develop understanding of fractions as numbers. 1. understand a fraction 1/b as the quantity formed...
TRANSCRIPT
Develop understanding of fractions as numbers.
1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
(Source: www.corestandards.org)
Definition: Fraction
• A fraction is the comparison of two numbers through the mathematical operation of division.
• The number on the top of the fraction is called the numerator.
• The number in the bottom of the fraction is called the denominator.
Examples of Fractions
3 11 5 9 34 12 7 5 2
numerator
denominator
Concept Exploration
=
1 package = 12 candies
Divide the package into 12 groups with the same number of candies
1 112 12
1 package per group
12
package packagegroups group
Observe 1/12 package = 1 candy.
Divide the package into 6 groups with the same number of candies
1 16 6
1 package per group
6
package packagegroups group
Observe 1/6 package = 2 candies.
Divide the package into 4 groups with the same number of candies
1 14 4
1 package per group
4
package packagegroups group
Observe 1/4 package = 3 candies.
Divide the package into 3 groups with the same number of candies
1 13 3
1 package per group
3
package packagegroups group
Observe 1/3 package = 4 candies.
Divide the package into 2 groups with the same number of candies
1 12 2
1 package per group
2
package packagegroups group
Observe 1/2 package = 6 candies.
Divide the package into 1 group with the same number of candies
1 1 package per group
1 1packagegroup
Observe 1/1 package = 12 candies.
Summarize Observations112
16
14
12
13
11
Observations in a TableFraction of a Whole
PackNumber of
Candies
1/12 11/6 21/4 31/3 41/2 61/1 12
Stop and Reflect
• What fraction concepts have we discovered?
Unit Fractions
• A fraction with a 1 in the numerator and a positive whole number in the denominator is called a unit fraction. All of the following are unit fractions.
1 1 1 1 1 112 6 4 3 2 1
Multiples of Unit Fractions
Recall of a package.112
How many are shown below?112
1 33
12 12
Multiples of Unit Fractions
How many are shown below?112
1 44
12 12
Number Line Activity• Draw a horizontal line across the
upper half of sheet of 8.5” by 11”paper.
• Line up 12 candies side-by-side along the line
• Mark a tick mark at the edge of each candy
Number Line Activity• At each tick mark, count how many
1/12 packs are to the left of the tick mark. Then label the tick mark
112
212
012
312
412
512
612
712
812
912
1012
1112
1212
Which number is bigger?Use the number line.
4 7?
12 12or
5 3?
12 12or
8 2?
12 12or
1 12?
12 12or
6 9?
12 12or
11 10?
12 12or
Stop and Reflect
• When two fractions have a common denominator, how can you tell which fraction is the larger number?
Multiples of Unit Fractions
Recall of a package.16
How many candies are in of a package?
2 3 4 5 6, , , ,and
6 6 6 6 6
4 candies, 6 candies, 8 candies, 10 candies, and 12 candies
Update the number line.
112
212
012
312
412
512
612
712
812
912
1012
1112
1212
16
06
26
36
46
56
66
Multiples of Unit Fractions
Recall of a package.14
How many candies are in and of a package?
44
2 3, ,
4 4
6 candies, 9 candies, and 12 candies
Update the number line.
112
212
012
312
412
512
612
712
812
912
1012
1112
1212
16
06
26
36
46
56
66
04
14
24
34
44
Multiples of Unit Fractions
Recall of a package.13
How many candies are in and of a package?
33
23
8 candies and 12 candies
Update the number line.
112
212
012
312
412
512
612
712
812
912
1012
1112
1212
16
06
26
36
46
56
66
04
14
24
34
44
03
13
23
33
Multiples of Unit Fractions
Recall of a package.12
How many candies are in of a package?22
12 candies
Update the number line.
112
212
012
312
412
512
612
712
812
912
1012
1112
1212
16
06
26
36
46
56
66
04
14
24
34
44
03
13
23
33
02
12
22
Stop and Reflect
• Look at the completed number line. What patterns or relationships do you see?
Which number is bigger?Use the number line.
1 5?
4 12or
3 1?
4 3or 5 8
?6 12or
2 4?
4 6or
2 7?
3 12or
1 5?
3 6or
Equivalent Fractions• Represent with four
fractions.
1 2 3 62 4 6 12
1 2 22 2 4
Observe1 3 32 3 6
1 6 62 6 12
Equivalent Fractions• Represent with three
fractions.
1 2 43 6 12
1 2 23 2 6
1 4 43 4 12
Observe
Equivalent Fractions• Write four fractions that are
equivalent to .1 2 24 2 8
1 3 34 3 12
14
1 4 44 4 16
1 5 54 5 20
Stop and Reflect
• How can you tell if a fraction is equivalent to a unit fraction?