comparing & ordering fractions our favorite subject
TRANSCRIPT
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
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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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Slides and Fraction Tents Master are available at:http://pdc.sdsu.edu
(click on “PDC Presentations”)