Transcript 5th_MA_NS_2.3_ADD_FRACTIONS_DW

Learning Objective
Name __________________________
Today, we will add fractions that have unlike1 denominators.
1
different
CFU
What are we going to do today?
Fraction
1
8
Activate (or provide) Prior Knowledge
Numerator
Denominator
A fraction is a number that names a part of a whole or a part of a group.
To add fractions with like1 denominators, add the numerators and keep the
denominator.
1
the same
Add and write your answer in simplest form.
4
5 8 13
1. + =
1
9 9 9
9
9
2
4
5

1
2. + =
7
7
7
7
CFU
Teacher completes problem #1. Students complete problem #2. Students, you already know how to add fractions with like
denominators and write your answer in simplest form. Today, we will use these skills to add fractions that have unlike denominators.
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5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Concept Development
To add fractions, both fractions must have a common denominator.
• If the fractions have unlike denominators, then we need to find the lowest common denominator (LCD).
• Create equivalent fractions so that the LCD is the new denominator.
The lowest common denominator is the lowest multiple shared by a set of denominators.
Equivalent fractions are fractions with the same value but different numbers in the numerator and denominator.
Adding Fractions that have Unlike Denominators
1 5  11  1 1
3 6

10
2 10
10
5 10
Unlike
Denominators
5
1

10
2
Lowest
Common
3
6
 
5
10 Denominators
11
1
=1
10
10
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Equivalent Fractions
1 2 3 4 5
6
   

 ...
2 4 6 8 10 12
NOT Adding
fractions correctly
1 3 4
 
2 5 7
CFU
Which fractions are ready to be
added? Explain your answer.
A
3 6
9 12



 ...
5 10 15 20
1 2
 
2 3
B
3 4
 
6 6
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Concept Development (Clarification and CFU)
To add fractions, both fractions must have a common denominator.
• If the fractions have unlike denominators, then we need to find the lowest common denominator (LCD).
• Create equivalent fractions so that the LCD is the new denominator.
The lowest common denominator is the lowest multiple shared by a set of denominators.
Equivalent fractions are fractions with the same value but different numbers in the numerator and denominator.
Finding the Lowest Common Denominator
and Equivalent Fractions
1 2
 
2 3
Unlike
Denominators
List of Multiples for 2 and 3
2 : 2, 4, 6, 8, 10, 12, 14, 16, 18...
3 : 3, 6, 9, 12, 15, 18, 21...
Equivalent Fractions
1 3 3
 
2 3 6
2 and 3 share the multiples 6, 12, 18,…
Equivalent Fractions:
2 2 4
 
3 2 6
1 3
2 4
 and 
2 6
3 6
The Lowest Common Denominator is 6
CFU
Given the list of multiples for 3 and 4 below, what is the LCD of
List of Multiples for 3 and 4
3: 3, 6, 9, 12, 15, 18, 21, 24, ...
4: 4, 8, 12, 16, 20, 24, 28, …
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1
3
and
1
4
?
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
To add fractions, both fractions must have like denominators.
Add fractions that have unlike denominators.
Step #1: Read the problem carefully.
Step #2: Find the lowest common denominator.
a. Make a list of multiples for each denominator value and identify the first shared multiple.
Step #3: Create equivalent fractions using the lowest common denominator.
Step #4: Add the new equivalent fractions.
a. Express the answer in simplest form.
Step #5: Interpret3 the sum.
1
1
+
=
2
3
1.
1
3
1
2
3: 3, 6, 9, 12
2: 2, 4, 6, 8
2
2
 
6
5
2

+
3
3
6
 
6
3
1
4. 4
+
8
6
8: 8, 16, 24, 32
6: 6, 12, 18, 24
2.
1
2
=
+
2
5
5: 5, 10, 15, 20
2: 2, 4, 6, 8, 10
4
12
4: 4, 8, 12, 16
12: 12, 24, 36, 48
5. Sherry bought 3 of a pound of milk
6. Tom bought 2 of a pound of jelly
4
chocolate and 1 of a pound of white
3
beans and 1 of a pound of gummy
chocolate. How much chocolate does
bears. How much candy did he buy?
3: 3, 6, 9, 12, 15
5: 5, 10, 15, 20
2 5
10
Sherry have?
4: 4, 8, 12, 16
2: 2, 4, 6, 8,
3 1 3
 
4 5 1 She has 1 1
4 1
+  1
1 2 2 4 4 pounds 4
 
of chocolate.
2 2 4
CFU (#2) How did I/you find the lowest common denominator?
(#3) How did I/you create equivalent fractions?
(#4a) How did I express the sum in simplest form?
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3. 3 + 1 =
tell what it means
3 3  9

4 3 12 10 2
5


+
1 1
1
12 2
6
 
12
12 1
1 5  5

9
2 5 10

+
2 2
4
10
 
5 2 10
2
4 3  12

24
8 3
16 8  2

+
1 4
4
24 8 3


24
6 4
3
5


13
13
15
3 5
He bought

+
15
1 3  3
15

of a pound of
15
5 3
candy.
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Importance
To add fractions, both fractions must have a common denominator.
1. Adding fractions that have unlike denominators can help you solve real-world problems
that use fractions.
James has eaten
1
4
of the pie. Erick has eaten
Together, they have eaten
3
of the pie.
4
1
2
of the pie.
1 1
 
4 2
1 2 2
 
2 2 4
1 2 3
 
4 4 4
2. Adding fractions that have unlike denominators will help you do well on tests.
CFU
Does anyone else have another reason as to why it is important to add fractions that have unlike denominators? (pair-share) Why is it
important to add fractions that have unlike denominators? You may give me one of my reasons or one of your own. Which reason is more
important to you? Why?
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5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
To add fractions, both fractions must have a common denominator.
Concept Closure
Which of the following problems is
ready to be added? Explain your answer.
A
3 1
+ =
5 6
B
__________________________________________________
3 1
+ =
7 7
__________________________________________________
Skill Closure
Add fractions that have unlike denominators.
Step #1: Read the problem carefully.
Step #2: Find the lowest common denominator.
a. Make a list of multiples for each denominator value and identify the first shared multiple.
Step #3: Create equivalent fractions using the lowest common denominator.
Step #4: Add the new equivalent fractions.
a. Express the answer in simplest form.
Step #5: Interpret the sum.
1.
3
1
+
=
4
8
2. Carmen bought
of a pound of nectarines? How many pounds of
4: 4, 8, 12, 16
8: 8, 16, 24, 32
3
4
1
8
2 6
 
2 +8
1
1
 
1 8

2
1
of a pound of grapes and
6
4
fruit did Carmen buy?
7
8
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What did you learn today about adding
fractions that have unlike denominators?
Day 1
__________________________________
__________________________________
4: 4, 8, 12, 16
6: 6, 12, 18, 24
1 3
3
 
7
4 3
12

+
2 2
4
12
 
6 2
12
Summary Closure
7
of
12
a pound of fruit.
Carmen bought
Day 2
__________________________________
__________________________________
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Independent Practice
To add fractions, both fractions must have a common denominator.
Add fractions that have unlike denominators.
Step #1: Read the problem carefully.
Step #2: Find the lowest common denominator.
a. Make a list of multiples for each denominator value and identify the first shared multiple.
Step #3: Create equivalent fractions using the lowest common denominator.
Step #4: Add the new equivalent fractions.
a. Express the answer in simplest form.
Step #5: Interpret the sum.
1. 5
6
+
1
3
=
6: 6, 12, 18, 24
3: 3, 6, 9, 12
8
+
3
=
12
8: 8, 16, 24, 32
12: 12, 24, 36, 48
3 3
9
 
8 3 24 15 3
+ 
3 2 6 24 3
 
12 2 24
5 1 5
 
6 1 6 7
1
+  1
1 2 2 6
6
 
3 2 6
4. Josephine bought two gold rings. One
1
contained of an ounce of gold. The
4
2
other one contained of an ounce of
5
gold. How much gold does she have
altogether?
4: 4, 8, 12, 16, 20
5: 5, 10, 15, 20
1 5
5
 
4 5 20 13
2 4 + 8 
20
 
5 4 20
2. 3
13
20
of an ounce
of gold.
She has
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
5
8
5. The Smith family bought a pizza.
1
Jason ate 2 of the pizza and Jamie ate
4
7
of the pizza. How much pizza was
eaten?
7: 7, 14, 21, 28
4: 4, 8, 12, 16, 20, 24, 28
2 4
8
 
7 4 28 15
+

1 7
7
28
 
4 7 28
3. 7
8
+
3
=
4
8: 8, 16, 24, 32
4: 4, 8, 12, 16
7 1 7
 
8 1 8 13
5
+ 

1
3 2 6 8
8
 
4 2 8
6. Sam bought 3 of a pound of walnuts
6
3
and
of a pound of peanuts. How many
12
pounds of nuts did he buy?
6: 6, 12, 18, 24
12: 12, 24, 36, 48
3 2 6
 
6 2 12 9 3 3
+
15
3
3 1 3  12 3  4
He
bought
of
the
pizza


28
12 1 12
of a pound 4
was eaten.
of nuts.
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Periodic Review 1
To add fractions, both fractions must have a common denominator.
Add fractions that have unlike denominators.
Step #1: Read the problem carefully.
Step #2: Find the lowest common denominator.
a. Make a list of multiples for each denominator value and identify the first shared multiple.
Step #3: Create equivalent fractions using the lowest common denominator.
Step #4: Add the new equivalent fractions.
a. Express the answer in simplest form.
Step #5: Interpret the sum.
1.
11
12
1
+ 4=
12: 12, 24, 36
4: 4, 8, 12, 16
2. 3 + 4 = 6: 6, 12, 18, 24,
12
6
12: 12, 24, 36, 48
6
2

10 2
2 12
5
+


1 4
6
12 2
 
1 12
11 1 11
 
12 1 12 14 2 7
1
+
1 3 3  12 2  6  16
 
4 3 12
3
6
4
12
4. Helena bought some vegetables. She
2
got 1 of a pound of carrots and
of a
6
8
pound of broccoli. What was the weight
of the vegetables altogether?
5. The Jones family bought a pizza. Eric
2
ate 3 of the pizza and Herbert ate of
6
7
the pizza. How much pizza was eaten?
8: 8, 16, 24, 32
6: 6, 12, 18, 24
3
1 3
 
8 3 24 11
+

2  4  8 24
6 4 24
11
She has
24
of a pound of
vegetables.
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
6: 6, 12, 18, 24, 30, 36, 42
7: 7, 14, 21, 28, 35, 42
3
7
2
6
6 18

6 42 32 2 16
+

7 14 42 2 = 21 of the
 
7 42
pizza was
eaten.

3. 7 + 3 =
12
12: 12, 24, 36, 48
16: 16, 32, 48, 64
16
7 4
28


48
12 4
+
9
3 3


48
16 3

37
48
4
6. Geoff has
of a pound of cashews
9
5
and buys
of a pound more. How many
8
pounds of cashews does he have
altogether?
9: 9, 18, 27, 36, 45, 54, 63, 72
8: 8, 16, 24, 32, 40, 48, 56, 64, 72
4 8 32
 
5
9 8 72 77
1
5 He has
+
72
5 9 45  72  172 pounds of
 
8 9 72
nuts.
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Periodic Review 2
To add fractions, both fractions must have a common denominator.
Add fractions that have unlike denominators.
Step #1: Read the problem carefully.
Step #2: Find the lowest common denominator.
a. Make a list of multiples for each denominator value and identify the first shared multiple.
Step #3: Create equivalent fractions using the lowest common denominator.
Step #4: Add the new equivalent fractions.
a. Express the answer in simplest form.
Step #5: Interpret the sum.
1. 4 + 3 =
6
8
2. 9 + 1 =
4
10
6: 6, 12, 18, 24
8: 8, 16, 24, 32
9
10
1
4
4 4 16
 
25
1
6 4 24

1
+
3 3
24
24
  9
8 3 24
1
10: 10, 20 , 30 , 40
4: 4, 8, 12, 16, 20
2 18
 
2 20  23  1 3
+
20
20
5
5
 
5 20
4. Alfredo bought some fruit. He got
4
5
of a pound of apples and of a pound of
8
pears. What was the weight of the fruit
altogether?
4: 4, 8, 12, 16
8: 8, 16, 24, 32
5. Juan got a bag of candy. He ate 2 of
4
the candy. His sister ate 3 of the candy.
8
How much of the bag of candy was
eaten?
4: 4, 8, 12, 16
8: 8, 16, 24, 32,
1
4
5
8
2
4
3
8
2 2

2 8
1+ 5
 
1 8


7
8
7
He has
8
of a pound
of fruit.
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2 4
 
2 8
+
1 3
 
1 8
7

8
7
8
of the
candy was
eaten.
3. 4 + 5 =
5
15
5: 10, 15, 20, 25
15: 15, 30, 45, 60
4 3 12
 
2
5 3 15 17
+
1

5 1 5
15
15
 
15 1 15
6. Alfred has 2 of a pound of cheese and
3
2
buys
of a pound more. How many
12
pounds of cheese does he have
altogether?
3: 3, 6, 9, 12
12: 12, 24, 36, 48
2 4 8
 
5
3 4 12 10 2 5
He
bought
+
6
2 1 2  12 2  6
of a pound
 
12 1 12
of cheese.
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Name _____________________________
Periodic Review 3
To add fractions, both fractions must have a common denominator.
Add fractions that have unlike denominators.
Step #1: Read the problem carefully.
Step #2: Find the lowest common denominator.
a. Make a list of multiples for each denominator value and identify the first shared multiple.
Step #3: Create equivalent fractions using the lowest common denominator.
Step #4: Add the new equivalent fractions.
a. Express the answer in simplest form.
Step #5: Interpret the sum.
1.
11
12
+
1
=
4
2. 3 + 4 =
10
5
12: 12, 24, 36, 48
4: 4, 8, 12, 16
6
3 2
 
5 2 10 10 10 1
+ 
 1
4 1 4 10 10 1
 
10 1 10
11 1 11
 
12 1 12 14 2 7
1
+ 


1
3
1
6
  3 12 2 6
4 3 12
2
4. Alice bought some beans. She got
8
of a pound of lima beans and 2 of a
5
pound of pinto beans. What was the
weight of the beans altogether?
8: 8, 16, 24, 32, 40
5: 5, 10, 15, 20, 25, 30, 35, 40
2 5 10
 
8 5 40 26 2 13
+

2  8 16  40 2 20

5 8 40
She has 13 of a pound of beans.
20
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5: 5, 10, 15, 20
10: 10, 20, 30, 40
5. Alex is making some punch. It will
3
take 5 of a cup of juice and
of a cup
8
16
of soda. How much punch will he have
altogether?
16: 16, 32
8: 8, 16, 24, 32
3. 5 + 1 = 12: 12, 24, 36, 48
12
4
4: 4, 8, 12, 16
5
5 1
 
12 1 + 12 8 4

3 12 4
1 3
 
4 3 12

2
3
6. Arnold has 3 of a pound of cashews
6
and buys 5 of a pound more. How
8
many pounds of cashews does he have
altogether?
6: 6, 12, 18, 24
8: 8, 16, 24, 32
3 4 12
 
6 4 24
3 9
1
+15  27
 1
5 1
5
3
5
11
 
 
8
24 3 8
He
will
have
16 1 16 11
3
24
8
+

of a cup of 16
3 2
6
1
16 punch.
 
He bought 1 pounds of nuts.
8 2 16
8
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
First five multiples of the numbers 2 through 20.
×
1
2
3
4
5
2
2
4
6
8
10
3
3
6
9
12
15
4
4
8
12
16
20
5
5
10
15
20
25
6
6
12
18
24
30
7
7
14
21
28
35
8
8
16
24
32
40
9
9
18
27
36
45
10
10
20
30
40
50
11
11
22
33
44
55
12
12
24
36
48
60
13
13
26
39
52
65
14
14
28
42
56
70
15
15
30
45
60
75
16
16
32
48
64
80
17
17
34
51
68
85
18
18
36
54
72
90
19
19
38
57
76
95
20
20
40
60
80
100
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Creating Equivalent (equal) Fractions




5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Problem re-written with new
equivalent fractions.
Original Problem


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
Denominators
must be the same
to add fractions.
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.