diagonal, which makes two triangles that match perfectly.

Each triangle has exactly half the area of the square. A square of fabric that measures 6 inches on each side has an area of 36 square inches, since area is length times width. Cut it on the diagonal and each triangle covers 18 square inches. A triangle's area is half of its base times its height, and here the base and height are both 6 inches.

Quilters then sew a light triangle to a dark one along the long edge. The two pieces join to form a new square, with one color on each side of a slanted line. Repeating the pattern across many patches creates pinwheels, zigzags and stars.

Planning requires care with measurements. Fabric is joined with a seam allowance, usually a quarter inch, which is the strip of cloth that disappears into the stitching. A quilter who forgets to count that strip will end up with patches that come out too small. Because of this, quilters often cut their squares a little larger than the finished size and trim them down afterward. Good quilts depend on exact angles and areas, and the math is part of the craft.

Questions

  1. What is a half-square triangle? in the text

  2. What is the area of a square that is 6 inches on each side? in the text

  3. What is the area of each triangle after the square is cut on the diagonal? in the text

  4. What is a seam allowance? in the text

  5. Why do quilters often cut their squares a little larger than the finished size? think about it

  6. What would happen if a quilter forgot to count the seam allowance? think about it

Words to know

diagonal
a straight line from one corner of a square to the opposite corner
area
the amount of flat space inside a shape
geometry
the part of math about shapes and sizes
allowance
an extra amount set aside for a purpose
patchwork
cloth made from many small pieces sewn together
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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 · 206 words · Flesch-Kincaid grade 3.5

Look at a patchwork quilt. You will often see small squares split from corner to corner into two colors. These are called half-square triangles. A quilter makes one by cutting a square along its diagonal. This makes two triangles that match.

Each triangle is half the area of the square. Say a square of cloth is 6 inches on each side. Its area is 36 square inches. Area is length times width. Cut it on the diagonal. Each triangle covers 18 square inches. A triangle's area is half of its base times its height. Here the base and the height are both 6 inches.

Then a quilter sews a light triangle to a dark one along the long edge. They make a new square. It has one color on each side of a slanted line. Many patches in a row make pinwheels, zigzags and stars.

A quilter must plan the measurements. Cloth is joined with a seam allowance. It is usually a quarter inch. That strip of cloth goes into the stitching. If a quilter forgets it, the patches come out too small. So quilters often cut squares a bit big. Then they trim them. Good quilts need exact angles and areas. The math is part of the craft.

▲ This passage · 245 words · Flesch-Kincaid grade 7.6

Look closely at a patchwork quilt and you will often find small squares that are split corner to corner into two colors. These patches are called half-square triangles, and they hide a lot of geometry. A quilter can make one by cutting a square of fabric along its diagonal, which makes two triangles that match perfectly.

Each triangle has exactly half the area of the square. A square of fabric that measures 6 inches on each side has an area of 36 square inches, since area is length times width. Cut it on the diagonal and each triangle covers 18 square inches. A triangle's area is half of its base times its height, and here the base and height are both 6 inches.

Quilters then sew a light triangle to a dark one along the long edge. The two pieces join to form a new square, with one color on each side of a slanted line. Repeating the pattern across many patches creates pinwheels, zigzags and stars.

Planning requires care with measurements. Fabric is joined with a seam allowance, usually a quarter inch, which is the strip of cloth that disappears into the stitching. A quilter who forgets to count that strip will end up with patches that come out too small. Because of this, quilters often cut their squares a little larger than the finished size and trim them down afterward. Good quilts depend on exact angles and areas, and the math is part of the craft.

■ Harder · 264 words · Flesch-Kincaid grade 10.8

Examine a patchwork quilt closely and you will frequently discover small squares that have been divided from corner to corner into two contrasting colors. These patches, known as half-square triangles, conceal a surprising amount of geometry. A quilter can create one by slicing a square of fabric along its diagonal, which produces two triangles that match each other perfectly.

Each triangle possesses exactly half the area of the original square. A square of fabric measuring 6 inches along each side has an area of 36 square inches, since area equals length multiplied by width. After the square is cut along its diagonal, each triangle covers 18 square inches. A triangle's area is half of its base multiplied by its height, and in this case the base and the height are both 6 inches.

The quilter then stitches a light triangle to a dark one along their long edges, and the two pieces combine to form a new square that displays one color on either side of a slanted line. Repeating the arrangement across numerous patches produces pinwheels, zigzags and stars.

Planning demands careful attention to measurements. Fabric is joined with a seam allowance, typically a quarter inch, which is the narrow strip of cloth that vanishes into the stitching. A quilter who neglects to account for that strip will find that the finished patches turn out too small. For this reason, quilters often cut their squares slightly larger than the intended finished size and trim them afterward. A well-made quilt depends upon precise angles and areas, and the mathematics is an essential part of the craft.

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 diagonal, area, geometry, allowance and patchwork 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 "Why Quilters Cut Squares in Half"?

It was written for 7th grade. It has 245 words and works out to a Flesch-Kincaid grade level of about 7.6. 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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