Comparing & Ordering Fractions

Our Favorite Subject

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What Should Students Understand about Fraction Concepts

Meaning of the denominator (number of equal-sized pieces into which the whole has been cut)

Meaning of the numerator (how many pieces are being considered)

The more pieces a whole is divided into, the smaller the size of the pieces

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What is Equivalence, Anyway?

“Equivalence” means “equal value”

A fraction can have many different

names Understanding that 1/2 is equivalent to

many other fractions helps you to use that benchmark

Simplify: when and why

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Ordering Fractions

5

7 , 

3

7 , 

6

7Fractions with the same denominator can

be compared by their numerators.

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Ordering Fractions

4

10 , 

4

37 , 

4

8Fractions with the same numerator can

be compared by their denominators.

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Ordering Fractions

4

9 , 

8

15 , 

1

2Fractions close to a benchmark can be compared by finding their distance from

the benchmark.

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Ordering Fractions

99

100 , 

6

7 , 

15

16Fractions close to one can be compared

by finding their distance from one.

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Strategies for Ordering Fractions

Same denominator

Same numerator

Benchmarks: close to 0, 1, 1/2

Same number of missing parts

from the whole (”Residual

strategy”)

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“Clothesline” Fractions Activity

1

1

2,

3

4,

10

“Clothesline” Fractions Activity

7

4 2

3 1 ,

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“Clothesline” Fractions Activity

15

29

8

15,

4

9,

12

“Clothesline” Fractions Activity

6

27

1

4,

3

13,

13

“Clothesline” Fractions Activity

15

16

1

8,

5

6,

14

“Clothesline” Fractions Activity

xX , 2x ,

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“Clothesline” Fractions Activity

1

2x

x

2,

(where x ≠0)

1

2x ,

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The Number Line Helps Develop

Fraction sense

Benchmarks

Relative magnitude (size) of

fractions

Algebraic connections

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Fractions aren’t just between zero and one; they live between all the numbers on the number line;

A fraction can have many different names; There are more strategies than just “finding a

common denominator” for comparing and ordering fractions;

Fractions can be ordered on a number line just like whole numbers.

The thinking involved when placing fractions on a number line can be symbolized algebraically.

What Should “Kids” Know?

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Contact Us:nbezuk@mail.sdsu.edusklass@projects.sdsu.edu

Slides and Fraction Tents Master are available at:http://pdc.sdsu.edu

(click on “PDC Presentations”)