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Fraction Circles and Fraction Strips

- By Lesley Baker

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.

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.

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.

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.

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.

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.

Use Circles to Add Fractions

- Example
- the sum may be found by visually combining the

two addends.

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.

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

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.

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.

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.

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

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

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

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.

Name the Fraction using Fraction Strips

Example

3/5

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

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

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.

Using Fractions to Subtract Fractions

Shade 3/4

Shade 1/3

Shade the Difference

Multiplying with Fraction Strips

- 1/3 x 1/4 1/12

1/4

1/3 of 1/4

Dividing with Fraction Strips

- Example (1/4) / (1/8) 2

1/4

1/8

(1/4) / (1/8)

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

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

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