6 th Grade Number Sense 2.4 (3Q) Determine the least common multiple and the greatest common divisor...

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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Learning Objective Name ___________________________

Today, we will reduce fractions.

CFUWhat are we going to do today?

Activate (or provide) Prior Knowledge

CFU Students, you already know how to find the GCF of two numbers by listing their factors. Today, we will reduce fractions by finding the GCF of the numerator and denominator.

A factor is a number that divides a given number evenly.The greatest common factor (GCF) of two numbers is thelargest number that divides both numbers evenly.

List the factors of the following numbers.

A. The factors of 18

1

B. The factors of 12

, 2 , 3, 6, 9, 18 1, 2 , 3, 4, 6, 12

C. What is the GCF of 12 and 18?

6The GCF of 12 and 18 is ________.

1, 2, 3, 6

Factors of 6





Concept Development

Example: Reduce using the greatest common factor (GCF): 1218

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.

CFUUse the list of factors to determine which fraction is in reduced form? How do you know? Why is the other not in reduced form?

What number will we need to divide by to reduce the fraction (A) above? How do you know?

Factors of 12 = 1, 2, 3, 4, 6, and 12

Factors of 18 = 1, 2, 3, 6, 9, and 18

12 6 2 =

18 6 3

To reduce a fraction means to change it into reduced form.• To reduce a fraction, divide the numerator and denominator by the GCF.

GCF = 6

1 same 2 called

1218

23

1, 2

1, 3

23

Reduced Fraction

No common factor except 1

7

21B 9

25A 1, 7

1, 3, 7, 21

1, 3, 9

1, 5, 25

B 3 A 7

FlashcardsReduced Form

1, 2, 3, 4, 6, 121, 2, 3, 6, 9, 18

1218

NOT a Reduced Fraction

1, 2, 3 and 6 are common factors





1.

Factors of 7:

_______________________

Factors of 21: ______________________

GCF:_______

2.

Factors of 5:

_______________________

Factors of 20: ______________________

GCF:_______

3.

Factors of 9:

_______________________

Factors of 12: ______________________

GCF:_______

4.

Factors of 12: ______________________

Factors of 15: ______________________

GCF:_______

Skill Development/Guided Practice

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?

7

215

20

9

12

1

1

7

7=

7

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 4 explain

1

3

Reduce fractions.

, 7

, 3 , 7, 21

1

1

5

5=

5

1

4

, 5

, 2 , 4, 5, 10, 20

1

1

3

3=

3

3

4

, 3

, 2 , 3, 4, 6, 12

, 9

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.

12

15

1 , 2 , 3, 4, 6, 12

1, 3 , 5, 15

3

3=

3

4

5


1, 2, 3, and 6 are commonfactor of 12 and 18

1218

23

Reduced Fraction






18

42

24

40

5. Factors of 18: _______________________

Factors of 42: _______________________

GCF:_______

6. Factors of 24: _______________________

Factors of 40: _______________________

GCF:_______

1 , 2 , 3, 6, 9, 18

1 , 2 , 3, 6, 7, 14, 21, 42

6

6=

6

3

7

1 , 2 , 3, 4, 6, 8

1 , 2 , 4, 5, 8, 10, 20, 40

8

8=

8

3

5

, 12, 24

Skill Development/Guided Practice (continued)


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?

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 _____.”

Reduce fractions. 2

3

Reduced Fraction




1218






CFUDoes 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?

1. Reducing fractions will make calculations easier.

Relevance

2. Reducing fractions will help you do well on tests.

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.





Skill Closure

1. Factors of 3: _______________________

Factors of 15: _______________________

GCF:_______

2. Factors of 14: _______________________

Factors of 18: _______________________

GCF:_______

1, 3

1, 3 , 5, 15

3

3=

3

1

5

1 , 2 , 7, 14

1 , 2 , 3, 6, 9, 18

2

2=

2

7

9

3

15

14

18


What did you learn today about reducing fractions?Day 1 _________________________________________________________________________________________________________________________________________________________________________________________________________

Day 2 _________________________________________________________________________________________________________________________________________________________________________________________________________


Reduce fractions.

Constructed Response Closure

Summary Closure

Alicia reduced the fraction to . Explain why her answer is not fully reduced.

______________________________________________________________________________________________________

12

24

2

4

23

Reduced Fraction




1218





Independent Practice Name ________________________________

1

1

11

11=

11

1

3

, 11

, 3 , 11, 33

1

1

5

5=

5

1

7

, 5

, 5 , 7, 35

1

1

3

3=

3

5

8

, 3

, 2 , 3, 4, 6, 8

, 5

11

335

35

15

24

, 15

, 12, 24

1.

Factors of 11:

_______________________

Factors of 33: ______________________

GCF:_______

2.

Factors of 5:

_______________________

Factors of 35: ______________________

GCF:_______

3.

Factors of 15:

_______________________

Factors of 24: ______________________

GCF:_______

4.

Factors of 27:

_______________________

Factors of 30: ______________________

GCF:_______

5.

Factors of 14:

_______________________

Factors of 48: ______________________

GCF:_______

6.

Factors of 12:

_______________________

Factors of 54: ______________________

GCF:_______

1 , 3, 9, 27

1, 2 , 3, 5

3

3=

3

9

1027

30, 6 , 10, 15, 30

1 , 2 , 7, 14

1 , 2 , 3, 4, 6, 8 , 12, 16

2

2=

2

7

24

14

48, 24,48

1 , 2 , 3, 4, 6, 12

1 , 2 , 3, 6, 9, 18, 27, 54

6

6=

6

2

912

54



Reduce fractions. 23

Reduced Fraction




1218





1.

Factors of 14:

_______________________

Factors of 42: ______________________

GCF:_______

2.

Factors of 22:

_______________________

Factors of 33: ______________________

GCF:_______

3.

Factors of 15:

_______________________

Factors of 75: ______________________

GCF:_______

4.

Factors of 12:

_______________________

Factors of 60: ______________________

GCF:_______

5.

Factors of 16:

_______________________

Factors of 56: ______________________

GCF:_______

6.

Factors of 40:

_______________________

Factors of 55: ______________________

GCF:_______

14

4222

33

15

75

1, 2, 7, 14

1, 2, 3, 6, 7, 14, 21, 42

14

14 14 1=

42 14 3

1, 2, 11, 22

1, 3, 11, 33

11

22 11 2=

33 11 3

1, 3, 5, 15

1, 3, 5, 15, 25, 75

15

15 15 1=

75 15 5

12

60

1, 12, 2, 6, 3, 4

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 12

12 12 1

=60 12 5

16

56

1, 2, 4, 8, 16

1, 2, 4, 7, 8, 14, 28, 56

8

16 8 2=

56 8 7

40

55

1, 2, 3, 4, 5, 8, 10, 20, 40

1, 5, 11, 55

5

40 5 8=

55 5 11

Periodic Review 1 Name ________________________________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.



Reduced Fraction




1218





1.

Factors of 8:

_______________________

Factors of 32: ______________________

GCF:_______

2.

Factors of 16:

_______________________

Factors of 36: ______________________

GCF:_______

3.

Factors of 64:

_______________________

Factors of 88: ______________________

GCF:_______

4.

Factors of 36:

_______________________

Factors of 81: ______________________

GCF:_______

5.

Factors of 28:

_______________________

Factors of 42: ______________________

GCF:_______

6.

Factors of 22:

_______________________

Factors of 40: ______________________

GCF:_______

8

3216

36

64

88

1, 2, 4, 8

1, 2, 4, 8, 16, 32

8

8 8 1=

32 8 4

1, 2, 4, 8, 16

1, 2, 3, 4, 6, 9, 12, 18, 36

4

16 4 4=

36 4 9

1, 2, 4, 8, 16, 32, 64

1, 2, 4, 8, 11, 22, 44, 88

8

64 8 8=

88 8 11

36

81

1, 2, 3, 4, 6, 9, 12, 18, 36

1, 3, 9, 27, 81

9

36 9 4=

81 9 9

28

42

1, 2, 4, 7, 14, 28

1, 2, 3, 6, 7, 14, 21, 42

14

28 14 2=

42 14 3

22

40

1, 2, 11, 22

1, 2, 4, 5, 8, 10, 20, 40

2

22 2 11=

40 2 20




Reduced Fraction




1218





1.

Factors of 36:

_______________________

Factors of 63: ______________________

GCF:_______

2.

Factors of 20:

_______________________

Factors of 85: ______________________

GCF:_______

3.

Factors of 28:

_______________________

Factors of 70: ______________________

GCF:_______

4.

Factors of 30:

_______________________

Factors of 50: ______________________

GCF:_______

5.

Factors of 18:

_______________________

Factors of 72: ______________________

GCF:_______

6.

Factors of 27:

_______________________

Factors of 45: ______________________

GCF:_______

1, 2, 4, 7, 14, 28

36

63

20

85

28

70

1, 2, 3, 4, 6, 9, 12, 18, 36

1, 3, 7, 9, 21, 63

9

36 9 4=

63 9 7

1, 2, 4, 5, 10, 20

1, 5, 17, 85

5

20 5 4=

85 5 17

1, 2, 5, 7, 10, 14, 35, 70

14

28 14 2=

70 14 5

30

50

1, 2, 3, 5, 6, 10, 15, 30

1, 2, 5, 25, 10, 50

10

30 10 3=

50 10 5

18

72

1, 2, 3, 6, 9, 18

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

18

18 18 1=

72 18 4

27

45

1, 3, 9, 27

1, 3, 5, 9, 15, 45

9

27 9 3=

45 9 5




Reduced Fraction




1218





Flashcard (Reduced Form)

Teacherwith CFU


Is the fraction in reduced form?

[ How did I know if the fraction was in reduced form? ]

1

8


Yes





Studentswith CFU


[ How did you know if the fraction was in reduced form? ]

3

10




Yes





Teacherwith CFU


[ How did I know if the number was in reduced form? ]

9

12




No





Studentswith CFU


2

10




[ How did you know if the fraction was in reduced form? ]

No






4

7




Yes

Students






7

21




No

Students






10

30




No

Students





Students


9

11




Yes





Students


5

9




Yes





Studentswith CFU

Return to Concept Development


8

12




No[ How did you know if the fraction was in reduced form? ]





Learning Objective : Today, we will reduce fractions.

Cognitive Strategies Teaching Strategies

Elaboration Demonstration

Targeted vocabulary: reduced form, common, referred, identify, interpret

Language Strategies

Vocabulary Words

Academic common, referred, identify, interpret

Content reduced form

Support

VocabularyStrategy

Multiple-Meaning

Synonym common, referred, identify, interpret

Definition reduced form

Homophone

Internal Context Clue

Listen, Speak Similar Sounds

ReadTracked Reading

Decoding Rules

Write Writing

Content Access Strategies

Comprehensible Input Cognates

Contextual Clues

Graphic Organizer

Contextualized Definitions

Pictures

EDI – Cognitive, Teaching and English Learners Strategies





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6 th Grade Number Sense 2.4 (3Q) Determine the least common multiple and the greatest common divisor...

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