Post on 29-Dec-2015
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
Learning Objective Name __________________________
Today, we will add fractions that have unlike1 denominators.
CFU
What are we going to do today?
Activate (or provide) Prior Knowledge
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
CFUTeacher 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.
1 different
5 81. + =
9 9
4 52. + =
7 7
13
9419
9
7217
Add and write your answer in simplest form.
1
8
Numerator
Denominator
Fraction
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
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.
... 2 3 4 5 64 6 0 12
1182
... 6 9 1215 20
35 10
Equivalent Fractions
NOT Addingfractions correctly
1 3 42 5 7
35
12
610
510
1110
Adding Fractions that have Unlike Denominators
1110
51102
3 65 10
1110
1= 110
Lowest Common
Denominators
UnlikeDenominators
CFUWhich fractions are ready to be added? Explain your answer.
3 46 6
B 1 22 3
A
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
Equivalent Fractions
Concept Development (Clarification and CFU)
CFUGiven the list of multiples for 3 and 4 below, what is the LCD of and ?
1 22 3
UnlikeDenominators
: 2, 4, , 8, 10, , 14, 16,6 12 1 .8..2List of Multiples for 2 and 3
2 and 3 share the multiples 6, 12, 18,…
12 63
3 3
Equivalent Fractions: and 1 3 2 42 6 3 6
Finding the Lowest Common Denominator and Equivalent Fractions
: 3, , 9, ,6 12 1 15, ,8 21...3
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.
The Lowest Common Denominator is 6
23 62
2 4
13
14
List of Multiples for 3 and 43: 3, 6, 9, 12, 15, 18, 21, 24, ...4: 4, 8, 12, 16, 20, 24, 28, …
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
1. 2. 3.
4. 5. Sherry bought of a pound of milk
chocolate and of a pound of white
chocolate. How much chocolate does
Sherry have?
6. Tom bought of a pound of jelly
beans and of a pound of gummy
bears. How much candy did he buy?
Skill Development/Guided Practice
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. 3 tell what it means
To add fractions, both fractions must have like denominators.
1
2
1
22
5
1
31
2
5
6
9
10
3
41
2
5
4 She has
pounds of chocolate.
11
4
2
31
5
13
15 He bought
of a pound of candy.
13
15
2
23
3
2
6
3
6
1
22
5
5
52
2
5
10
4
10
1
12
2
3
4
2
4
5
53
3
10
15
3
15
+ +
++
3
41
2
1
5
+ = 3: 3, 6, 9, 122: 2, 4, 6, 8
+ = 5: 5, 10, 15, 202: 2, 4, 6, 8, 10
4: 4, 8, 12, 162: 2, 4, 6, 8,
3: 3, 6, 9, 12, 155: 5, 10, 15, 20
2
3
3
4+
1
12=
1
3
4
81
6
4: 4, 8, 12, 1612: 12, 24, 36, 48
8: 8, 16, 24, 326: 6, 12, 18, 24
10
12
3
41
12
3
31
1
9
12
1
12+
16
24
4
81
6
3
34
4
12
24
4
24+
2
2
5
6
88
2
3
+
11
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?
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
Importance
CFUDoes 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?
1. Adding fractions that have unlike denominators can help you solve real-world problems that use fractions.
2. Adding fractions that have unlike denominators will help you do well on tests.
14
James has eaten of the pie. Erick has eaten of the pie.
Together, they have eaten of the pie.
12
34
1 14 2
1 2 22 2 4
1 2 34 4 4
To add fractions, both fractions must have a common denominator.
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
Concept Closure
Skill Closure
To add fractions, both fractions must have a common denominator.
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.
Add fractions that have unlike denominators.
Summary Closure
__________________________________________________
__________________________________________________
Which of the following problems isready to be added? Explain your answer.
3 1+ =5 6
A 3 1+ =7 7
B
1.
2. Carmen bought of a pound of grapes and
of a pound of nectarines? How many pounds of
fruit did Carmen buy?
1
42
6
7
12Carmen bought of
a pound of fruit.
7
12
3
41
8
7
8
3
3
2
2
3
12
4
12
2
2
1
1
6
8
1
8+
+
1
4
2
63
41
8+ =
4: 4, 8, 12, 168: 8, 16, 24, 32
4: 4, 8, 12, 166: 6, 12, 18, 24
What did you learn today about adding fractions that have unlike denominators?
Day 1 ____________________________________________________________________
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
Independent Practice Name _____________________________
1. 2. 3.
4. Josephine bought two gold rings. One
contained of an ounce of gold. The
other one contained of an ounce of
gold. How much gold does she have
altogether?
5. The Smith family bought a pizza.
Jason ate of the pizza and Jamie ate
of the pizza. How much pizza was
eaten?
6. Sam bought of a pound of walnuts
and of a pound of peanuts. How
many pounds of nuts did he buy?
1
4 2
5
5
6
1
3
3
12
2
71
4
15
28 of the pizza was eaten.
15
28
4
4
7
7
8
28
7
28
+
2
7
1
42
5
13
20She has
of an ounce of gold.
13
20
5
5
4
4
5
20
8
20
+
3
63
12
9
12
3
3
He bought
of a pound of nuts.
2
2
1
1
6
12
3
12
3
4 3
4
+
3
63
12
7
8
3
4
1
4
5
61
3
7
6
1
1
2
2
5
6
2
6
+
3
83
12
15
24
3
3
2
2
9
24
6
24
+
7
83
4
13
8
1
1
2
2
7
8
6
8+
+ 6: 6, 12, 18, 243: 3, 6, 9, 12
=
4: 4, 8, 12, 16, 205: 5, 10, 15, 20
3
8+ = 8: 8, 16, 24, 32
12: 12, 24, 36, 48
7: 7, 14, 21, 284: 4, 8, 12, 16, 20, 24, 28
+ =8: 8, 16, 24, 324: 4, 8, 12, 16
6: 6, 12, 18, 2412: 12, 24, 36, 48
51
8
5
8
3
3
To add fractions, both fractions must have a common denominator.
11
6
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.
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
1. 2. 3.
4. Helena bought some vegetables. She
got of a pound of carrots and of a
pound of broccoli. What was the weight
of the vegetables altogether?
5. The Jones family bought a pizza. Eric
ate of the pizza and Herbert ate of
the pizza. How much pizza was eaten?
6. Geoff has of a pound of cashews
and buys of a pound more. How
many pounds of cashews does he have
altogether?
8
24
32
42 of the pizza was eaten.
16
21
6
6
7
7
18
42
14
42
+
3
7
11
24
She has
of a pound of vegetables.
11
24
3
3
4
4
+ 77
72He has pounds of nuts.
8
8
9
9
32
72
45
72
5
172
51
72+
2
6
14
12
2
2
1
1
3
3
11
12
3
12
7 1
16 6
+ 10
12
2
2
2
2
1
1
6
12
4
12
5
6+
37
48
4
4
3
3
28
48
9
48+
1
8
2
6
1
82
6
3
24
3
72
6
4
95
8
4
95
8
11
12
1
4
11
121
4
3
64
12
3
64
12
7
123
16
7
123
16
2
2
+ = 12: 12, 24, 364: 4, 8, 12, 16
+ =
=
+ =6: 6, 12, 18, 24, 12: 12, 24, 36, 48
12: 12, 24, 36, 4816: 16, 32, 48, 64
8: 8, 16, 24, 326: 6, 12, 18, 24
6: 6, 12, 18, 24, 30, 36, 427: 7, 14, 21, 28, 35, 42
9: 9, 18, 27, 36, 45, 54, 63, 728: 8, 16, 24, 32, 40, 48, 56, 64, 72
Periodic Review 1 Name _____________________________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.
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
1. 2. 3.
4. Alfredo bought some fruit. He got
of a pound of apples and of a pound
of pears. What was the weight of the
fruit altogether?
5. Juan got a bag of candy. He ate of
the candy. His sister ate of the
candy. How much of the bag of candy
was eaten?
6. Alfred has of a pound of cheese and
buys of a pound more. How many
pounds of cheese does he have
altogether?
1
45
8
4
6
3
8
9
10
1
4
of the candy was eaten.
+7
8
He has
of a pound of fruit.
7
8
2
2
1
1
2
8
5
8
+10
12
2
2
He bought of a pound of cheese.
4
4
1
1
8
12
2
12
5
6
5
6+
2
32
12
4
55
15
3
8
25
24
4
4
3
3
16
24
9
24
1
124
+
23
20
2
2
5
5
18
20
5
20
3
120+
17
15
3
3
1
1
12
15
5
15
2
115
+
1
45
8
2
32
12
4
63
8
9
101
4
4
55
15
+ = + =+ =
4: 4, 8, 12, 168: 8, 16, 24, 32
4: 4, 8, 12, 168: 8, 16, 24, 32,
2
4
2
43
8
2
2
4
8
1
1
3
8
7
8
7
8
3: 3, 6, 9, 1212: 12, 24, 36, 48
6: 6, 12, 18, 248: 8, 16, 24, 32
10: 10, 20 , 30 , 404: 4, 8, 12, 16, 20
5: 10, 15, 20, 2515: 15, 30, 45, 60
Periodic Review 2 Name _____________________________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.
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
1. 2. 3.
4. Alice bought some beans. She got
of a pound of lima beans and of a
pound of pinto beans. What was the
weight of the beans altogether?
5. Alex is making some punch. It will
take of a cup of juice and of a cup
of soda. How much punch will he have
altogether?
6. Arnold has of a pound of cashews
and buys of a pound more. How
many pounds of cashews does he have
altogether?
2
5
11
16
He will have of a cup of punch.
11
16
1
1
2
2
5
16
6
16
+
26
40
She has of a pound of beans.1320
5
5
8
8
10
40
16
40
+
27
24
He bought pounds of nuts.
4
4
3
3
12
24
15
24
11
8
11
8
+
14
12
2
2
1
1
3
3
11
12
3
12
1
16
+ 10
10
10
10
2
2
1
1
6
10
4
10
11
1 +
8
12
4
4
1
1
3
3
5
12
3
12
2
3+
2
82
5
5
163
8
3
65
8
2
8 5
16
3
8
3
65
8
11
121
4
11
12
1
4
3
54
10
3
5
5
121
4
5
121
4
+ = + =4
10+ =12: 12, 24, 36, 484: 4, 8, 12, 16
5: 5, 10, 15, 2010: 10, 20, 30, 40
12: 12, 24, 36, 484: 4, 8, 12, 16
8: 8, 16, 24, 32, 405: 5, 10, 15, 20, 25, 30, 35, 40
16: 16, 328: 8, 16, 24, 32
6: 6, 12, 18, 248: 8, 16, 24, 32
13
20
Periodic Review 3 Name _____________________________To add fractions, both fractions must have a common denominator.
3
3
9
8
7
6
2
2
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.
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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
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504030201010
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3024181266
2520151055
201612844
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1086422
54321×
First five multiples of the numbers 2 through 20. 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.
DataWORKS Educational Research(800) 495-1550 • www.dataworks-ed.com©2012 All rights reserved. Comments? feedback@dataworks-ed.com
Denominators
must be the same to add fractions.
Original ProblemProblem re-written with new
equivalent fractions.