Transcript Comparing Fractions and Decimal Numbers

Learning Objective
Name _______________________
Today, we will compare fractions and decimal numbers.
CFU
What are we going to do today?
Activate (or provide) Prior Knowledge
A decimal number and a fraction both represent part of a whole.
• A fraction can be changed into a decimal number using long division.
Represent these fractions as decimals.
1.
0.75
4 3.000
-28
20
- 20
0
3
= 0.75
4
2.
3
5
0.6
5 3.000
-30
0
3
= 0.6
5
CFU
Students, you already know how to represent fractions as decimals.
Today, we will use our knowledge of these equal amounts to compare fractions to decimal numbers .
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6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Concept Development
To compare numbers means to determine1 whether a number is less than, greater than,
or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Comparison Symbols
• To compare decimal numbers, line up the decimal numbers by place value.
< less than
o Compare the digits2 from left to right.
> greater than
o The same digit in the same place value has equal value.
= equal to
o The greater digit in the same place value has a greater value.
1
2
figure out
numbers 0 to 9
Comparing Fractions and Decimal Numbers
0.78
>
3
4
0
0
7
7
8
5
Place Value
0.75
4 3.00
3
= 0.75
4
CFU
2
Which long division problem shows how to change the fraction
into a decimal number? How do you know?
5
A 2 5.00
B
5 2.00
2
changed into a decimal number is
5
2
A
< 0.45
5
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If the fraction
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0.40, which comparison is true? How do you know?
B
2
5
>
0.45
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
1.
3.
0.73 >
7
10
0.7
10 7.0
-70
0
2.
0.36 >
3
10
0
7
3
0
3
6
0
7
0
0
3
0
0.77 <
4
5
0.8
5 4.0
- 40
0
4.
0.18 <
1
5
0
7
7
0
1
8
0
8
0
0
2
0
CFU
(#1) How did I/you change the fraction to a decimal number?
(#3) How did I/you compare each digit?
(#4) How did I/you complete the number sentence?
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Comparison Symbols
<
>
=
less than
greater than
equal to
0.3
10 3.0
-30
0
0.2
5 1.0
-10
0
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
5.
7.
0.25 =
1
4
0.25
4 1.00
-08
20
- 20
0
6.
0.4
=
0
4
0
4
2
5
0
2
5
0
2
5
0.65 >
3
5
0
6
5
0
4
9
0
6
0
0
4
7
0.6
5 3.0
- 30
0
CFU
(#1) How did I/you change the fraction to a decimal number?
(#3) How did I/you compare each digit?
(#4) How did I/you complete the number sentence?
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8.
0.49 >
47
100
Comparison Symbols
<
>
=
less than
greater than
equal to
0.4
5 2.0
-2 0
0
0.47
100 47.00
- 4 00
7 00
- 70 0
0
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Relevance
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
1. Comparing fraction and decimal numbers will help you compare amounts in the real world.
Alfredo is comparing the price of bananas to apples. Apples are a half dollar each and bananas are $0.25
each.
$0.50 each
$0.25 each
Alfredo knows that the bananas are cheaper than the apples.
2. Comparing fractions and decimal numbers will help you do well on tests.
CFU
Does anyone else have another reason why it is relevant to compare fractions and decimal numbers? (pair-share) Why is it relevant to
compare fractions and decimal numbers? You may give one of my reasons or one of your own. Which reason is more relevant to you?
Why?
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6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
Skill Closure
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
1.
0.92 >
0.9
10 9.0
-90
0
9
10
0
9
2
0
9
0
2.
Constructed Response Closure
Christian and Naomi are comparing fractions and decimal numbers.
Christian claims that
4
4
10
3
5
0.56 <
is less than 0.35.
Naomi believes 10 is greater than 0.35.
Whom do you agree with? Explain your answer.
Comparison Symbols
<
>
=
0.6
5 3.0
-3 0
0
less than
greater than
equal to
0
5
6
0
6
0
Christian’s Work
Naomi's Work
4
= 0.4
10
4
= 0.4
10
0
0
4
0
4
3
5
0
3
5
Summary Closure
What did you learn today about comparing fractions and decimal numbers?
Day 1 _______________________________________________________
Day 2 _______________________________________________________
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6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Independent Practice
Name _______________________
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
Comparison Symbols
<
>
=
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
1.
4.
0.21 >
2
10
0.2
10 2.0
-20
0
2.
0.40 =
4
10
0.4
10 4.0
-40
0
3.
0.77 >
74
100
0
2
1
0
4
0
0
7
7
0
2
0
0
4
0
0
7
4
0.39 <
2
5
0.25 =
1
4
0.37 =
37
100
0
3
7
0
3
7
0.3 7
100 37.00
- 3 00
7 00
- 70 0
0
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5.
0
3
0
4
9
0.4
5 2.0
-2 0
0
6.
0
2
5
0
2
5
less than
greater than
equal to
0.7 4
100 74.00
- 7 00
40 0
- 40 0
0
0.25
4 1.00
-08
20
- 20
0
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1
Name _______________________
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
Comparison Symbols
<
>
=
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
1.
4.
0.6
10 6.0
-60
0
0.9
10 9.0
-90
0
0.67
>
6
10
0
6
7
0
9
0
2
4
0
6
0
0
9
0
2
2
0.36 <
2
5
0.81 =
81
100
0
8
1
0
8
1
0.8 1
100 81.00
- 8 00
10 0
- 10 0
0
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Comments? [email protected]
2.
5.
0.90 =
0.50 =
9
10
1
2
0.5
2 1.0
-10
0
3.
6.
0.24 >
0
5
0
3
0
5
0
4
22
100
6
less than
greater than
equal to
0.2 2
100 22.00
- 200
2 00
- 20 0
0
0.4
5 2.0
-20
0
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2
Name _______________________
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
Comparison Symbols
<
>
=
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
1.
4.
0.04 <
0
0
0
3
0.55 =
3
10
0.3
10 3.0
-30
0
2.
4
55
100
0
5
5
0
5
5
0.5 5
100 55.00
- 5 00
5 00
- 50 0
0
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©2012 All rights reserved.
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5.
0.70 =
7
10
0.7
10 7.0
-70
0
3.
0.29 >
28
100
0
7
0
0
2
9
0
7
0
0
2
8
0.80 =
4
5
0.61 >
3
5
0.8
5 4.0
-4 0
0
6.
0
8
0
6
0
8
0
6
1
less than
greater than
equal to
0.2 8
100 28.00
- 200
8 00
- 80 0
0
0.6
5 3.0
-30
0
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3
Name _______________________
To compare numbers means to determine whether a number is less than, greater than, or equal to another number.
• To compare fractions and decimal numbers, change the fraction to a decimal number.
Fraction to Decimal
Comparison Symbols
<
>
=
0.75
3
= 4 3.00
4
Compare fractions and decimal numbers.
Step #1: Change the fraction to a decimal number. Hint: Use long division.
Step #2: Line up the decimal numbers by place value.
Step #3: Compare each digit starting from the left.
a. If the digits have the same value, move to the place value to the right.
b. If the digits have different value, determine which digit has the greater value.
Step #4: Complete the number sentence. Hint: Write the correct comparison symbol.
1.
4.
0.06 >
1
20
0.0 5
20 1.00
- 1 00
0
2.
0.80 =
8
10
0.8
10 8.0
-80
0
3.
0.19 <
23
100
0
0
6
0
8
0
0
1
9
0
0
5
0
8
0
0
2
3
0.87 =
87
100
0
8
7
0
8
7
0.8 7
100 87.00
- 8 00
7 00
- 70 0
0
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©2012 All rights reserved.
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5.
0.35 =
7
20
0
3
5
0
3
5
0.3 5
20 7.00
-6 0
10 0
- 10 0
0
6.
0.56 >
0
5
0
5
less than
greater than
equal to
0.2 3
100 23.00
- 200
3 00
- 30 0
0
0.5 5
11
20 11.00
20
- 1 00
10 0
10 0
6
0
5
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
EDI – Cognitive, Teaching and English Learners Strategies
Learning Objective : Today, we will order fractions and mixed numbers on a number line.
Cognitive Strategies
Teaching Strategies
Elaboration
Demonstration
Targeted vocabulary: compare numbers, determine, digits
Language Strategies
Vocabulary Words
Academic
determine, digits
Content
compare numbers
Support
Multiple-Meaning
Synonym
Vocabulary
Strategy
Definition
compare numbers, determine, digits
Homophone
Internal Context Clue
Listen, Speak
Read
Similar Sounds
Tracked Reading
Decoding Rules
Write
Writing
Content Access Strategies
Comprehensible
Input
Cognates
Graphic Organizer
Contextual Clues
Contextualized
Definitions
Pictures
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.
Blank Page
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©2012 All rights reserved.
Comments? [email protected]
6th Grade Number Sense 1.1 (3Q)
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
Lesson to be used by EDI-trained teachers only.