Download 6th_MA_NS_2.4_REDUCE_FRACTIONS_DW

Name __________________________
L ea rn i n g Obj e cti v e
Today, we will reduce fractions.
CFU
What are we going to do today?
Acti va t e ( o r p r o vi de ) P ri o r K n o wl edg e
A factor is a number that divides a given number evenly.
The greatest common factor (GCF) of two numbers is
the largest number that divides both numbers evenly.
List the factors of the following numbers.
A. The factors of 18
B. The factors of 12
C. What is the GCF of 12 and 18?
The GCF of 12 and 18 is ________.
CFU
Students, you already know how to find the GCF of two numbers by listing their factors. Today, we will
use reduce fractions by finding the GCF of the numerator and denominator.
DataWORKS Educational Research
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Comments? [email protected]
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Co n c e pt D ev el opm e n t
The reduced form of a fraction is when the numerator and denominator have
no common1 factor except 1.
• A fraction in reduced form is also referred2 to as in simplest form or lowest terms.
To reduce a fraction means to change it into reduced form.
• To reduce a fraction, divide the numerator and denominator by the GCF.
1 same
2 called
12
Example: Reduce 18 using the greatest common factor (GCF):
GCF = 6
12  6
2
=
18  6
3
CFU
Use the list of factors to determine which fraction is in reduced form? How do you know? Why is the other
not in reduced form?
A
7
21
1, 7
1, 3, 7, 21
B
9
25
1, 3,9
1, 5, 25
What number will we need to divide by to reduce the fraction (A) above? How do you know?
A 7
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B 3
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Ski l l Dev el o pm en t /G u i ded P ra cti c e
The reduced form of a fraction is when the numerator and denominator have no common factor except 1.
To reduce a fraction means to change it into reduced form.
Reduce fractions.
Step #1: Find the factors of the numerator and denominator.
Step #2: Identify3 the GCF and write it on the line. (circle)
Step #3: Reduce the fraction by dividing the numerator and denominator
by the GCF. (circle)
Step #4: Interpret4 the reduced fraction. “The reduced form of ___ is ___.”
3
find
1.
4
explain
7
21
2.
Factors of 7: _______________________
Factors of 5: _______________________
Factors of 21: ______________________
Factors of 20: ______________________
GCF:_______
3.
GCF:_______
9
12
4.
12
15
Factors of 9: _______________________
Factors of 12: ______________________
Factors of 12: ______________________
Factors of 15: ______________________
GCF:_______
5.
5
20
GCF:_______
18
42
6.
24
40
Factors of 18: ______________________
Factors of 24: ______________________
Factors of 42: ______________________
Factors of 40: ______________________
GCF:_______
GCF:_______
CFU
(#2) How did I/you identify the GCF?
(#3) How did I/you reduce the fraction?
(#4) How did I/you interpret the reduced fraction?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Rel e va n c e
The reduced form of a fraction is when the numerator and denominator have no
common factor except 1.
To reduce a fraction means to change it into reduced form.
1. Reducing fractions will make calculations easier.
A pizza is cut into 12 equal
pieces. John and his friend
ate 6 slices. How much of
the pizza did they eat?
6 6
1
=
12  6
2
They ate half of the pizza.
2. Reducing fractions will help you do well on tests.
CFU
Does anyone else have another reason why it is relevant to reduce fractions? (pair-share) Why is it
relevant to reduce fractions? You may give me my reason or one of your own. Which reason is more
relevant to you? Why?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
The reduced form of a fraction is when the numerator and denominator have no common factor except 1.
To reduce a fraction means to change it into reduced form.
Skill Closure
Reduce fractions.
Step #1: Find the factors of the numerator and denominator.
Step #2: Identify the GCF and write it on the line. (circle)
Step #3: Reduce the fraction by dividing the numerator and denominator
by the GCF. (circle)
Step #4: Interpret the reduced fraction. “The reduced form of ___ is ___.”
1.
3
15
Factors of 3:
_____________________________
Factors of 15:
_____________________________
GCF:_______
2.
14
18
Factors of 14:
_____________________________
Factors of 18:
_____________________________
GCF:_______
Co n st ru ct e d R e sp on s e C l o su r e
Alicia reduced the fraction
12
2
to . Explain why her answer is not fully reduced.
24
4
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Su mm ar y C l o su r e
What did you learn today about reducing fractions?
Day 1 _______________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Day 2 _______________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Name __________________________
In d ep en d en t P ra cti c e
The reduced form of a fraction is when the numerator and denominator have no common factor except 1.
To reduce a fraction means to change it into reduced form.
Reduce fractions.
Step #1: Find the factors of the numerator and denominator.
Step #2: Identify the GCF and write it on the line. (circle)
Step #3: Reduce the fraction by dividing the numerator and denominator
by the GCF. (circle)
Step #4: Interpret the reduced fraction. “The reduced form of ___ is ___.”
1.
11
33
2.
Factors of 11: ______________________
Factors of 5: _______________________
Factors of 33: ______________________
Factors of 35: ______________________
GCF:_______
3.
GCF:_______
15
24
4.
27
30
Factors of 15: ______________________
Factors of 27: ______________________
Factors of 24: ______________________
Factors of 30: ______________________
GCF:_______
5.
5
35
GCF:_______
14
48
6.
12
54
Factors of 14: ______________________
Factors of 12: ______________________
Factors of 48: ______________________
Factors of 54: ______________________
GCF:_______
DataWORKS Educational Research
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GCF:_______
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Name __________________________
P eri odi c R evi ew 1
The reduced form of a fraction is when the numerator and denominator have no common factor except 1.
To reduce a fraction means to change it into reduced form.
Reduce fractions.
Step #1: Find the factors of the numerator and denominator.
Step #2: Identify the GCF and write it on the line. (circle)
Step #3: Reduce the fraction by dividing the numerator and denominator
by the GCF. (circle)
Step #4: Interpret the reduced fraction. “The reduced form of ___ is ___.”
1.
14
42
2.
Factors of 14: ______________________
Factors of 22: ______________________
Factors of 42: ______________________
Factors of 33: ______________________
GCF:_______
3.
GCF:_______
15
75
4.
12
60
Factors of 15: ______________________
Factors of 12: ______________________
Factors of 75: ______________________
Factors of 60: ______________________
GCF:_______
5.
22
33
GCF:_______
16
56
6.
40
55
Factors of 16: ______________________
Factors of 40: ______________________
Factors of 56: ______________________
Factors of 55: ______________________
GCF:_______
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
GCF:_______
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Name __________________________
P eri odi c R evi ew 2
The reduced form of a fraction is when the numerator and denominator have no common factor except 1.
To reduce a fraction means to change it into reduced form.
Reduce fractions.
Step #1: Find the factors of the numerator and denominator.
Step #2: Identify the GCF and write it on the line. (circle)
Step #3: Reduce the fraction by dividing the numerator and denominator
by the GCF. (circle)
Step #4: Interpret the reduced fraction. “The reduced form of ___ is ___.”
1.
8
32
2.
Factors of 8: _______________________
Factors of 16: ______________________
Factors of 32: ______________________
Factors of 36: ______________________
GCF:_______
3.
GCF:_______
64
88
4.
36
81
Factors of 64: ______________________
Factors of 36: ______________________
Factors of 88: ______________________
Factors of 81: ______________________
GCF:_______
5.
16
36
GCF:_______
28
42
6.
22
40
Factors of 28: ______________________
Factors of 22: ______________________
Factors of 42: ______________________
Factors of 40: ______________________
GCF:_______
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
GCF:_______
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
Name __________________________
P eri odi c R evi ew 3
The reduced form of a fraction is when the numerator and denominator have no common factor except 1.
To reduce a fraction means to change it into reduced form.
Reduce fractions.
Step #1: Find the factors of the numerator and denominator.
Step #2: Identify the GCF and write it on the line. (circle)
Step #3: Reduce the fraction by dividing the numerator and denominator
by the GCF. (circle)
Step #4: Interpret the reduced fraction. “The reduced form of ___ is ___.”
1.
36
63
2.
Factors of 36: ______________________
Factors of 20: ______________________
Factors of 63: ______________________
Factors of 85: ______________________
GCF:_______
3.
GCF:_______
28
70
4.
30
50
Factors of 28: ______________________
Factors of 30: ______________________
Factors of 70: ______________________
Factors of 50: ______________________
GCF:_______
5.
20
85
GCF:_______
18
72
6.
27
45
Factors of 18: ______________________
Factors of 27: ______________________
Factors of 72: ______________________
Factors of 45: ______________________
GCF:_______
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
GCF:_______
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.
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DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
6th Grade Number Sense 2.4 (3Q)
Determine the least common multiple and the greatest common divisor of whole
numbers; use them to solve problems with fractions (e.g., to find a common
denominator to add two fractions or to find the reduced form of a fraction).
Lesson to be used by EDI-trained teachers only.