Fraction Circles and Fraction Strips

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Fraction Circles and Fraction Strips

• By Lesley Baker

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Fraction Circles

• Useful tools to help understand and learn about
  fractions.
• Easily constructed and each stage of construction
  can be used as a teaching tool.

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Use Circles to Demonstrate the Meaning of
Numerator and Denominator

• Example
• Call the circle a unit. This unit is divided
  into seven equal parts. If we take only the
  colored parts, we have taken two of the seven
  equal parts.
• The top number 2 in the numeral 2/7 is the
  numerator. The numerator tell us how many of the
  parts in the unit are to be taken.

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Use Circles to Demonstrate the Meaning of
Denominator and Numerator

• The bottom number 7 in the numeral 2/7 is the
  denominator. The denominator tells us the total
  number of equal parts into which the unit is
  divided. In this example there are 7 equal parts
  in the circle.
• The line between the numerator and denominator is
  known as the fraction bar. It is also called the
  division bar.

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Use Circles to Demonstrate the Meaning of
Denominator and Numerator

• The fraction represented here is 2/7 because two
  of the 7 parts in the circle are colored.

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Use Circles to Rename Fractions from Mixed Form
to Fraction Form

• Example
• In the example below, you will notice that each
  of the two whole circles has 5 colored pieces and
  the part circle has 2 colored pieces, giving 12
  colored pieces.
• 12 is the numerator of the fraction. Because each
  circle has 5 equal parts the denominator is 5,
  giving a fraction of 12/5.

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Use Circles to Compare Fractions

• Example
• Visualize the fractions 1/4 and 5/6 as pictured
  to the right.
• As you can see 1/4 is less than half the circle
  where 5/6 is more then half the circle therefore
  5/6 is larger.

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Use Circles to Add Fractions

• Example
• the sum may be found by visually combining the
  two addends.

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Subtracting Fractions with Circles

• Example
• after removing the two whole circles, you are
  left with 1 2/3 red circles. Removing the 1/2
  circle from the 1 2/3 circle that is left in the
  minuend will leave 1/6 1/3 2/3 circle for the
  difference of 1 1/6 circles.

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Multiply Fractions with Circles

• The parts of multiplication are the first factor,
  the second factor, and the product
• The first factor is the number of circles in each
  row, or 3 2/3
• The second factor is 3 because there are 3 rows.
• Written out, the example would look like this

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Multiply Fractions with Circles

• You can see from the picture that there are 9
  complete circles. The three partial circles can
  be combined to form 2 more complete circles for a
  total of 11 circles. The product, then, is 11.

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Dividing Fractions with Circles

• The parts of a division example are the dividend,
  the divisor, and the quotient.
• The dividend in this picture is 3 1/5 circles.
• The picture shows a divisor of 4/5 circles.
• The quotient is the number of divisor circles
  that will fit into the dividend circles.

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Dividing Fractions with Circles

• Imagine you are covering the dividend circles
  with the divisor circles. You might have to
  imagine some cutting and pasting to cover the
  dividend with the divisor. The third row,
  representing the quotient, shows how the divisor
  will fit into the dividend. There is a color
  change of dark blue and light blue after each
  divisor has been fit into the dividend. You can
  see from the image that 4 divisor circles fit
  into the dividend. The quotient then is 4.

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Activity with Fraction Circles

• Begin with the halves fraction circle
• Shade each half a different color
• Write inside the dotted line
• Discuss the numerator and denominator of 1/2 and
  2/2 and why 2/2 is the same as one.

1/2
1/2
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Activity with Fraction Circles

• Continue with the thirds fraction circle
• Shade each third a different color.
• Write inside and close to the dotted line
• Place it over the thirds fraction circle and when
  the centers are aligned fasten with a brass paper
  fastener passed through the center

1/3
1/3
1/3
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Activity with Fraction Circles

• Compare the relative size of the fraction 1/2 and
  the fraction 1/3 and discuss the fact that
  although the denominator is larger the size of
  the fraction is smaller.
• You can do the same for more fractions.

1/3
1/3
1/2
1/2
1/3
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Fraction Strips

• Strips all of the same lengths.
• Divided into sections to represent fractions.
• Useful to help understand and learn about
  fractions.
• Easy to make.

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Name the Fraction using Fraction Strips
Example
3/5
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Fractions of a Gas Tank

• Have students using pencil crayon, fill in the
  chart below by shading in the required fraction.

one quarter
one half
three quarters
the whole
full
full
full
full
empty
empty
empty
empty
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Compare Fractions with Fraction Strips

• Line up each fraction to see which fraction has
  the greatest length. Use gt, lt, or to compare
  each example.

• Example
• 1/2 2/4

1/2
1/2
1/4
1/4
1/4
1/4
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Using Fraction Strips to Add Fractions

• To find which fraction bars match 1/12 1/4, you
  need to find the least common denominator or LCD
  (covered in previous lesson). The LCM (least
  common multiple, previously covered) of 12 and 4
  is 12, so the LCD (least common denominator) is
  12. Since the LCD is twelve, you use like
  fraction strips to see how many twelfths equal
  1/12 1/4.

• There is already 1/12 there. By putting 1/4
  beside the twelfths strip you can see that 1/4
  equals 3/12. If 1/43/12, then 1/12 3/124/12
  (which can be reduced to 1/3).
• Example Activity
• Have students make up their own equations
  using fraction strips.

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Using Fractions to Subtract Fractions
Shade 3/4
Shade 1/3
Shade the Difference
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Multiplying with Fraction Strips

• 1/3 x 1/4 1/12

1/4
1/3 of 1/4
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Dividing with Fraction Strips

• Example (1/4) / (1/8) 2

1/4
1/8
(1/4) / (1/8)
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TEKS

• 111.22 Mathematics, Grade 6
• (b) Knowledge and skills
• (A)  compare and order non-negative rational
  numbers
• (B)  generate equivalent forms of rational
  numbers including whole numbers, fractions, and
  decimals

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TEKS

• 111.23. Mathematics, Grade 7
• (b)  Knowledge and skills
• (A) represent multiplication and division
  situations involving fractions and decimals with
  concrete models, pictures, words, and numbers
• (B) use addition, subtraction, multiplication,
  and division to solve problems involving
  fractions and decimals