Try It Out! Sample Pack | Math | Grade 5 | Lesson 5
Measuring Up to the GA Standards
The Try It Out! sample pack features:
• 1 full student lesson with complete Teacher Edition lesson • 1 full Table of Contents for your grade level • Correlation to your state standards
Developed to meet the rigor of the standards, Measuring Up employs support for using and applying critical thinking skills with direct standards instruction that elevate and engage student thinking.
Standards-based lessons feature introductions that set students up for success with:
aVocabulary in Action
aRelevant real-world connections
aClearly identified learning goals
aConnections to prior learning
Guided Instruction and Independent Learning strengthen learning with:
aDeep thinking prompts
aCollaborative learning
aSelf-evaluation
aDemonstration of problem-solving logic
aApplication of higher-order thinking
Flexible design meets the needs of whole- or small-group instruction.Use for:
aIntroducing standards
aReinforcement or standards review
aIntervention
aRemediation
aTest Preparation
Extend learning with online digital resources!Measuring Up Live 2.0 blends instructional print resources with online, dynamic assessment and practice. Meet the needs of all students for standards mastery with resources that pinpoint student needs with customized practice.
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CH
APT
ER
2 WORDS TO KNOW
decimal
expanded form
place value
Lesson 5READ, WRITE, AND COMPARE
DECIMALS 5.NBT.3, 5.NBT.3a, 5.NBT.3b
INTRODUCTIONReal-World ConnectionKelly has 0.613 pound of blueberries. Hannah has sixty-four hundredths
of a pound of blueberries. Who has a greater amount of blueberries?
Let’s see who has the greater amount of blueberries at the end of
the lesson after we practice the skills in the Guided Instruction and
Independent Practice!
What I Am Going to Learn● How to read and write decimal numbers
● How to compare decimal numbers
● How to write decimal numbers in expanded form
What I May Already Know 4.NF.6, 4.NF.7
● I know how to use decimal notation for fractions with a
denominator of 10 or 100.
● I know how to compare decimals to hundredths.
Vocabulary in Action● Decimals can be written in words.
● When you write a decimal in words you say “and” for the
decimal point.
● For example, 34.56 is thirty-four and fi fty-six hundredths.
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READ, WRITE, AND COMPARE DECIMALS Lesson 5
● Decimals can be written in expanded form.
● When you use expanded form, each digit is multiplied by its
place value.
● For example, 34.56 is 3 � 10 � 4 � 1 � 5 � 0.1 � 6 � 0.01
● Decimals written as numbers can be compared by place value.
● 34.56 < 34.6 because they each have 34, but 34.6 is greater
than 34.5 in the tenths place.
EXAMPLE
Write the number 213.675 in words.
Step One Write the whole number part. Use “and” for the
decimal point.
two hundred thirteen and…
Step Two For the decimal part, look at the place value of the
last digit.
The last digit is 5 and is in the thousandths place, so there are
six hundred seventy-fi ve thousandths.
Step Three Write the number.
213.675 is two hundred thirteen and six hundred seventy-fi ve
thousandths.
Ones Decimals
Hundreds Tens Ones . Tenths Hundredths Thousandths
2 1 3 . 6 7 5
TURN AND TALK
Why is it important to say “and”
for the decimal point?
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Lesson 5 READ, WRITE, AND COMPARE DECIMALS
EXAMPLE
Write 578.429 in expanded form.
Each digit in the number is multiplied by its place value, the same as
you would do with whole numbers. The decimal place values can be
fractions or decimals.
Step One Find the value of each digit.
Ones Decimals
Hundreds Tens Ones . Tenths Hundredths Thousandths
5 7 8 . 4 2 9
5 is 500 � 5 � 100
7 is 70 � 7 � 10
8 is 8 � 8 � 1
4 is 0.4 � 4 � 1 __
10
2 is 0.02 � 2 � 1 ___
100
9 is 0.009 � 9 � 1 _____
1,000
Step Two Combine the values.
5 � 100 � 7 � 10 � 8 � 1 � 4 � 1 __
10 � 2 �
1 ___
100 � 9 �
1 _____
1,000
We use decimal notation for amounts of money. Pennies are
hundredths of a dollar and dimes are tenths of a dollar.
THINK ABOUT IT
When you write a decimal number
in words, you are naming the
decimal part as a fraction:
Five hundred seventy-eight
and four hundred twenty-nine
thousandths.
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READ, WRITE, AND COMPARE DECIMALS Lesson 5
You can use place value to compare decimal numbers in the same way
you compare whole numbers.
EXAMPLE
Is 0.4 greater than, less than, or equal to 0.3?
Step One Write the numbers as fractions with the
same denominator.
0.4 � 4 __
10 , 0.3 �
3 __
10
Step Two Compare the numerators.
4 __
10 >
3 __
10 , so 0.4 > 0.3.
Is 0.21 greater than, less than, or equal to 0.4?
Step One Write the numbers as fractions with the
same denominator.
0.21 � 21
___
100 , 0.4 �
4 __
10 �
40 ___
100
Step Two Compare the numerators.
21 ___
100 <
40 ___
100 , so 0.21 < 0.4.
GUIDED INSTRUCTION 1. Write 86.03 in words.
Step One Write the whole number followed by “and.”
eighty-six and…
Step Two Use a place value chart to see the place value of the
last decimal digit.
Ones Decimals
Hundreds Tens Ones . Tenths Hundredths Thousandths
0 8 6 . 0 3 0
The last decimal digit is 3 and is in the hundredths place.
Step Three Write 86.03 in words
eighty-six and hundredths
HINT, HINT
When you say a decimal number,
do not say, “86 point 03”. Say, “86
and 3 hundredths”. This will help
you to think about the place value.
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Lesson 5 READ, WRITE, AND COMPARE DECIMALS
2. Write 27.304 in expanded form.
Step One Arrange the digits in a place value chart.
Ones Decimals
Hundreds Tens Ones . Tenths Hundredths Thousandths
2 7 . 3 0 4
Step Two Write the value of each digit, using decimal fractions.
2 is 20 � 2 � 10
7 is 7 � 7 � 1
3 is 0.3 � 3 � 1 __
10
4 is 0.004 � 4 � 1 _____
1,000
Step Three Write an equation showing the sum.
27.304 � 2 � � 7 � 1 � 3 � � 4 � 1 _____
1,000
3. Compare 0.056 and 0.59.
Step One Write the decimals in fraction form with the same
denominator.
0.056 � 56 _____
1,000
0.59 � 59
___
100 �
590 _____
1,000
Step Two Compare the fractions.
56 _____
1,000 <
590 _____
1,000
So, 0.056 0.59
4. Select THREE expressions that are equal to 113.082.
Ⓐ 100 � 10 � 3 � 0.8 � 0.02
Ⓑ 100 � 10 � 3 � 0.08 � 0.002
Ⓒ 100 � 10 � 3 � 8 ___
10 �
2 ____
100
Ⓓ 100 � 10 � 3 � 8 ___
100 �
2 _____
1,000
Ⓔ 1 � 100 � 1 � 10 � 3 � 1 � 8 � 1 ___
100 � 2 �
1 _____
1,000
Ⓕ 1 � 100,000 � 1 � 10,000 � 3 � 1,000 � 8 � 10 � 2 � 1
TIPS AND TRICKS
Make sure you evaluate each
answer. Do not stop after you fi nd
the fi rst correct answer.
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READ, WRITE, AND COMPARE DECIMALS Lesson 5
How Am I Doing?
What questions do you have?
Imagine what the price might be of something you enjoy. Write the
price, and then write it again in expanded form.
Each place value in a decimal gets 10 times smaller. A measurement
of 6.765 inches is very precise, but probably not necessary. Can you
think of a situation where this much accuracy would be important?
Color in the traffi c signal
that shows how you are
doing with the skill.
I am stuck.
I almost have it.
I understand
the skill.
TURN AND TALK
Pretend you are going to teach
younger students about decimals.
Think about how you would teach
someone to compare decimals
to thousandths. Then, working
with a partner, create a short
demonstration. You can use grids,
pictures, place-value blocks,
technology, or any other method
other than place-value charts.
Then present your demonstration
to the class.
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Lesson 5 READ, WRITE, AND COMPARE DECIMALS
INDEPENDENT PRACTICEAnswer the questions.
1. What is 51.017 in word form?
Ⓐ fi fty-one thousand and seventeen
Ⓑ fi fty-one and seventeen hundredths
Ⓒ fi fty-one and seventeen tenths
Ⓓ fi fty-one and seventeen thousandths
2. Compare the decimals. Write the correct symbol in each box.
0.04 0.14 1.5 1.15 3.01 3.010
3. What is 195.438 in expanded form using decimals?
Write your answer in the box.
4. Write an expression for 105.067 in expanded form by multiplying
each digit by a decimal fraction.
Write your answer in the box.
HINT, HINT
When reading a number in word
form, write out each number next
to the words.
HINT, HINT
When there is a 0 in a number you
are writing in expanded form, be
sure to pay close attention to the
place values of the other digits.
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READ, WRITE, AND COMPARE DECIMALS Lesson 5
5. Which statement is true?
Ⓐ 621.071 � 621.711
Ⓑ 621.071 � 621.711
Ⓒ 621.071 � 621.711
6. Which statement is true?
Ⓐ 0.910 � 0.91
Ⓑ 45.234 � 45.134
Ⓒ 6.71 � 6.071
Ⓓ 79.012 � 79.012
7. Part AGeorge’s backpack weighs 15.207 pounds. Stephen’s backpack
weighs 15.216 pounds. Whose backpack weighs more?
Write your answer in the box.
Part BExplain how you found your answer. Write an expression using
�, �, or � to record the results of your comparison.
TIPS AND TRICKS
Compare the digits one at a time,
using place value and starting at
the left.
WORK SPACE
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Lesson 5 READ, WRITE, AND COMPARE DECIMALS
WORK SPACE
8. Felix wrote an expression for the expanded form of 307.043
by multiplying each digit by a decimal fraction. His work is
shown below.
307.043 � 3 � 100 � 7 � 1 � 4 � 1 ___ 10
� 3 � 1 ____
100
Is Felix correct? If not, explain the error he made and write the
correct expression.
8.
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READ, WRITE, AND COMPARE DECIMALS Lesson 5
EXIT TICKET
Now that you have mastered reading, writing, and comparing decimal numbers, let’s
solve the problem in the Real-World Connection.
Kelly has 0.613 pounds of blueberries. Hannah has sixty-fourth hundredths of a pound
of blueberries. Who has the greater amount of blueberries?
5.NBT.3, 5.NBT.3a, 5.NBT.3b
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[ ii ]
Letter to Students vi
Letter to Parents and Families vii
What You’ll See in Measuring Up to the Georgia Standards of Excellence viii
5.NBT.1, 5.NBT.2
5.NBT.5
5.NBT.6
5.OA.1, 5.OA.2
Chapter 1 OPERATIONS WITH WHOLE NUMBERS
1. Understand Place-Value Patterns 1
2. Multiply Whole Numbers 10
3. Divide Whole Numbers 18
4. Write and Interpret Numerical Expressions 29
Chapter 1 Practice Test 38
5.NBT.3, 5.NBT.3a-b
5.NBT.4
Chapter 2 DECIMALS
5. Read, Write, and Compare Decimals 42
6. Round Decimals 52
GSE
GSE
LESSON
LESSON
Introduction
CONTENTS
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[ iii ]
5.NF.1
5.NF.2
5.NF.3
5.NF.4, 5.NF.4a
5.NF.4, 5.NF.4b
5.NF.5, 5.NF.5a-b
5.NF.7, 5.NF.7a
5.NF.7, 5.NF.7b
5.NF.6, 5.NF.7, 5.NF.7c
5.MD.2
Chapter 3 OPERATIONS WITH FRACTIONS
10. Add and Subtract Fractions 94
11. Solve Word Problems Involving Fraction 104Addition and Subtraction
12. Divide Whole Numbers with Fraction Quotients 114
13. Multiply Whole Numbers by Fractions 124
14. Multiply Fractions by Fractions 134
15. Compare Factors and Products 144
16. Divide Unit Fractions by Whole Numbers 153
17. Divide Whole Numbers by Unit Fractions 162
18. Solve Word Problems Involving Fraction 171Multiplication and Division
19. Make and Use Line Plots 181
Chapter 3 Practice Test 190
GSE LESSON
5.NBT.7
5.NBT.7
5.NBT.7
7. Add and Subtract Decimals 60
8. Multiply Decimals 70
9. Divide Decimals 80
Chapter 2 Practice Test 90
GSE LESSON
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[ iv ]
5.MD.1
5.MD.3, 5.MD.3a-b,
5.MD.4
5.MD.5, 5.MD.5a-b
5.MD.5, 5.MD.5c
Chapter 4 MEASUREMENT
20. Convert Measurement Units 195
21. Understand Volume 204
22. Find Volume of Rectangular Prisms 214
23. Find Volume of Solids 223
Chapter 4 Practice Test 233
GSE LESSON
5.G.3, 5.G.4
5.G.1
5.G.2
5.OA.3
Chapter 5 GEOMETRY
24. Classify Two-Dimensional Figures 239
25. Understand the Coordinate Plane 248
26. Graph Points to Represent Problems 257
27. Use Pattern Rules 267
Chapter 5 Practice Test 276
GSE LESSON
CONTENTS
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[ v ]
Acknowledgments 282
Correlation to the Georgia Standards of Excellence 283
Glossary 287
Copy Masters 290
References
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[ 283 ][ 283 ]Correlation to the Georgia Standards of Excellence | masteryeducation.com
Correlation to the Georgia Standards of Excellence
This worktext is customized to the TGeorgia Standards of Excellence for Mathematics. Most lessons focus on one content standard for in-depth review. Mathematical Practices are interwoven throughout each lesson to connect practices to content at point-of-use and promote depth of understanding.
Georgia Standards of Excellence Lessons
Operations and Algebraic Thinking 5.OA
Write and interpret numerical expressions.
MGSE5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions
with these symbols.
4
MGSE5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply
by 2” as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without
having to calculate the indicated sum or product.
4
Analyze patterns and relationships.
MGSE5.OA.3 Generate two numerical patterns using a given rule. Identify apparent relationships
between corresponding terms. Form ordered pairs consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a coordinate plane.
27
Number and Operations in Base Ten 5.NBT
Understand the place value system.
MGSE5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as
it represents in the place to its right and 1 __ 10 of what it represents in the place to its left.
1
MGSE5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by
powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied
or divided by a power of 10. Use whole-number exponents to denote powers of 10.
1
MGSE5.NBT.3 Read, write, and compare decimals to thousandths. 5
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded
form, e.g., the expanded form of 347.392 is written as 3 × 100 + 4 × 10 + 7 × 1 + 3 × ( 1 __ 10 ) +
9 × ( 1 ___ 100 ) + 2 × (
1 _____ 1,000 ).
5
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =,
and < symbols to record the results of comparisons.
5
MGSE5.NBT.4 Use place value understanding to round decimals to the hundredths place. 6
Perform operations with multi-digit whole numbers and with decimals to hundredths.
MGSE5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm (or other
strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.
2
CORRELATIONS
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CORRELATIONS
Georgia Standards of Excellence Lessons
MGSE5.NBT.6 Fluently divide up to 4-digit dividends and 2-digit divisors by using at least one of the
following methods: strategies based on place value, the properties of operations, and/or the relationship
between multiplication and division. Illustrate and explain the calculation by using equations or concrete
models.(e.g., rectangular arrays, area models).
3
MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship between
addition and subtraction; relate the strategy to a written method and explain the reasoning used.
7, 8, 9
Number and Operations-Fractions 5.NF
Use equivalent fractions as a strategy to add and subtract fractions.
MGSE5.NF.1 Add and subtract fractions with unlike denominators by fi nding a common denominator
and equivalent fractions to produce like denominators.
10
MGSE5.NF.2 Solve word problems involving addition and subtraction of fractions, including cases of
unlike denominators (e.g., by using visual fraction models or equations to represent the problem).
Use benchmark fractions and number sense of fractions to estimate mentally and assess the
reasonableness of answers. For example, recognize an incorrect result 2 __ 5 + 1 __ 2 = 3 __ 7 , by observing that 3 __ 7 < 1 __ 2 .
11
Apply and extend previous understandings of multiplication and division to multiply and divide
fractions.
MGSE5.NF.3 Interpret a fraction as division of the numerator by the denominator ( a __ b = a ÷ b). Solve
contextual problems involving division of whole numbers leading to answers in the form of fractions or
mixed numbers by using visual fraction models or equations to represent the problem.
12
MGSE5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole
number by a fraction.
13, 14
a. Interpret the product ( a __ b ) × q as a × q ÷ b (partition the quantity q into b equal parts and then
multiply by a). Interpret the product ( a __ b ) × q as (a x q) ÷ b (multiply a times the quantity q and then
partition the product into b equal parts).
13
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and show that the area is the same as would be found
by multiplying the side lengths.
14
MGSE5.NF.5 Interpret multiplication as scaling (resizing), by: 15
a. Compare the size of a product to the size of one factor on the basis of the size of the other factor,
without performing the indicated multiplication. Example: 4 x 10 is twice as large as 2 x 10.15
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater
than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar
case); explain why multiplying a given number by a fraction less than 1 results in a product smaller
than the given number; and relate the principle of fraction equivalence a __ b =
(n × a) ______ (n × b) to the eff ect of
multiplying a __ b by 1.
15
MGSE5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by
using visual fraction models or equations to represent the problem.
18
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Georgia Standards of Excellence Lessons
MGSE5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole
numbers and whole numbers by unit fractions.
16, 17, 18
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
For example, create a story context for ( 1 __ 3 ) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that ( 1 __ 3 ) ÷ 4 = 1 __ 12 because ( 1 __ 12 ) × 4 = 1 __ 3 .
16
b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ ( 1 __ 5 ), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ ( 1 __ 5 ) = 20 because 20 × ( 1 __ 5 ) = 4.
17
c. Solve real world problems involving division of unit fractions by non-zero whole numbers and
division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to
represent the problem. For example, how much chocolate will each person get if 3 people share 1 __ 2 lb of chocolate equally? How many 1 __ 3 -cup servings are in 2 cups of raisins?
18
Measurement and Data 5.MD
Convert like measurement units within a given measurement system.
MGSE5.MD.1 Convert among diff erent-sized standard measurement units within a given measurement
system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world
problems.
20
Represent and interpret data.
MGSE5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit ( 1 __ 2 ,
1 __ 4 ,
1 __ 8 ). Use
operations on fractions for this grade to solve problems involving information presented in line plots.
For example, given diff erent measurements of liquid in identical beakers, fi nd the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
19
Geometric measurement: understand concepts of volume and relate volume to multiplication and to
addition.
MGSE5.MD.3 Recognize volume as an attribute of solid fi gures and understand concepts of
volume measurement.
21
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and
can be used to measure volume.
21
b. A solid fi gure which can be packed without gaps or overlaps using n unit cubes is said to have a
volume of n cubic units.
21
MGSE5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft, and
improvised units.
21
MGSE5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and
mathematical problems involving volume.
22, 23
a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with
unit cubes and show that the volume is the same as would be found by multiplying the edge
lengths, equivalently by multiplying the height by the area of the base. Represent whole-number
products of three factors as volumes (e.g., to represent the associative property of multiplication).
22
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CORRELATIONS
Georgia Standards of Excellence Lessons
b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to fi nd volumes of right
rectangular prisms with whole-number edge lengths in the context of solving real world and
mathematical problems.
22
c. Recognize volume as additive. Find volumes of solid fi gures composed of two non-overlapping right
rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to
solve real world problems.
23
Geometry 5.G
Graph points on the coordinate plane to solve real-world and mathematical problems.
MGSE5.G.1 Use a pair of perpendicular number lines, called axes, to defi ne a coordinate system, with
the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point
in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the
fi rst number indicates how far to travel from the origin in the direction of one axis, and the second
number indicates how far to travel in the direction of the second axis, with the convention that the
names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and
y-coordinate).
25
MGSE5.G.2 Represent real world and mathematical problems by graphing points in the fi rst quadrant of
the coordinate plane, and interpret coordinate values of points in the context of the situation.
26
Classify two-dimensional fi gures into categories based on their properties.
MGSE5.G.3 Understand that attributes belonging to a category of two-dimensional fi gures also belong
to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
24
MGSE5.G.4 Classify two-dimensional fi gures in a hierarchy based on properties (polygons, triangles,
and quadrilaterals).
24
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[ 42 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el E
Copyi
ng
is p
rohib
ited
.
CHAPTER 2
WO
RD
S T
O K
NO
W
deci
mal
expan
ded form
pla
ce v
alue
Less
on 5
RE
AD
, W
RIT
E, A
ND
CO
MPA
RE
DEC
IMA
LS
5.N
BT
.3, 5.N
BT
.3a,
5.N
BT
.3b
INTR
OD
UCT
ION
Rea
l-W
orld
Con
nec
tion
Kelly
has
0.6
13 p
ound
of
blu
eb
err
ies.
Han
nah
has
six
ty-f
our
hund
red
ths
of
a p
ound
of
blu
eb
err
ies.
Who
has
a g
reat
er
amo
unt
of
blu
eb
err
ies?
Let’
s se
e w
ho
has
the g
reat
er
amo
unt
of
blu
eb
err
ies
at t
he e
nd
of
the le
sso
n a
fter
we p
ract
ice t
he s
kills
in t
he G
uid
ed Inst
ruct
ion a
nd
Indep
enden
t Pra
ctic
e!
Wh
at I
Am
Goi
ng
to L
earn
● H
ow
to
read
and
wri
te d
eci
mal
num
bers
● H
ow
to
co
mp
are d
eci
mal
num
bers
● H
ow
to
wri
te d
eci
mal
num
bers
in e
xpan
ded
fo
rm
Wh
at I
May
Alr
eady
Kn
ow 4.
NF.
6, 4
.NF.
7
● I kn
ow
ho
w t
o u
se d
eci
mal
no
tati
on f
or
frac
tio
ns
wit
h a
deno
min
ato
r o
f 10 o
r 100.
● I kn
ow
ho
w t
o c
om
par
e d
eci
mal
s to
hund
red
ths.
Voc
abu
lary
in A
ctio
n●
Dec
imal
s ca
n b
e w
ritt
en in
wo
rds.
● W
hen y
ou w
rite
a d
eci
mal
in w
ord
s yo
u s
ay “
and
” fo
r th
e
deci
mal
po
int.
● Fo
r exa
mp
le, 34.5
6 is
thi
rty-
four
and
fi fty
-six
hun
dre
dth
s.
[ 43 ]
Chap
ter
2 | D
ecim
als
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
RE
AD
, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
Less
on 5
● D
eci
mal
s ca
n b
e w
ritt
en in
expan
ded
form
.
● W
hen y
ou u
se e
xpan
ded
fo
rm, eac
h d
igit
is m
ult
iplie
d b
y it
s
pla
ce v
alue.
● Fo
r ex
amp
le, 34.5
6 is
3 �
10 �
4 �
1 �
5 �
0.1
� 6
� 0
.01
● D
eci
mal
s w
ritt
en a
s num
bers
can
be c
om
par
ed
by
pla
ce v
alue.
● 34.5
6 <
34.6
beca
use
they
eac
h h
ave 3
4, b
ut
34.6
is g
reat
er
than
34.5
in t
he t
enth
s p
lace
.
EX
AM
PLE
Wri
te t
he n
um
ber
213.6
75 in
wo
rds.
Step
One
Wri
te t
he w
ho
le n
um
ber
par
t. U
se “
and
” fo
r th
e
deci
mal
po
int.
two
hund
red
thir
teen a
nd
…
Step
Tw
o Fo
r th
e d
eci
mal
par
t, lo
ok
at t
he p
lace
val
ue o
f th
e
last
dig
it.
The la
st d
igit
is 5
and
is in
the t
ho
usa
nd
ths
pla
ce, so
there
are
six
hund
red
seve
nty
-fi v
e t
ho
usa
nd
ths.
Step
Thre
e W
rite
the n
um
ber.
213.6
75 is
tw
o h
und
red
thir
teen a
nd
six
hund
red
seve
nty
-fi v
e
tho
usa
nd
ths. O
ne
sD
ecim
als
Hund
red
s Tens
Ones
.Tenth
sH
und
red
ths
Tho
usa
nd
ths
21
3.
67
5
TU
RN
AN
D T
ALK
Why
is it
imp
ort
ant
to s
ay “
and
”
for
the d
eci
mal
po
int?
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[ 45 ]
Chap
ter
2 | D
ecim
als
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
RE
AD
, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
Less
on 5
Yo
u c
an u
se p
lace
val
ue t
o c
om
par
e d
eci
mal
num
bers
in t
he s
ame w
ay
you c
om
par
e w
ho
le n
um
bers
.
EX
AM
PLE
Is 0
.4 g
reat
er
than
, le
ss t
han
, o
r eq
ual
to
0.3
?
Step
One
Wri
te t
he n
um
bers
as
frac
tio
ns
wit
h t
he
sam
e d
eno
min
ato
r.
0.4
�
4
__
10 ,
0.3
�
3
__
10
Step
Tw
o C
om
par
e t
he n
um
era
tors
.
4
__
10 >
3
__
10 ,
so
0.4
> 0
.3.
Is 0
.21 g
reat
er
than
, le
ss t
han
, o
r eq
ual
to
0.4
?
Step
One
Wri
te t
he n
um
bers
as
frac
tio
ns
wit
h t
he
sam
e d
eno
min
ato
r.
0.2
1 �
21
__
_
100 ,
0.4
�
4
__
10 �
40
__
_
100
Step
Tw
o C
om
par
e t
he n
um
era
tors
.
21
__
_
100 <
40
__
_
100 ,
so
0.2
1 <
0.4
.
GU
IDED
INST
RUCT
ION
1.
Wri
te 8
6.0
3 in w
ord
s.
Step
One
Wri
te t
he w
ho
le n
um
ber
follo
wed
by
“and
.”
eig
hty
-six
and
…
Step
Tw
o U
se a
pla
ce v
alue c
har
t to
see t
he p
lace
val
ue o
f th
e
last
deci
mal
dig
it.
On
es
Decim
als
Hund
red
s Tens
Ones
.Tenth
sH
und
red
ths
Tho
usa
nd
ths
08
6.
03
0
The la
st d
eci
mal
dig
it is
3 a
nd
is in
the h
und
red
ths
pla
ce.
Step
Thre
e W
rite
86.0
3 in
wo
rds
eig
hty
-six
and
th
ree
hund
red
ths
HIN
T, H
INT
Wh
en y
ou s
ay a
deci
mal
nu
mb
er,
do
no
t sa
y, “
86 p
oin
t 03”.
Say
, “8
6
and
3 h
un
dre
dth
s”. T
his
will
help
you t
o t
hin
k ab
ou
t th
e p
lace
val
ue.
[ 44 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el E
Copyi
ng
is p
rohib
ited
.
Less
on 5
R
EA
D, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
EX
AM
PLE
Wri
te 5
78.4
29 in
exp
and
ed
fo
rm.
Eac
h d
igit
in t
he n
um
ber
is m
ult
iplie
d b
y it
s p
lace
val
ue, th
e s
ame a
s
you w
ould
do
wit
h w
ho
le n
um
bers
. T
he d
eci
mal
pla
ce v
alues
can b
e
frac
tio
ns
or
deci
mal
s.
Step
One
Find
the v
alue o
f eac
h d
igit
.
On
es
Decim
als
Hund
red
s Tens
Ones
.Tenth
sH
und
red
ths
Tho
usa
nd
ths
57
8.
42
9
5 is
500 �
5 �
100
7 is
70 �
7 �
10
8 is
8 �
8 �
1
4 is
0.4
� 4
�
1
__
10
2 is
0.0
2 �
2 �
1
__
_
100
9 is
0.0
09 �
9 �
1
__
__
_
1,0
00
Step
Tw
o C
om
bin
e t
he v
alues.
5 �
100 �
7 �
10 �
8 �
1 �
4 �
1
__
10 �
2 �
1
__
_
100 �
9 �
1
__
__
_
1,0
00
We u
se d
eci
mal
no
tati
on f
or
amo
unts
of
mo
ney
. Pe
nnie
s ar
e
hund
red
ths
of
a d
olla
r an
d d
imes
are t
enth
s o
f a
do
llar.
TH
INK
AB
OU
T IT
Wh
en y
ou w
rite
a d
eci
mal
nu
mb
er
in w
ord
s, y
ou a
re n
amin
g th
e
deci
mal
par
t as
a f
ract
ion:
Five
hu
nd
red
seve
nty
-eig
ht
and
fo
ur
hu
nd
red
tw
enty
-nin
e
tho
usa
nd
ths.
9781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 289781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 28 1/31/2019 5:20:00 PM1/31/2019 5:20:00 PM
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[ 47 ]
Chap
ter
2 | D
ecim
als
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
RE
AD
, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
Less
on 5
How
Am
I D
oin
g?
What
ques
tions
do y
ou h
ave?
Imag
ine
what
the
pri
ce m
ight
be
of so
met
hin
g yo
u e
njo
y. W
rite
the
pri
ce, an
d t
hen
wri
te it
agai
n in e
xpan
ded
form
.
Eac
h p
lace
val
ue
in a
dec
imal
get
s 10 t
imes
sm
alle
r. A
mea
sure
men
t
of 6.7
65 inch
es is
very
pre
cise
, but
pro
bab
ly n
ot
nec
essa
ry. C
an y
ou
thin
k of a
situ
atio
n w
her
e th
is m
uch
acc
ura
cy w
ould
be
import
ant?
Colo
r in
the
traffi
c
sign
al
that
show
s how
you a
re
doin
g w
ith t
he
skill
.
I am
stu
ck.
I al
most
ha v
e it
.
I under
stan
d
the
skill
.
TU
RN
AN
D T
ALK
Pre
ten
d y
ou a
re g
oin
g to
teac
h
you
nge
r st
ud
ents
ab
ou
t d
eci
mal
s.
Th
ink
abo
ut
ho
w y
ou w
ou
ld t
eac
h
som
eo
ne t
o c
om
par
e d
eci
mal
s
to t
ho
usa
nd
ths.
Th
en
, w
ork
ing
wit
h a
par
tner,
cre
ate a
sh
ort
dem
on
stra
tio
n. Y
ou c
an u
se g
rid
s,
pic
ture
s, p
lace
-val
ue b
lock
s,
tech
no
logy
, o
r an
y o
ther
meth
od
oth
er
than
pla
ce-v
alu
e c
har
ts.
Th
en p
rese
nt
you
r d
em
on
stra
tio
n
to t
he c
lass
.
[ 46 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el E
Copyi
ng
is p
rohib
ited
.
Less
on 5
R
EA
D, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
2.
Wri
te 2
7.3
04 in e
xpan
ded
form
.
Step
One
Arr
ange
the d
igit
s in
a p
lace
val
ue c
har
t.
On
es
Decim
als
Hund
red
s Tens
Ones
.Tenth
sH
und
red
ths
Tho
usa
nd
ths
27
.3
04
Step
Tw
o W
rite
the v
alue o
f eac
h d
igit
, usi
ng
deci
mal
fra
ctio
ns.
2 is
20 �
2 �
10
7 is
7 �
7 �
1
3 is
0.3
� 3
�
1
__
10
4 is
0.0
04 �
4 �
1
__
__
_
1,0
00
Step
Thre
e W
rite
an e
quat
ion s
ho
win
g th
e s
um
.
27.3
04 �
2 �
10
� 7
� 1
� 3
�
1 __
10
�
4 �
1
_____
1,0
00
3.
Com
par
e 0.0
56 a
nd 0
.59.
Step
One
Wri
te t
he d
eci
mal
s in
fra
ctio
n f
orm
wit
h t
he s
ame
deno
min
ato
r.
0.0
56 �
56
__
__
_
1,0
00
0.5
9 �
59
__
_
100 �
590
__
__
_
1,0
00
Step
Tw
o C
om
par
e t
he fra
ctio
ns.
56
__
__
_
1,0
00 <
590
__
__
_
1,0
00
So, 0.0
56
< 0
.59
4.
Sele
ct T
HR
EE e
xpre
ssio
ns
that
are
equal
to 1
13.0
82.
Ⓐ 10
0 �
10 �
3 �
0.8
� 0
.02
Ⓑ 10
0 �
10 �
3 �
0.0
8 �
0.0
02
Ⓒ 10
0 �
10 �
3 �
8
___
10 �
2
____
100
Ⓓ 10
0 �
10 �
3 �
8
__
_
100 �
2
__
__
_
1,0
00
Ⓔ
1 �
100 �
1 �
10 �
3 �
1 �
8 �
1
__
_
100 �
2 �
1
__
__
_
1,0
00
Ⓕ
1 �
100,0
00 �
1 �
10,0
00 �
3 �
1,0
00 �
8 �
10 �
2 �
1
TIP
S A
ND
TR
ICK
S
Mak
e s
ure
yo
u e
valu
ate e
ach
answ
er.
Do
no
t st
op
aft
er
you fi n
d
the fi r
st c
orr
ect
an
swer.
Ⓑ
Ⓓ
Ⓔ
9781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 299781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 29 1/31/2019 5:20:03 PM1/31/2019 5:20:03 PM
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[ 49 ]
Chap
ter
2 | D
ecim
als
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
RE
AD
, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
Less
on 5
5.
Whic
h s
tate
men
t is
tru
e?
Ⓐ
621.0
71 �
621.7
11
Ⓑ
621.0
71 �
621.7
11
Ⓒ
621.0
71 �
621.7
11
6.
Whic
h s
tate
men
t is
tru
e?
Ⓐ
0.9
10 �
0.9
1
Ⓑ
45.2
34 �
45.1
34
Ⓒ
6.7
1 �
6.0
71
Ⓓ
79.0
12 �
79.0
12
7.
Par
t A
Geo
rge’
s bac
kpac
k w
eigh
s 15.2
07 p
ounds.
Ste
phen
’s b
ackp
ack
wei
ghs
15.2
16 p
ounds.
Whose
bac
kpac
k w
eigh
s m
ore
?
W
rite
your
answ
er in t
he
box.
Ste
phen
’s
Par
t B
Expla
in h
ow
you found y
our
answ
er. W
rite
an e
xpre
ssio
n u
sing
�, �
, or
� t
o r
ecord
the
resu
lts
of yo
ur
com
par
ison.
Sam
ple
answ
er: B
oth
wei
ghts
sta
rt w
ith th
e sa
me
who
le n
umbe
r, so
I ch
ange
d th
e de
cim
als
tofra
ctio
ns to
com
pare
them
. 15.
207
� 1
5 20
7 __
__
1,00
0 an
d
15.2
16 �
15
216
____
1,00
0 . 1
5 20
7 __
__
1,00
0 �
15
216
____
1,00
0 ,
so 1
5.20
7 �
15.
216.
Ⓒ
TIP
S A
ND
TR
ICK
S
Co
mp
are t
he d
igit
s o
ne a
t a
tim
e,
usi
ng
pla
ce v
alu
e a
nd
sta
rtin
g at
the le
ft.
Ⓑ
WO
RK
SPA
CE
[ 48 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el E
Copyi
ng
is p
rohib
ited
.
Less
on 5
R
EA
D, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
IND
EPEN
DEN
T PR
ACTI
CEA
nsw
er
the q
uest
ions.
1.
What
is
51.0
17 in w
ord
form
?
Ⓐ
fi fty
-one t
ho
usa
nd
and
seve
nte
en
Ⓑ
fi fty
-one a
nd
seve
nte
en h
und
red
ths
Ⓒ
fi fty
-one a
nd
seve
nte
en t
enth
s
Ⓓ
fi fty
-one a
nd
seve
nte
en t
ho
usa
nd
ths
2.
Com
par
e th
e dec
imal
s. W
rite
the
corr
ect
sym
bol in
eac
h b
ox.
0.0
4
� 0.1
4
1.5
�
1.1
5
3.0
1
� 3.0
10
3.
What
is
195.4
38 in e
xpan
ded
form
usi
ng
dec
imal
s?
W
rite
your
answ
er in t
he
box.
100
� 9
0 �
5 �
0.4
� 0
.03
� 0
.008
4.
Wri
te a
n e
xpre
ssio
n for
105.0
67 in e
xpan
ded
form
by
mult
iply
ing
each
dig
it b
y a
dec
imal
fra
ctio
n.
W
rite
your
answ
er in t
he
box.
1
� 1
00 �
5 �
1 �
6 �
1 ___
100 �
7 �
1
____
_ 1,
000
HIN
T, H
INT
Wh
en r
ead
ing
a n
um
ber
in w
ord
form
, w
rite
ou
t eac
h n
um
ber
next
to t
he w
ord
s.
Ⓓ
HIN
T, H
INT
Wh
en t
here
is a
0 in
a n
um
ber
you
are w
riti
ng
in e
xp
and
ed
fo
rm, b
e
sure
to
pay
clo
se a
ttenti
on t
o t
he
pla
ce v
alu
es
of th
e o
ther
dig
its.
9781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 309781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 30 1/31/2019 5:20:06 PM1/31/2019 5:20:06 PM
[ 31 ]Chapter 2 | Decimals | masteryeducation.comCopying is prohibited.
[ 51 ]
Chap
ter
2 | D
ecim
als
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
RE
AD
, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
Less
on 5
EXIT
TIC
KET
Now
that
you h
ave
mas
tere
d r
eadin
g, w
riti
ng,
and c
om
par
ing
dec
imal
num
ber
s, let
’s
solv
e th
e pro
ble
m in t
he
Rea
l-W
orl
d C
onnec
tion.
Kel
ly h
as 0
.613 p
ounds
of blu
eber
ries
. H
annah
has
six
ty-f
ourt
h h
undre
dth
s of a
pound
of blu
eber
ries
. W
ho h
as t
he
grea
ter
amount
of blu
eber
ries
?
Han
nah
has
a gr
eate
r am
ount
of b
lueb
errie
s th
an K
elly.
0.61
3 �
61
3 __
___
1,00
0 si
xty-
four
hun
dred
ths
� 64
__
_ 10
0 �
640
____
_ 1,
000
613
____
_ 1,
000 �
64
0 __
___
1,00
0 S
o, H
anna
h ha
s a
grea
ter a
mou
nt o
f blu
eber
ries
than
Kel
ly.
5.N
BT.
3, 5
.NB
T.3a
, 5.N
BT.
3b
[ 50 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el E
Copyi
ng
is p
rohib
ited
.
Less
on 5
R
EA
D, W
RIT
E, A
ND
CO
MPA
RE D
EC
IMA
LS
WO
RK
SPA
CE
8.
Felix
wro
te a
n e
xpre
ssio
n for
the
expan
ded
form
of 307.0
43
by
mult
iply
ing
each
dig
it b
y a
dec
imal
fra
ctio
n. H
is w
ork
is
show
n b
elow
.
307.0
43 �
3 �
100 �
7 �
1 �
4 �
1
___
10 �
3 �
1
____
100
Is
Fel
ix c
orr
ect?
If not,
expla
in t
he
erro
r he
mad
e an
d w
rite
the
corr
ect
expre
ssio
n.
Sam
ple
answ
er: F
elix
is n
ot c
orre
ct. 3
� 1
00 �
7 �
1 �
4 �
1 __
10
� 3
�
1 __
_ 10
0 �
300
� 7
� 0
.4 �
0.0
3 �
307.
43, n
ot 3
07.0
43. F
elix
did
not
acc
ount
for t
he
plac
e va
lue
of th
e ze
ro a
fter t
he d
ecim
al. T
he c
orre
ct
expr
essi
on is
3 �
100
� 7
� 1
� 4
�
1 __
_ 10
0 �
3 �
1
____
1,00
0 .
8.
9781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 319781609797409_MUSS_GA_Math_Gr5_ATE_Ch2.indd 31 1/31/2019 5:20:07 PM1/31/2019 5:20:07 PM
[ 32 ] masteryeducation.com | Mathematics | Level E Copying is prohibited.
Lesson 5 READ, WRITE, AND COMPARE DECIMALS
TEACHER NOTESREAL-WORLD GOALS FOR STUDENTS
• Students will understand how to read decimal numbers.
• Students will understand how to write decimal numbers in words and expanded form.
• Students will compare decimal numbers.
TIPS FOR THE STRUGGLING LEARNER
• Students may struggle with decimals with a zero digit: 0.304, 0.340, 0.034. In all three cases,
students need to say the number and the place value of the last digit. Although a number
such as 0.340 is 34 hundredths, if the zero is shown, it is a signifi cant digit. It is better for
students to say three hundred forty thousandths than to worry about whether the zero is
a placeholder or not.
• If students struggle with reading the values of decimals, provide them with place value
charts. Students can write the decimals in the chart to help them understand the value of
each number.
• To reinforce place value, encourage struggling learners to say the value of the decimal
rather than using a phrase similar to “point 34.”
TIPS FOR THE ENGLISH LANGUAGE LEARNER
• English learners may confuse the words for whole-number place values, such as thousand,
and their decimal equivalents, such as thousandth. Focus students’ attention on the letters
th and point out that they indicate a decimal place value in words such as tenth, hundredth,
and thousandth.
ACTIVITIES FOR THE ADVANCED LEARNER
• Given a set of decimals that are close in value, have students compare which decimal is
greater and by how much. For example, 4.1 is 1 thousandth more than 4.099.
• Have students name and write decimal numbers to further place values, up to millionths.
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