Project GRAD Atlanta Teaching Plans
Fifth Grade
Unit Overview
Unit 3: Fractional Understanding and Operations
(7 weeks)
Georgia Performance Standards
M5N1a
Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite).
M5N1b
M5N1c
Find multiples and factors,
Analyze and use divisibility rules.
M5N4a
Understand division of whole numbers can be represented as a fraction (a/b = a ÷ b).
M5N4b
M5N4c
Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is
the same as multiplying or dividing by one.
Find equivalent fractions and simplify fractions
M5N4d
Model the multiplication and division of common fractions.
M5N4e
Explore finding common denominators using concrete, pictorial, and computational models.
M5N4f
Use <, >, or = to compare fractions and justify the comparison.
M5N4g
Add and subtract common fractions and mixed numbers with unlike denominators.
M5N4h
Use fractions (proper and improper) and decimals interchangeably.
M5N4i
Estimate products and quotients.
Essential Questions
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How do we know if a number is prime or composite?
How do we determine by which factors a number is divisible?
How can we determine whether a number is odd or even?
How are factors and multiples defined?
How does knowing the divisibility rules help us solve problems?
How are fractions and decimals related?
What are some strategies we can use to compare fractions and decimals?
How are division, fractions, and mixed numbers related?
How can we find equivalent fractions?
In what ways can we model equivalent fractions?
How can we use equivalent fractions to simplify fractions?
What happens to the value of a fraction when the numerator and denominator are
multiplied or divided by the same number?
How are equivalent fractions related?
How do we use equivalent fractions to find common denominators?
How do we add and subtract fractions with unlike denominators?
What strategies can we use to compare fractions?
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How can we find equivalent fractions?
How are fractions and decimals related?
How can we use fractions to help us solve problems?
Which problem solving strategies can we use to solve this problem?
How can we model the multiplication and division of common
fractions?
What contexts require multiplication and/or division of fractions to
solve problems?
How can we find equivalent fractions and simplify fractions?
How can we model the multiplication and division of common
fractions?
How can we find common denominators using concrete,
pictorial, and computational models?
How can we add and subtract common fractions and mixed
numbers with unlike denominators?
How can we use fractions (proper and improper) and decimals
interchangeably?
Enduring Understandings
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A fraction is another representation for division.
Equivalent fractions represent the same value.
Whole numbers can be classified into subsets.
Divisibility rules can be used to find equivalent fractions quickly.
Fractions and decimals are different representations for the same amounts and
can be used interchangeably.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
1
State
Standards
M5N1
Objectives
Identify patterns in multiples
(10/24/11)
2
M5N1
Identify patterns in multiples
3
Week: 1
Problem Solving
Mental Math: MMMG, “Tack on Trailing Zeros,” pp. 81 - 82
Complete a simple frequency table or line plot
Compare and convert length, weight and time measurement units
Divide a decimal by a decimal
Unit
Day
Unit:
Solve problems involving multiplication and division of money amounts by whole
numbers
Focus Lessons
Resources
Materials
GPS Framework Unit 3: Fractional
Understanding and Operations, “The
Sieve of Eratosthenes,” pp. 12 – 17 (Day
1)
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GPS Framework Unit 3: Fractional
Understanding and Operations, “The
Sieve of Eratosthenes,” pp. 12 – 17 (Day
2)
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“Sieve of Eratosthenes” Recording
Sheet
Colored pencils, markers, highlighters
or crayons
“Exploring the Sieve of Eratosthenes”
Recording Sheet
Colored pencils, markers, highlighters
or crayons
3
M5N1
Investigate and apply divisibility rules
Math Expressions, “Going Further:
Divisibility Rules for 2, 5, and 10, p. 644
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Student Activity Workbook, p. 305
4
M5N1
Synthesize skills with multiples,
factors, place value, and numeric
expressions
GPS Framework Unit 3: Fractional
Understanding and Operations, “Number
Riddles,” pp. 18 – 22 (Day 1)
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“Number Riddles” Recording Sheet
“Sieve of Eratosthenes” Recording
Sheet (from Unit Day 1)
5
M5N1
Synthesize skills with multiples,
factors, place value, and numeric
expressions
GPS Framework Unit 3: Fractional
Understanding and Operations, “Number
Riddles,” pp. 18 – 22 (Day 2)
Materials from previous lesson
3
Variety of Instructional Tasks
Homework
Weekly Focus: Use patterns to solve a problem with “Multiple Patterns” from Math Expressions, p. 49.
Maintenance: Practice multiplication of decimals with “Number Search” from Math Expressions, “Multiply by Decimals” Activity
2 Multiply Two Decimals, pp. 564 – 567
Maintenance: Estimate and measure perimeter with Geometry and Fractions with Tangrams, pp. 56 – 59. (assorted titles)
Weekly Focus: Identify factor
pairs for whole numbers
through 100
Maintenance: Solve problems
with data from charts or graphs
Skill: Divide a decimal by a
decimal
Exploration: Create a class chart of common equivalent fractions with “Fraction Experts” from Constructing Ideas About
Fractions, Decimals, and Percents, pp. 2 – 7, to use throughout Unit 3.
Refer to Math Expressions’
“Homework/ Remembering” and
HM Georgia resources
Intervention:
Reflection with Closure/Journal
Is it possible to have a prime number greater than 100? How could I find larger prime numbers?
Assessments
Weekly Focus: Selected Quick Check and Math Expressions Unit 1 items
Skill Mastery: Divide a decimal by a decimal
5.35 ÷ 0.5 =
22.8 ÷ 0.24 =
14.79 ÷ 0.3 =
3.44 ÷ 1.6 =
Higher Level Questions
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Will divisibility rules apply beyond two- and three-digit numbers?
Which types of numbers have the most factors? Why?
Which relationships among factors make it easier to recall divisibility rules and find
common factors?
Vocabulary
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Divisibility
Multiple
Factor
Equivalent
1.8 ÷ 2.4 =
Literacy GPS
ELA5R3. Understands and acquires new
vocabulary and uses it correctly in
reading and writing.
ELA5W2d. Produces informational writing
that includes appropriate facts and
details.
ELA5LSV1l. Clarifies, illustrates, or
expands on a response when asked to
do so.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
Unit:
3
Week: 2
Problem Solving
Number Sense: Count forward and backward by halves and five tenths (Skill
Mastery)
Apply order of operations to solve for the unknown
Add and subtract fractions with like denominators
Division of whole numbers
Solve problems involving measurement units for mass and weight
Math Expressions, “Metric Measures of Mass” and “Customary Measures of
Weight,” pp. 501 - 502
Focus Lessons
Unit
Day
State
Standards
6
M5N4a, f
M5A1b
Recognize fractions as division
problems
7
M5N4a, f
M5A1b
Recognize fractions as division
problems
8
M5N4b, c, e
9
M5N4b, c, e
Resources
Objectives
Materials
GPS Framework Unit 3: Fractional
Understanding and Operations, “The
Quotient is Greater than 1,” pp. 23 – 26
(Day 1)
GPS Framework Unit 3: Fractional
Understanding and Operations, “The
Quotient is Greater than 1,” pp. 23 – 26
(Day 2)
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Develop an understanding of
equivalent fractions through area,
length, and set models
GPS Framework Unit 3: Fractional
Understanding and Operations, “Playing
with Fractions,” pp. 27 – 49 (Day 1)
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Develop an understanding of
equivalent fractions through area,
length, and set models
GPS Framework Unit 3: Fractional
Understanding and Operations, “Playing
with Fractions,” pp. 27 – 49 (Day 2)
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Materials from previous lesson
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10
M5N4b, c, e
Develop an understanding of
equivalent fractions through area,
length, and set models
GPS Framework Unit 3: Fractional
Understanding and Operations, “Playing
with Fractions,” pp. 27 – 49 (Day 3)
5
“The Quotient is Greater than One”
student recording sheet
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“Playing with Fractions, Circle
Fractions” student recording sheet
Fraction Cakes
“Playing with Fractions, Paper
Folding” student sheet
“Playing with Fractions, Fraction
Strips” student recording sheet
Paper strips
“Playing with Fractions, Fractions of a
Set” student recording sheet
Two color counters
Variety of Instructional Tasks
Homework
Weekly Focus: Solve problems involving fractional parts of wholes with “Given One Part, Show the Whole” and “Given Parts,
Show the Whole” from Geometry and Fractions with Geoboards, pp. 32 – 33 and 29.
Weekly Focus: Generate and
model simple equivalent
fractions
Maintenance: Construct and classify polygons with “Polygon Chart” from Geometry and Fractions with Tangrams, p. 21.
Maintenance: Investigate and apply divisibility rules to solve problems with “Divide and Conquer,” including the ‘Going Beyond’
activities, from Problem Parade, pp. 81 – 82.
Exploration: Apply function rules to solve problems with “Function Factory A-C” and “Forth and Back A-C” from Groundworks
Algebra Puzzles and Problems, pp. 80 – 83 and 88 – 91.
Maintenance: Solve word
problems involving adding and
subtracting fractions with like
denominators
Skill: Count forward and
backward by halves and fivetenths
Intervention:
Refer to Math Expressions’ “Homework/
Remembering” and HM Georgia
resources
Reflection with Closure/Journal
Do fractions have a finite or infinite amount of equivalents? How can I prove that?
Assessments
Weekly Focus: Selected Quick Check items
Skill Mastery: Fill in the missing numbers to complete the counting sequences
1.
1/2
1
1 1/2
_____
_____
3
2.
28
28 1/2 _____ _____
30
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3.
3.5
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2.5 _____
_____
1
4.
12
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_____ 10.5
_____ ____
5.
18
18.5
_____ _____
20
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_____
_____
9
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Higher Level Questions
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Is it necessary to simplify fractions?
When would finding equivalent fractions be helpful in real-world situations?
Prove that equivalent fractions only look different and do represent equal
quantities.
How do you apply the identity property of multiplication when finding equivalent
fractions?
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32
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22
Vocabulary
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Simplify
Common
denominator
Improper fraction
Proper fraction
Equivalent
Literacy GPS
ELA5R3. Understands and acquires new
vocabulary and uses it correctly in
reading and writing.
ELA5W2d. Produces informational writing
that includes appropriate facts and
details.
ELA5LSV1d. Uses language cues to
indicate different levels of certainty or
hypothesizing.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
11
State
Standards
M5N4b, c, e, f
Objectives
Explore the relationship between
equivalent fractions
Focus Lessons
Resources
GPS Framework Unit 3: Fractional
Understanding and Operations,
“Equivalent Fractions,” pp. 50 – 57 (Day 1)
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“Equivalent Fractions, ” student
recording sheet
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“Equivalent Fractions, ” student
recording sheet
M5N4b, c, e, f
M5N4a, b, c
Explore the relationship between
equivalent fractions
Write equations for equivalent
fractions using the product and
quotient of a fraction equivalent to one
Generate and explain equivalent
fractions
GPS Framework Unit 3: Fractional
Understanding and Operations,
“Equivalent Fractions,” pp. 50 – 57 (Day 2)
Materials from previous lesson
Math Expressions, “Discover Equivalent
Fractions,” pp. 415 - 423
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Student Activity Book, pp. 203 – 206
Fraction cakes or bars
Equivalent Fractions, master M31
Fraction Match-Up Cards, master M32
Scissors and rulers
Math Expressions, “Equivalent Fractions
and Multipliers,” pp. 425 - 431
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Student Activity Book, pp. 207 – 208
Tens and Hundreds Grids, master
M33
Timer or a clock with a second hand
Understand and apply the terms
equivalent and simplify
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Materials
Teacher Professional Learning
Day
(11/8/11)
13
Week: 3
Estimate and solve single- and multi-step problems
Use a variable to represent the unknown quantity
Apply the Logical Reasoning strategy to solve process problems
PSEIM, Set 7, pp. 25 - 28
Write equations for equivalent
fractions using the product and
quotient of a fraction equivalent to one
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3
Problem Solving
Mental Math: MMMG, “Tack on Trailing Zeros,” pp. 83 – 84
Find the Greatest Common Factor of two whole numbers
Multiply decimal amounts by decimal amounts
Find factor pairs and classify as prime or composite
Unit
Day
Unit:
M5N4a, b, c
Simplify and unsimplify fractions
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7
Variety of Instructional Tasks
Homework
Weekly Focus: Identify equivalent fractions with “Equivalent Fraction Rummy” from Math Games and Activities, Volume 2, pp.
037 and 98 – 104. (available in the Game Packet)
Weekly Focus: Find common
denominators
Maintenance: Construct and classify polygons with “Polygon Chart” from Geometry and Fractions with Tangrams, p. 21.
Maintenance: Simplify
fractions, including improper
fractions
Maintenance: Investigate and apply divisibility rules to solve problems with “Divide and Conquer,” including the ‘Going Beyond’
activities, Problem Parade, pp. 81 – 82.
Exploration: Apply function rules to solve problems with “Function Factory A-C” and “Forth and Back A-C” from Groundworks
Algebra Puzzles and Problems, pp. 80 – 83 and 88 – 91.
Skill: Find factor pairs and
classify numbers as prime or
composite
Refer to Math Expressions’
“Homework/ Remembering” and
HM Georgia resources
Intervention:
Reflection with Closure/Journal
How does understanding of factors and multiples help finding equivalent fractions?
Assessments
Weekly Focus: Selected Quick Check and Math Expressions Unit 3 items
Skill Mastery: List the factor pairs for the following numbers. Classify as prime or composite:
78
33
35
49
Higher Level Questions
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How do you apply the identity property of multiplication when finding equivalent
fractions?
What fraction concepts and estimation strategies can be used to compare
fractions?
Is finding the Least Common Denominator always the most efficient method to
compare fractions?
Why are common fractions used in some real-world situations and their decimal
equivalents are used in others?
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Vocabulary
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Simplify
Common
denominator
Greatest common factor
(GCF)
Equivalent
Literacy GPS
ELA5R3. Understands and acquires new
vocabulary and uses it correctly in
reading and writing.
ELA5W2d. Produces informational writing
that includes appropriate facts and
details.
ELA5LSV1c. Responds to questions with
appropriate information.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
Unit:
3
Week: 4
Problem Solving
Number of the Week: Include representations using fractional amounts and
order of operations
Simplify fractions
Use divisibility rules
Estimate and solve single- and multi-step problems
Use a variable to represent the unknown quantity
Apply the Make a Table/Look for a Pattern strategy to solve process problems
PSEIM, Set 13, pp. 49 - 52
Focus Lessons
Resources
Unit
Day
State
Standards
15
M5N4b, c, e, g, h
Solve problems requiring adding and
subtracting fractions and mixed
numbers with unlike denominators
GPS Framework Unit 3: Fractional
Understanding and Operations, “Gone
Hiking,” pp. 58 – 65 (Day 1)
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“Gone Hiking” student recording sheet
Fraction cakes or fraction bars
16
M5N4b, c, e, g, h
Solve problems requiring adding and
subtracting fractions and mixed
numbers with unlike denominators
GPS Framework Unit 3: Fractional
Understanding and Operations, “Gone
Hiking,” pp. 58 – 65 (Day 2)
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“Gone Hiking” student recording sheet
Fraction cakes or fraction bars
17
M5N1b, c
M5N4b, c, e, f
Find the common denominators for
two fractions
Connections 5, “Dandy Denominators,” pp.
52 - 54
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Fraction cakes or other fraction
manipulative in place of Fraction
Factory Pieces
18
M5N4a, f, h
Convert common fractions to
decimals
Math Expressions, “Find Decimal
Equivalents of Fractions,” pp. 747 - 752
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Student Activity Book, pp. 351 – 352
MathBoard materials
Number cubes
Stop watch or clock with a second
hand
Optional: Calculators
19
M5N4a, h
Find decimal equivalents for less
common fractions
Constructing Ideas About Fractions,
Decimals and Percents, “Repeaters,” pp.
68 – 73
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Objectives
Materials
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Base ten materials, including a
representation for thousandths
Calculators
Student sheet, p. 70
Variety of Instructional Tasks
Homework
Weekly Focus: Identify fractions and decimal equivalents with “Fraction and Decimal Match Up” from GPS Framework Unit 3:
Fractional Understanding and Operations, pp. 65 – 72.
Maintenance: Use four or five number generators to apply order of operations with “Snail Trail” from the MIM Professional
Development Manual, Powerful Counting Techniques
Maintenance: Compare fractions with “Fraction War” from All Hands on Deck,” p. 117, and identify equivalent fractions with
“Equivalent Fraction Rummy” from Math Games and Activities, Volume 2, pp. 037 and 98 – 104 (available in the Game Packet)
Exploration: Develop integer concepts with the Tug-of-War game from the Game Packet or the Chamber Game from the
Instructional Packet.
Weekly Focus: Identify
common fraction and decimal
equivalents
Maintenance: Compare and
order fractions and mixed
numbers
Skill: Use divisibility rules
Refer to Math Expressions’
“Homework/ Remembering” and
HM Georgia resources
Intervention:
Reflection with Closure/Journal
Is it necessary to have both decimal and fractional representations for the same quantity? Would it be possible to use only decimal or fractional numbers?
Assessments
Weekly Focus: Selected Quick Check items
Skill Mastery: Use divisibility rules to determine whether each number is divisible by 2, 3, 4, 5, 6, 9 or 10
4012 ______
678 _______
5742 ______
8820 ________
Higher Level Questions
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Is finding the Least Common Denominator always the most efficient method to
compare fractions?
Why are common fractions used in some real-world situations and their decimal
equivalents are used in others?
What estimation strategies and benchmark quantities can you apply to compare
fractional and decimal amounts?
What is an efficient strategy for using divisibility rules and knowledge of factors
and multiples to find common denominators and equivalent fractions?
Vocabulary
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Simplify
Common
denominator
Improper fraction
Proper fraction
Greatest common factor
(GCF)
Equivalent
318 _______
Literacy GPS
ELA5R3. Understands and acquires new
vocabulary and uses it correctly in
reading and writing.
ELA5LSV1d. Uses language cues to
indicate different levels of certainty or
hypothesizing.
ELA5LSV1l. Clarifies, illustrates, or
expands on a response when asked to
do so.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
20
State
Standards
Estimate and solve single- and multi-step problems
Use a variable to represent the unknown quantity
Apply the Draw a Picture strategy to solve process problems
PSEIM, Set 16, pp. 61 - 64
Focus Lessons
Resources
Materials
Apply common fraction and decimal
equivalents to order common
fractions and decimals
GPS Framework Unit 3: Fractional
Understanding and Operations, “Fraction
and Decimal Line-Up,” pp. 73 – 87
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Laundry cards from Framework task
Clothesline and pins (string and paper
clips or tape)
M5N4a, h
Represent and describe common
fraction, decimal and percent
equivalents
Investigations Name That Portion,
“Fraction and Percent Grids,” pp. 19 - 22
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Student Sheets 5 & 6, pp. 137 – 138
Grid paper to make 10 x 10 grids for
each student group
Map pencils or crayons
Optional: Equivalents Chart from
Week 4 and calculators
“Picture This!” student recording
sheet
Pattern blocks
Paper
Markers, crayons, or colored
pencils
“Picture This!” student recording
sheet
Pattern blocks
Paper
Markers, crayons, or colored
pencils
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22
M5N4c, g, h
Add and subtract fractions with unlike
denominators using pattern blocks to
represent the fractions
GPS Framework Unit 3: Fractional
Understanding and Operations, “Picture
This!,” pp. 88 – 91 (Day 1)
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GPS Framework Unit 3: Fractional
Understanding and Operations, “Picture
This!,” pp. 88 – 91 (Day 2)
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Instructional Sequence Knowing How Real
Fractions Behave, Lessons 9 and 10, pp.
19 – 22
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Convert mixed numbers to decimals
23
M5N4c, g, h
Add and subtract fractions with unlike
denominators using pattern blocks to
represent the fractions
Convert mixed numbers to decimals
24
Week: 5
M5N4c, e, f, h
(11/28/11)
21
Objectives
3
Problem Solving
Mental Math: MMMG, “Front-End Multiplying,” pp. 85 – 87
Measure and classify interior angles of polygons; determine degrees of rotation
around a point
Find equivalent fractions
Multiply and divide money amounts
Unit
Day
Unit:
M5N4e, g
M5A1a
Add and subtract fractions with unlike
denominators
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Fraction cakes
Chart paper
Variety of Instructional Tasks
Homework
Weekly Focus: Understand rules of adding and subtracting fractions with “Fraction Dos and Don’ts” from Constructing Ideas
About Fractions, Decimals, and Percents, pp. 50 – 56.
Maintenance: Use four or five number generators to apply order of operations with “Snail Trail” from the MIM Professional
Development Manual, Powerful Counting Techniques
Maintenance: Compare fractions with “Fraction War” from All Hands on Deck,” p. 117, and identify equivalent fractions with
“Equivalent Fraction Rummy” from Math Games and Activities, Volume 2, pp. 037 and 98 – 104. (available in the Game Packet)
Exploration: Develop integer concepts with the Tug-of-War game from the Game Packet or the Chamber Game from the
Instructional Packet.
Intervention:
Weekly Focus: Add and
subtract fractions and mixed
numbers
Maintenance: Model fraction
and decimal equivalents
Skill: Multiply and divide money
amounts
Refer to Math Expressions’
“Homework/ Remembering” and
HM Georgia resources
Reflection with Closure/Journal
Which factors do I use most often when finding common denominators and equivalent fractions? Why is that?
Assessments
Weekly Focus: Selected Quick Check and Math Expressions Unit 3 items
Skill Mastery: Multiply and divide money amounts
$6.27 x 33 =
$27.48 x 2 =
$39.00 ÷ 4 =
$7.50 ÷ 15 =
Higher Level Questions
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•
What estimation strategies and benchmark quantities can you apply to compare
fractional and decimal amounts?
What is an efficient strategy for using divisibility rules and knowledge of factors
and multiples to find common denominators and equivalent fractions?
Vocabulary
•
•
•
•
Improper fraction
Proper fraction
Mixed number
Factor
$42.66 ÷ 6 =
Literacy GPS
ELA5W2d. Produces informational writing
that includes appropriate facts and
details.
ELA5LSV1c. Responds to questions with
appropriate information.
ELA5LSV1l. Clarifies, illustrates, or
expands on a response when asked to
do so.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
State
Standards
Objectives
3
Week: 6
Problem Solving
Apply the perimeter formula using fractional amounts.
Refer to HM Georgia, pp. 422 - 423
Number Sense: Skip-count by 50 to/from any multiple to any number up to
10,000
Add and subtract fractions and mixed numbers
Determine the mean, median, mode, and range for a data set
Find equivalent fractions
Unit
Day
Unit:
Focus Lessons
Resources
Materials
25
M5N4e, g
M5A1a
Add and subtract fractions and mixed
numbers with unlike denominators
Math Expressions, “Solve with Unlike
Mixed Numbers,” 461 - 466
•
•
Student Activity Book, pp. 217 – 218
Play money
26
M5N4e, g
M5A1a
Add and subtract fractions and mixed
numbers with unlike denominators
Math Expressions, “Practice with Unlike
Mixed Numbers,” pp. 469 - 473
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•
•
•
•
Student Activity Book, pp. 219 – 220
Index cards numbered 1 – 20
Grid paper, master M17
Colored pencils and rulers
Optional: Fraction cakes or strips
27
M5N1
M5N4
M5D1a, b
M5D2
Model multiplication of a fraction by a
whole number
GPS Framework Unit 3: Fractional
Understanding and Operations, “Birthday
Cookout,” pp. 92 – 97
•
“Birthday Cookout” student recording
sheet
28
M5N4d, i
M5A1a
Explore how to take a fraction of a
fraction
Math Expressions, “Multiply a Fraction by
a Fraction,” pp. 725 – 731
•
•
•
MathBoard materials
Colored pencils
Index cards
Math Expressions, “When Dividing is Also
Multiplying,” pp. 755 – 758
•
•
•
•
Fraction cakes
Student Activity Book, pp. 353 – 354
Scissors
Optional: Counters and masking tape
Multiply any two fractions together
Use variables to represent the
unknown products
29
M5N4d, i
Recognize that dividing a whole
number (w) by a unit fraction gives the
same result as w x d
13
Variety of Instructional Tasks
Homework
Weekly Focus: Practice multiplying fractions with “Multiplying Fractions” from Instructional Sequence Knowing How Real
Fraction Behave, pp. 25 – 30 and 37 – 39.
Weekly Focus: Multiply
fractions
Maintenance: Measure angles and determine degrees of rotation with “Angle Measure” and “Pattern Block Sums of Angles”
from Geometry and Fractions with Pattern Blocks, pp. 38 – 39 and 14.
Maintenance: Solve word
problems involving fractions and
mixed numbers
Maintenance: Develop number sense and mental math strategies with “Trizo” from Math Games and Activities, Volume 2.
(available in the Game Packet)
Skill: Find equivalent fractions
Exploration: Extend patterns to solve problems with “Lattice Logic A-C” and “Construction Count A-C” from Groundworks
Algebra Puzzles and Problems, pp. 104 – 107 and 112 – 115.
Refer to Math Expressions’
“Homework/ Remembering” and
HM Georgia resources
Intervention:
Reflection with Closure/Journal
Use pictures, a number line or only words to explain the solution to 3/4 x 2/3. Why is that my preferred representation?
Assessments
Weekly Focus: Selected Quick Check and Math Expressions Unit 5 items
Skill Mastery: Find equivalent fractions
2/9 =
8/12 =
1/3 =
4/8 =
3/5 =
Higher Level Questions
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•
•
How can you effectively estimate whole number sums and differences when
adding and subtracting fractional amounts?
How can you immediately know when a fractional sum or difference is in its
simplest form?
How does multiplication of fractions relate to multiplication of decimals?
Even though you are multiplying, why aren’t the products always larger than the
factors?
Vocabulary
•
•
•
•
•
Common denominator
Greatest common factor
(GCF)
Sum
Difference
Product
Literacy GPS
ELA5W2d. Produces informational writing
that includes appropriate facts and
details.
ELA5LSV1d. Uses language cues to
indicate different levels of certainty or
hypothesizing.
ELA5LSV1l. Clarifies, illustrates, or
expands on a response when asked to
do so.
Project GRAD Atlanta Teaching Plans
Fifth Grade
Warm-Up/Quick Practice
30
State
Standards
M5N4d, i
M5A1a
Objectives
Divide a fraction by a fraction
3
Week: 7
Problem Solving
Mental Math: MMMG, “Front-End Multiplying,” pp. 88 - 90
Convert common fractions to decimals
Apply order of operations to solve for the unknown
Compare and order fractions
Unit
Day
Unit:
Add, subtract, or multiply fractions to solve problems
Math Expressions, “Word Problems with Mixed Operations,” p. 764
Focus Lessons
Resources
Materials
Math Expressions, “Division as Reverse
Multiplication,” pp. 775 - 782
•
•
•
Student Activity Book, pp. 359 – 360
Square or MathBoard materials
Number cards 1 -10
Use variables to represent unknown
quotients
31
M5N4b, d, i
Model multiplication and division of
fractions
GPS Framework Unit 3: Fractional
Understanding and Operations, “My
Multiplication and Division of Fractions
Book,” pp. 98 – 108 (Day 1)
•
•
Crayons, markers, and/or colored pencils
“My Multiplication and Division of Fractions
Book” Directions Sheet
32
M5N4b, d, i
Model multiplication and division of
fractions
GPS Framework Unit 3: Fractional
Understanding and Operations, “My
Multiplication and Division of Fractions
Book,” pp. 98 – 108 (Day 2)
•
•
Crayons, markers, and/or colored pencils
“My Multiplication and Division of Fractions
Book” Directions Sheet
33
M5N1
M5N4
Apply understanding of fractions to
solve problems
GPS Framework Unit 3: Fractional
Understanding and Operations, “Culminating
Task: You’re Invited to a Fabulous Fraction
Party,” pp. 98 – 108 (Day 1)
•
“You’re Invited to a Fabulous Fraction
Party” student sheet
“Shopping for Groceries” student sheet
“What’s in the Pantry?” student sheet
Recipes
“You’re Invited to a Fabulous Fraction
Party, Recipes for Eight” student recording
sheet
GPS Framework Unit 3: Fractional
Understanding and Operations, “Culminating
Task: You’re Invited to a Fabulous Fraction
Party,” pp. 98 – 108 (Day 2)
Materials from previous lesson
34
(12/16/11)
(12/19/11)
M5N1
M5N4
Apply understanding of fractions to
solve problems
Unit 3 Post Test
15
•
•
•
•
Variety of Instructional Tasks
Homework
Weekly Focus: Practice dividing fractions with “Dividing Fractions” from Instructional Sequence Knowing How Real Fraction
Behave, pp. 31 – 36 and 41 – 42.
Weekly Focus: Divide fractions
Maintenance: Measure angles and determine degrees of rotation with “Angle Measure” and “Pattern Block Sums of Angles”
from Geometry and Fractions with Pattern Blocks, pp. 38 – 39 and 14.
Maintenance: Students
continue work on Culminating
Task to present on Friday
Maintenance: Develop number sense and mental math strategies with “Trizo” from Math Games and Activities, Volume 2.
(available in the Game Packet)
Skill: Compare and order
fractions
Exploration: Extend patterns to solve problems with “Lattice Logic A-C” and “Construction Count A-C” from Groundworks
Algebra Puzzles and Problems, pp. 104 – 107 and 112 – 115.
Refer to Math Expressions’
“Homework/ Remembering” and
HM Georgia resources
Intervention:
Reflection with Closure/Journal
Which division situations will result in quotients that are larger than the dividend? Why?
Assessments
Weekly Focus: Selected Quick Check and Math Expressions Unit 5 items
Skill Mastery: Compare the following:
7/8 Ο 3/8
Order the following:
2/5, 1/5, 6/10
1/4 Ο 3/8
5/6, 4/6, 1/2
Higher Level Questions
•
•
•
•
•
How can you estimate the product when multiplying with fractional amounts?
How does division of fractions relate to division of decimals?
Create two different picture models to represent the solutions to fraction division
problems.
Even though you are dividing, why aren’t the quotients always smaller than the
dividends?
What strategies can you use to estimate the quotient when dividing by fractional
amounts?
2/3 Ο 4/6
Vocabulary
•
•
•
•
•
•
•
•
•
Simplify
Common
denominator
Improper fraction
Proper fraction
Divisibility
Multiple
Factor
Greatest common factor
(GCF)
Equivalent
Literacy GPS
ELA5W2d. Produces informational writing
that includes appropriate facts and
details.
ELA5LSV1d. Uses language cues to
indicate different levels of certainty or
hypothesizing.
ELA5LSV1l. Clarifies, illustrates, or
expands on a response when asked to
do so.