Transcript 5th_MA_NS_1.5_FRACTIONS_NUMBERLINE_DW

Name _______________________
Learning Objective
Today, we will identify1 fractions on a number line.
1
locate
CFU
What are we going to do today?
What does identify mean?
Activate (or provide) Prior Knowledge
Simplify each fraction to lowest terms.
2
2
2
1
1. 2
2. 4
4
2
6
2
2
3
Create equivalent fractions.
3.
1 4

2 4
=
4
8
4.
2 4

3 4
=
8
12
CFU
Teacher completes problems #1 and #3. Students complete problems #2 and #4. Students, you already know how to simplify fractions
and that there is more than one way to represent fractions. Today, we will use our knowledge of representing fractions to identify their
location on a number line.
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©2011 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Concept Development
CFU
A fraction is a number that describes a part of a whole or part of a set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
Parts
4 ? How do you know?
5
Numerator
3
4
Sections
Which of the two number lines from
0 to 1 below can be used to identify
A.
Denominator
5
0 1 2 3 4 1
5
5 5 5 5
B.
A number line shows the order of numbers based on their value.
3
Example: The fraction
shown on a number line from 0 to 1
4
Fill in the values of each tick mark on
the number line for answer A above.
Remember,
4 sections between 0 and 1
2 1

4 2
1
1
Distance
from 0 to1 1
4
4
4
0
4
3
4
1
2
1
4
1
1
Location
Sections
1
4
1
1
4
1 whole
4
1
4
1
0
Use your whiteboard insert to help
answer the following question.
Which fractions could represent the
location of point D on the number
line?
D
3
4
1
0
A.
4
8
B.
1
6
C.
1
2
How did you know the fraction
matched point D?
In your own words, what is a number
line? A number line is _________.
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify2 that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
2
2
6
location
sections
1
0
6 sections
check to be sure it is true
A
●
0
C
●
B
●
D
●
1
3
1. Which point shows the location of on the
4 4 sections
number line?
1
2. Which point shows the location of 4 on
4 sections
the number line?
Point A
Point A
Point B
Point C
Point D
E
●
0
x2
2
3. Which point shows the location of on
6 sections 3
4
the number line?

6
Point E Point F Point G Point H
x2
F
●
Point B
G
●
Point C
H
●
Point D
1
x2
1
4. Which point shows the location of 3 on
6 sections
the number line?
2
6
Point E Point F Point G Point H
x2
CFU Why did I count the sections and compare that number to the denominator of my fraction? Why was it sometimes necessary to create
an equivalent fraction? How did I use the numerator to locate the fraction on the number line? Why did you count the sections and
compare that number to the denominator of your fraction? Why was it sometimes necessary to create an equivalent fraction? How did you
use the numerator to locate the fraction on the number line?
DataWORKS Educational Research
5th Grade Number Sense 1.5 (2Q)
(800) 495-1550 • www.dataworks-ed.com
©2011 All rights reserved.
Comments? [email protected]
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
Y
●
X
●
W
●
2
6
1
6 sections
Z
●
2
1
6. Which point is located between and ?
5
5
5 sections
Point W
Point W
Point Y
Point Z
Q
●
P
●
7
3
7. Which point is located between and ?
8
8 sections 4
Point P Point Q Point R Point S
x2
6
8
x2
Point X
R
●
sections
0
4
3
5. Which point is located between and ?
5
5
5 sections
Point X
location
Point Y
Point Z
S
●
x2
3
1
8. Which point is located between and ?
8
8 sections 4
Point P Point Q Point R Point S

2
8
x2
CFU Why did I count the sections and compare that number to the denominator of my fraction? Why was it sometimes necessary to create
an equivalent fraction? How did I use the numerator to locate the fraction on the number line? Why did you count the sections and
compare that number to the denominator of your fraction? Why was it sometimes necessary to create an equivalent fraction? How did you
use the numerator to locate the fraction on the number line?
DataWORKS Educational Research
5th Grade Number Sense 1.5 (2Q)
(800) 495-1550 • www.dataworks-ed.com
©2011 All rights reserved.
Comments? [email protected]
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Importance
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
1. Identifying fractions will help you read rulers and yardsticks to make
accurate measurements.
Tabitha wanted to measure the width of this number
cube. Shown below is a close-up of the measurement
she took. Which fraction is closest to the width of the
number cube?
1
4
2. Identifying fractions will
help you do well on tests.
1
2
3
4
1
4
1
1
2
3
4
1
4
2 inches
The width of the number cube is
an inch.
CFU
Does anyone else have another reason why it is important to identify fractions on a number
line? (pair-share) Why is it important to identify fractions on a number line? You may give
one of my reasons or one of your own. Which reason is more important to you? Why?
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Closure
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
1. In your own words, what is a number line?
2. Identify fractions on a number line below.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a matching
denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer .
P
●
Q
●
R
●
S
●
What did you learn today about
identify fractions on a number
line?
1
0
3
on the number line?
8 8 sections
Point S
1. Which point shows the location of
Point P
Point Q
Point R
2. Which point shows the location of
Point P
Point Q
Point R
1
on the number line?
2 8 sections
Point S
x4
4
8
x4
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Day 1 ______________________
___________________________
___________________________
___________________________
___________________________
___________________________
Day 2 ______________________
___________________________
___________________________
___________________________
___________________________
___________________________
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Independent Practice
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
W
●
X
●
0
Y
●
location
sections
1
0
6 sections
Z
●
1
3
1. Which point shows the location of on the
5 5 sections
number line?
1
2. Which point shows the location of 5 on
5 sections
the number line?
Point W
Point W
Point X
Point Y
P
●
Point Z
Q
●
R
●
0
3
3. Which point shows the location of on x 2
4
the number line?
8 sections
6

8
Point P Point Q Point R Point S
x2
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Point X
S
●
Point Y
Point Z
1
11
4. Which point shows the location of 4 on x 2
the number line?
8 sections
2
8
Point P Point Q Point R Point S
x2
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Independent Practice (continued)
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
W
●
X
●
0
Y
●
P
●
Q
●
1
1
7. Which point is located between and ?
4
8 sections 8
Point R
R
●
Point S
x2

2
8
x2
DataWORKS Educational Research
1
0
6 sections
Z
●
6. Which point is located between
Point W
Point X
Point Y
S
●
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Comments? [email protected]
4
3
and ?
5
5
Point Z 5 sections
1
0
Point Q
sections
1
2
3
5. Which point is located between 5 and 5 ?
Point W Point X Point Y Point Z 5 sections
Point P
location
1
5
8. Which point is located between and ?
8
8 sections 2
Point P
Point Q
Point R
Point S
x4
4
8
x4
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
B
●
A
●
C
●
0
location
sections
1
0
6 sections
D
●
1
3
1. Which point shows the location of on the
10
number line?
10 sections
7
2. Which point shows the location of 10 on
10 sections
the number line?
Point A
Point A
Point B
Point C
Point D
E
●
0
1
3. Which point shows the location of on x 4
3
the number line?
12 sections
4

12
Point E Point F Point G Point H
x4
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
F
●
Point B
G
●
Point C
Point D
H
●
1
3
4. Which point shows the location of 4 on x 3
the number line?
12 sections
 9
12
Point E Point F Point G Point H
x3
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1 (continued)
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
P
●
R
●
Q
●
S
●
1
0
6 sections
2
3
5. Which point is located between and ?
8
8 sections 8
3
4
6. Which point is located between and ?
8
8 sections 8
Point P
Point P
Point R
Point S
W
●
X
●
Point Q
Y
●
Point R
1
7
and ?
2
12
12 sections
Point Y Point Z
Point W
Point X
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Point S
Z
●
1
0
7. Which point is located between
sections
1
0
Point Q
location
x6
6
12
x6

5
9
8. Which point is located between
and ?
6
12 sections 12
Point W
Point X
Point Y
Point Z
x2

10
12
x2
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
A
●
0
C
●
B
●
location
sections
1
0
6 sections
D
●
1
1
1. Which point shows the location of 4 on
4 sections
the number line?
3
2. Which point shows the location of on the
4 4 sections
number line?
Point A
Point A
Point B
Point C
Point D
E
●
0
1
3. Which point shows the location of 3 on x 2
the number line?
6 sections
2
6
Point E Point F Point G Point H
x2
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
F
●
Point B
G
●
Point C
H
●
Point D
1
2
4. Which point shows the location of on x 2
3
the number line?
6 sections
4

6
Point E Point F Point G Point H
x2
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2 (continued)
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
P
●
Q
●
R
●
Point R
Point S
Point P
Point Q
X
●
Y
●
Point R
Point S
Z
●
1
0
11
3
7. Which point is located between
and ?
4
16 sections 16
Point X
6 sections
5
4
6. Which point is located between and ?
9
9 sections 9
W
●
Point W
1
0
1
1
2
5. Which point is located between
and
?
9
9 sections 9
Point Q
sections
S
●
0
Point P
location
Point Y
Point Z
x4

12
16
x4
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
1
7
8. Which point is located between
and ?
2
16 sections 16
Point W
Point X
Point Y
Point Z
x8

8
16
x8
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
A
●
0
B
●
C
●
location
sections
1
0
6 sections
D
●
1
6
1. Which point shows the location of on the
10
number line?
10 sections
9
2. Which point shows the location of 10 on
10 sections
the number line?
Point A
Point A
Point B
Point C
Point D
E
●
0
1
3. Which point shows the location of on x 6
2
the number line?
12 sections
6

12
Point E Point F Point G Point H
x6
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©2011 All rights reserved.
Comments? [email protected]
F
●
Point B
G
●
Point C
Point D
H
●
1
2
4. Which point shows the location of 3 on x 4
the number line?
12 sections
 8
12
Point E Point F Point G Point H
x4
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3 (continued)
2
6
A fraction is a number that describes a part of a whole or set.
• The numerator is the part of the whole or set of things.
• The denominator is the total number of sections.
A number line shows the order of numbers based on their value.
Identify fractions on a number line.
Step #1: Read the question carefully.
Step #2: Verify that the number of sections on the number line from 0 to 1 match the denominator value.
a. If the number of sections is different than the denominator, create an equivalent fraction with a
matching denominator.
Step #3: Identify the location of a point on a number line using the numerator.
Step #4: Circle the correct answer.
P
●
R
●
Q
●
S
●
1
0
6 sections
1
2
5. Which point is located between and ?
8
8 sections 8
5
6
6. Which point is located between and ?
8
8 sections 8
Point P
Point P
Point R
Point S
W
●
X
●
Point Q
Point R
Y
●
x2
1
11
and 1 ?
12
1
12 sections
7. Which point is located between
x 12
Point W
12

12
x 12
Point Y
DataWORKS Educational Research
Point S
Z
●
0
Point X
sections
1
0
Point Q
location
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Comments? [email protected]
Point Z
1
1
8. Which point is located between
and ?
4
12 sections 6
Point W
Point X
Point Y
Point Z

2
12
x2
x3
3

12
x3
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Whiteboard Insert
Number Line from 0 to 1
Divided into 4 sections
0  40
1
4
2
4
3
4
1  44
0
1
4
1
2
3
4
1
Divided into 6 sections
0  60
1
6
2
6
3
6
4
6
5
6
1  66
0
1
6
1
3
1
2
2
3
5
6
1
Divided into 8 sections
0  80
1
8
2
8
3
8
4
8
5
8
6
8
7
8
1 88
0
1
8
1
4
3
8
1
2
5
8
3
4
7
8
1
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.
Blank Page
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 1.5 (2Q)
Identify and represent on a number line decimals, fractions, mixed numbers,
and positive and negative integers.
Lesson to be used by EDI-trained teachers only.