Download - Try It Out! Measuring Up to the OH Standards
Try It Out! Sample Pack | Math | Grade 6 | Lesson 14
Measuring Up to the OH 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 featureintroductions 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 IndependentLearning 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 ofwhole- 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 andpractice. 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
rational number
inequality
Lesson 14 COMPARE AND ORDER RATIONAL
NUMBERS 6.NS.C.7, 6.NS.C.7a, 6.NS.C.7b
INTRODUCTIONReal-World ConnectionFive friends play in a golf tournament. The table shows each player’s score.
In golf, the player with the lowest score wins the game. Ana wants to know
who won the tou rnament. Let’s practice the skills in the Guided Instruction
and Independent Practice and see who won the tournament at the end of
the lesson!
Golf Tournament
Player Score
Ana �4
Marcos �2
Lily �8
Tom �6
Luciente �16
What I Am Going to Learn● How to order rational numbers
● How to compare rational numbers by using an inequality
What I May Already Know 2.NBT.A.4, 4.NF.A.2, 5.NBT.A.3b
● I know how to compare whole numbers.
● I know how to compare fractions.
● I know how to compare decimals to thousandths.
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COMPARE AND ORDER RATIONAL NUMBERS Lesson 14
Vocabulary in Action● A rational number is any number that can be written as a ratio of
two integers.
● Examples of rational numbers: 0.25, 3 __
4 , �5, 32.
● Rational numbers can be compared using a number line. As you
move left, the value of the numbers decreases. As you move right,
the value of the numbers increases.
● You can write an inequality to compare rational numbers, using
� or �.
EXAMPLE
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
Compare the following numbers:
2 and 5
2 is to the left of 5 on the number line: 2 � 5.
Say: 2 is less than 5.
1 and �4
1 is to the right of �4 on the number line: 1 � �4.
Say: 1 is greater than negative 4.
�3 and �6
�3 is to the right of �6 on the number line: �3 � �6
Say: Negative 3 is greater than negative 6.
You can use a number line to order rational numbers.
EXAMPLE
Order the numbers 4, �2, and 1 from least to greatest.
Graph the numbers on a number line:
–5 –4 –3 –2 –1 0 1 2 3 4 5
Read the numbers from left to right, which is least to greatest: �2, 1, 4.
THINK ABOUT IT
Any positive number will be greater
than any negative number.
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Lesson 14 COMPARE AND ORDER RATIONAL NUMBERS
GUIDED INSTRUCTION 1. Use the number line to compare each pair of numbers. Write > or <.
�3 and 2 0 and �1 �5 and �4
�3 and 2
�3 is to the left of 2.
�3 � 2
0 and �1
0 is to the right of �1.
0 �1
�5 and �4
�5 is to the left of �4.
�5 �4
2. Order each set of numbers from least to greatest.
9, 0, �2, 3
�2 is less than 0 and any positive numbers.
In order: –2, 0, 3, 9
8, �6, �1, 10
�6 is farther to the left than �1.
In order: , �1, 8, 10
7, �4, 4, 11
�4 is less than the positive numbers.
In order: , 4, 7,
3. Which rational numbers are less than �3? Select the two correct answers.
Ⓐ 1 __ 4 Ⓑ �8
Ⓒ 5 Ⓓ �1
Ⓔ �4.5 Ⓕ 0
HINT, HINT
You can use � or � for the same
comparison: 6 � 4, or 4 � 6.
–5 –4 –3 –2 –1 0 1 2 3 4 5
–5 –4 –3 –2 –1 0 1 2 3 4 5
–5 –4 –3 –2 –1 0 1 2 3 4 5
SKETCH IT
Draw a number line in the space
above. Remember, numbers
decrease moving left.
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COMPARE AND ORDER RATIONAL NUMBERS Lesson 14
How Am I Doing?
What questions do you have?
Think of two rational numbers. Compare the numbers using � or �.
What is an example where you would compare numbers?
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
Work with a partner. You are
asked to fi nd a number that is
greater than �3 and less than
�3. Explain where you would
fi nd a number that matches the
description. Is �10 a correct
response? Explain your answer.
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Lesson 14 COMPARE AND ORDER RATIONAL NUMBERS
INDEPENDENT PRACTICEAnswer the questions.
1. The table shows the point balances for several players in a math game.
Write an inequality to show the relationship between the least amount
of points and the greatest amount of points.
Write your answer in the box.
2. The two thermometers show diff erent temperatures. Use the numbers
in the box to compare the temperatures.
The numbers cannot be used more than once. Write each number in
the appropriate box.
5 10 15 20 �5 �10 �15 �20
°C � °C
3. Greta writes a set of rational numbers in order from least to greatest.
Which could be Greta’s set of numbers?
Ⓐ 0, �16 1 __
4 , 27, 59
Ⓑ �18, �5.5, 5, 17
Ⓒ �9, 0, �13, 34
Ⓓ 7, 10
___ 2 , �24, �73
4. In golf, a lower score is a better score. A golfer says her score is worse
than �5 but better than 5. What might her score have been?
Math Maze Points
Person Points
Derek 35.11
Marie �22.75
Xin 17.09
Will �6.06
°C
50
40
30
20
10
0
�10
�30
�20
°C
50
40
30
20
10
0
�10
�30
�20
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COMPARE AND ORDER RATIONAL NUMBERS Lesson 14
5. The table shows the elevations, relative to sea level, of several places.
Draw a line to show each place in order from highest to lowest, 1–5.
City Elevation
City Elevation (ft)
Boston, MA 141
New Orleans, LA �8
Washington, D.C. 1
Death Valley, CA �282
Denver, CO 5,183
Boston, MA 1
New Orleans, LA 2
Washington, D.C. 3
Death Valley, CA 4
Denver, CO 5
6. Circle the number that correctly completes the statement.
�9 � �11
�15
10
8
0
� 5
7. Val says it was 0ºF on Monday and �12ºF on Wednesday. She says
Tuesday was warmer than Wednesday but colder than Monday. What
might the temperature have been on Tuesday?
WORK SPACE
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Lesson 14 COMPARE AND ORDER RATIONAL NUMBERS
8. Part AWrite an inequality to compare �7 and 0. Write another inequality to
compare 33 and 0.
Part BWrite a real-world situation in which these three numbers
(�7, 33, and 0) are ordered from least to greatest.
Explain how you ordered the numbers.
8. WORK SPACE
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COMPARE AND ORDER RATIONAL NUMBERS Lesson 14
EXIT TICKET
Now that you have mastered comparing rational numbers, let’s solve the problem in the
Real-World Connection.
Five friends play in a golf tournament. The table shows each player’s score. In golf, the player
with the lowest score wins the game. Who won the tournament? Explain how you know.
Golf Tournament
Player Score
Ana �4
Marcos �2
Lily �8
Tom �6
Luciente �16
6.NS.C.7, 6.NS.C.7a, 6.NS.C.7b
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ANNOTATED
TEACHER EDITION
[ ii ]
6.RP.A.1
6.RP.A.2
6.RP.A.3, 6.RP.A.3a
6.RP.A.3, 6.RP.A.3b
6.RP.A.3, 6.RP.A.3c
6.RP.A.3, 6.RP.A.3d
Introduction
Letter to Students vi
Letter to Parents and Families vi
What You’ll See in Measuring Up to the Ohio Learning Standards vii
CONTENTS
Chapter 1 RATIOS AND RATES
1. Understand Ratios 1
2. Understand Unit Rates 11
3. Make and Use Tables of Equivalent Ratios 20
4. Solve Unit Rate Problems 31
5. Find Percent as a Rate 39
6. Convert Measurement Units 48
Chapter 1 Practice Test 57
OLS LESSON
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[ iii ]
6.NS.A.1
6.NS.B.2
6.NS.B.3
6.NS.B.3
6.NS.B.4
6.NS.C.5, 6.NS.C.6,
6.NS.C.6a
6.NS.C.6, 6.NS.C.6b-c
6.NS.C.7, 6.NS.C.7a-b
6.NS.C.7, 6.NS.C.7c-d
6.NS.C.8
Chapter 2 NUMBER AND OPERATIONS
OLS LESSON
7. Divide Fractions 62
8. Divide Whole Numbers 71
9. Add and Subtract Decimals 80
10. Multiply and Divide Decimals 89
11. Find Common Factors and Common Multiples 98
12. Understand Positive and Negative Numbers 107
13. Represent Positive and Negative Numbers 114
14. Compare and Order Rational Numbers 124
15. Understand Absolute Value 132
16. Solve Problems in the Coordinate Plane 140
Chapter 2 Practice Test 149
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[ iv ]
CONTENTS
6.G.A.1
6.G.A.2
6.G.A.3
6.G.A.4
6.G.A.4
Chapter 4 GEOMETRY
24. Find Area of Polygons 219
25. Find Volume of Right Rectangular Prisms 230
26. Drawing Polygons in the Coordinate Plane 239
27. Represent Solids Using Nets 250
28. Find Surface Area 261
Chapter 4 Practice Test 274
OLS LESSON
6.EE.A.1
6.EE.A.2, 6.EE.A.2a-b,
6.EE.B.6
6.EE.A.2, 6.EE.A.2c
6.EE.A.3, 6.EE.A.4
6.EE.B.5, 6.EE.B.7
6.EE.B.5, 6.EE.B.8
6.EE.C.9
Chapter 3 EXPRESSIONS AND EQUATIONS
17. Write and Evaluate Expressions with Exponents 153
18. Read and Write Expressions with Variables 162
19. Evaluate Expressions with Variables 170
20. Write and Identify Equivalent Expressions 178
21. Write and Solve Equations 187
22. Write and Solve Inequalities 196
23. Model Real-World Relationships 205
Chapter 3 Practice Test 215
OLS LESSON
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[ v ]
References
Acknowledgments 337
Correlation to the Ohio Learning Standards 338
Glossary 342
Copy Masters 347
6.SP.A.3
6.SP.A.1, 6.SP.A.2
6.SP.B.4
6.SP.B.4
6.SP.B.5, 6.SP.B.5a-d
Chapter 5 STATISTICS
29. Calculating Measures of Center and Measures of Spread 280
30. Understanding Statistical Data 290
31. Make Dot Plots and Histograms 300
32. Make Box Plots 311
33. Summarize Numerical Data Sets 320
Chapter 5 Practice Test 331
OLS LESSON
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CORRELATIONSCorrelation to the Ohio Learning Standards
This worktext is customized to the Ohio Learning Standards 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.
Ohio Learning Standards Lessons
Ratios and Proportional Relationships 6.RP
A. Understand ratio concepts and use ratio reasoning to solve problems.
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
1
2. Understand the concept of a unit rate a __ b associated with a ratio a:b with b ≠ 0, and use rate language in the
context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of fl our to 4 cups of sugar, so there is 3 __ 4 cup of fl our for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
2
3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or equations.
3, 4, 5, 6
a. Make tables of equivalent ratios relating quantities with whole-number measurements, fi nd missing values in
the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
3
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
4
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30
___ 100 times the quantity); solve
problems involving fi nding the whole, given a part and the percent.
5
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities.
6
The Number System 6.NS
A. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions,
e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for ( 2 __ 3 ) ÷ ( 3 __ 4 ) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that ( 2 __ 3 ) ÷ ( 3 __ 4 ) = 8 __ 9 because 3 __ 4 of 8 __ 9 is 2 __ 3 . (In general, ( a __ b ) ÷ ( c __ d ) = ad __ bc .) How much chocolate will each person get if
3 people share 1 __ 2 lb of chocolate equally? How many 3 __ 4 -cup servings are in 2 __ 3 of a cup of yogurt? How wide is a
rectangular strip of land with length 3 __ 4 mi and area 1 __ 2 square mi?
7
B. Compute fl uently with multi-digit numbers and fi nd common factors and multiples.
2. Fluently divide multi-digit numbers using the standard algorithm. 8
3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 9, 10
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Ohio Learning Standards Lessons
4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common
multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of
two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no
common factor. For example, express 36 + 8 as 4(9 + 2).
11
C. Apply and extend previous understandings of numbers to the system of rational numbers.
5. Understand that positive and negative numbers are used together to describe quantities having opposite
directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/
negative electric charge); use positive and negative numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation.
12
6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes
familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
12, 13
a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line;
recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its
own opposite.
12
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane;
recognize that when two ordered pairs diff er only by signs, the locations of the points are related by
refl ections across one or both axes.
13
c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; fi nd and
position pairs of integers and other rational numbers on a coordinate plane.
13
7. Understand ordering and absolute value of rational numbers. 14, 15
a. Interpret statements of inequality as statements about the relative position of two numbers on a number
line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
14
b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 °C > –7 °C to express the fact that –3 °C is warmer than –7 °C.
14
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret
absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
15
d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
15
8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
Include use of coordinates and absolute value to fi nd distances between points with the same fi rst coordinate or
the same second coordinate.
16
Expressions and Equations 6.EE
A. Apply and extend previous understandings of arithmetic to algebraic expressions.
1. Write and evaluate numerical expressions involving whole-number exponents. 17
2. Write, read, and evaluate expressions in which letters stand for numbers. 18, 19
a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
18
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CORRELATIONSOhio Learning Standards Lessons
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coeffi cient); view
one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
18
c. Evaluate expressions at specifi c values of their variables. Include expressions that arise from formulas used in
real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in
the conventional order when there are no parentheses to specify a particular order (Order of Operations).
For example, use the formulas V = s3 and A = 6 s2 to fi nd the volume and surface area of a cube with sides of length s = 1 __ 2 .
19
3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
20
4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless
of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
20
B. Reason about and solve one-variable equations and inequalities.
5. Understand solving an equation or inequality as a process of answering a question: which values from a specifi ed
set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a
specifi ed set makes an equation or inequality true.
21, 22
6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem;
understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number
in a specifi ed set.
18
7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q
for cases in which p, q and x are all nonnegative rational numbers.
21
8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or
mathematical problem. Recognize that inequalities of the form x > c or x < c have infi nitely many solutions;
represent solutions of such inequalities on number line diagrams.
22
C. Represent and analyze quantitative relationships between dependent and independent variables.
9. Use variables to represent two quantities in a real-world problem that change in relationship to one another;
write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity,
thought of as the independent variable. Analyze the relationship between the dependent and independent
variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
23
Geometry 6.G
A. Solve real-world and mathematical problems involving area, surface area, and volume.
1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles
or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and
mathematical problems.
24
2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the
appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying
the edge lengths of the prism. Apply the formulas V = lwh and V = b h to fi nd volumes of right rectangular prisms
with fractional edge lengths in the context of solving real-world and mathematical problems.
25
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Ohio Learning Standards Lessons
3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to fi nd the length of a
side joining points with the same fi rst coordinate or the same second coordinate. Apply these techniques in the
context of solving real-world and mathematical problems.
26
4. Represent three-dimensional fi gures using nets made up of rectangles and triangles, and use the nets to fi nd
the surface area of these fi gures. Apply these techniques in the context of solving real-world and mathematical
problems.
27, 28
Statistics and Probability 6.SP
A. Develop understanding of statistical variability.
1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts
for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
30
2. Understand that a set of data collected to answer a statistical question has a distribution which can be described
by its center, spread, and overall shape.
30
3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number,
while a measure of variation describes how its values vary with a single number.
29
B. Summarize and describe distributions.
4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 31, 32
5. Summarize numerical data sets in relation to their context, such as by: 33
a. Reporting the number of observations. 33
b. Describing the nature of the attribute under investigation, including how it was measured and its units
of measurement.
33
c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean
absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern
with reference to the context in which the data were gathered.
33
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context
in which the data were gathered.
33
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mas
tery
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tion.c
om
| M
athem
atic
s | Lev
el F
Copyi
ng
is p
rohib
ited
.
CHAPTER 2
WO
RD
S T
O K
NO
W
rati
onal
num
ber
inequal
ity
Less
on 1
4 C
OM
PAR
E A
ND
OR
DE
R R
AT
ION
AL
NU
MB
ER
S 6
.NS.
C.7
, 6
.NS.
C.7
a, 6
.NS.
C.7
b
INTR
OD
UCT
ION
Rea
l-W
orld
Con
nec
tion
Five
fri
end
s p
lay
in a
go
lf t
ourn
ament.
The t
able
sho
ws
eac
h p
laye
r’s
sco
re.
In g
olf,
the p
laye
r w
ith t
he lo
west
sco
re w
ins
the g
ame. A
na
wan
ts t
o k
no
w
who
wo
n t
he t
ou rn
ament.
Let’
s p
ract
ice t
he s
kills
in t
he G
uid
ed Inst
ruct
ion
and
Indep
enden
t Pra
ctic
e an
d s
ee w
ho
wo
n t
he t
ourn
ament
at t
he e
nd
of
the le
sso
n!
Golf
Tourn
amen
t
Pla
yer
Score
Ana
�4
Mar
cos
�2
Lily
�8
To
m�
6
Luci
ente
�1
6
Wh
at I
Am
Goi
ng
to L
earn
● H
ow
to
ord
er
rati
onal
num
bers
● H
ow
to
co
mp
are r
atio
nal
num
bers
by
usi
ng
an in
eq
ual
ity
Wh
at I
May
Alr
eady
Kn
ow
2.N
BT.
A.4
, 4
.NF.
A.2
, 5
.NB
T.A
.3b
● I k
now
ho
w t
o c
om
par
e w
hole
num
ber
s.
● I k
now
ho
w t
o c
om
par
e fr
actio
ns.
● I k
now
ho
w t
o c
om
par
e dec
imal
s to
tho
usan
dth
s.
[ 125 ]
Chap
ter
2 | N
um
ber
and O
per
atio
ns
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
CO
MPA
RE A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
Less
on 1
4
Voc
abu
lary
in A
ctio
n●
A r
atio
nal
num
ber
is a
ny
num
ber
that
can
be w
ritt
en a
s a
rati
o o
f
two
inte
gers
.
● Exa
mp
les
of
rati
onal
num
bers
: 0
.25
, 3
__
4 ,
�5
, 3
2.
● R
atio
nal
num
bers
can
be c
om
par
ed
usi
ng
a num
ber
line. A
s yo
u
mo
ve le
ft, th
e v
alue o
f th
e n
um
bers
decr
eas
es.
As
you m
ove
rig
ht,
the v
alue o
f th
e n
um
bers
incr
eas
es.
● Y
ou c
an w
rite
an in
equal
ity
to c
om
par
e r
atio
nal
num
bers
, usi
ng
� o
r �
.
EX
AM
PLE
–8–7
–6–5
–4–3
–2–1
01
23
45
67
8
Co
mp
are t
he f
ollo
win
g num
bers
:
2 a
nd 5
2 is
to
the le
ft o
f 5
on t
he n
um
ber
line: 2
� 5
.
Say:
2 is
less
tha
n 5.
1 a
nd �
4
1 is
to
the r
ight
of
�4
on t
he n
um
ber
line: 1
� �
4.
Say:
1 is
gre
ater
tha
n ne
gative
4.
�3 a
nd �
6
�3
is t
o t
he r
ight
of
�6
on t
he n
um
ber
line: �
3 �
�6
Say:
Neg
ativ
e 3 is
gre
ater
tha
n ne
gative
6.
Yo
u c
an u
se a
num
ber
line t
o o
rder
rati
onal
num
bers
.
EX
AM
PLE
Ord
er
the n
um
bers
4, �
2, an
d 1
fro
m le
ast
to g
reat
est
.
Gra
ph t
he n
um
bers
on a
num
ber
line:
–5–4
–3–2
–10
12
34
5
Read
the n
um
bers
fro
m le
ft t
o r
ight,
whic
h is
leas
t to
gre
atest
: �
2, 1
, 4
.
TH
INK
AB
OU
T IT
Any
po
siti
ve n
um
ber
will
be
great
er
than
any
nega
tive
num
ber.
9781609797652_MUSS_OH_Math_Gr6_ATE_Ch2.indd 839781609797652_MUSS_OH_Math_Gr6_ATE_Ch2.indd 83 1/25/2019 3:43:41 PM1/25/2019 3:43:41 PM
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[ 127 ]
Chap
ter
2 | N
um
ber
and O
per
atio
ns
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
CO
MPA
RE A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
Less
on 1
4
How
Am
I D
oin
g?
What
ques
tions
do y
ou h
ave?
Thin
k of tw
o r
atio
nal
num
ber
s. C
om
par
e th
e num
ber
s usi
ng
� o
r �
.
What
is
an e
xam
ple
wher
e yo
u w
ould
com
par
e num
ber
s?
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
hav
e it
.
I under
stan
d
the
skill
.
TU
RN
AN
D T
ALK
Wo
rk w
ith a
par
tner.
Yo
u a
re
aske
d t
o fi n
d a
nu
mb
er
that
is
great
er
than
�3 a
nd
less
th
an
�3. E
xp
lain
wh
ere
yo
u w
ou
ld
fi nd
a n
um
ber
that
mat
ches
the
desc
rip
tio
n. Is
�10 a
co
rrect
resp
on
se?
Exp
lain
yo
ur
answ
er.
[ 126 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el F
Copyi
ng
is p
rohib
ited
.
Less
on 1
4
C
OM
PAR
E A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
GU
IDED
INST
RUCT
ION
1.
Use
the
num
ber
lin
e to
com
par
e ea
ch p
air
of num
ber
s. W
rite
> o
r <
.
�
3 a
nd 2
0 a
nd �
1
�
5 a
nd �
4
�3 a
nd 2
�3
is t
o t
he le
ft o
f 2
.
�3
� 2
0 a
nd �
1
0 is
to
the r
ight
of
�1
.
0
� �
1
�5 a
nd �
4
�5
is t
o t
he le
ft o
f �
4.
�5
�
�4
2.
Ord
er e
ach s
et o
f num
ber
s fr
om
lea
st t
o g
reat
est.
9, 0, �
2, 3
�2 is
less
than
0 a
nd
any
po
siti
ve n
um
bers
.
In o
rder:
–2
, 0
, 3
, 9
8, �
6, �
1, 10
�6
is f
arth
er
to t
he le
ft t
han
�1
.
In o
rder:
�
6, �
1, 8
, 1
0
7, �
4, 4, 11
�4
is le
ss t
han
the p
osi
tive
num
bers
.
In o
rder:
�
4, 4
, 7
, 11
3.
Whic
h r
atio
nal
num
ber
s ar
e le
ss t
han
�3?
Sele
ct t
he
two c
orr
ect
answ
ers.
Ⓐ
1
__
4
Ⓑ
�8
Ⓒ
5
Ⓓ
�1
Ⓔ
�4.5
Ⓕ
0
HIN
T, H
INT
Yo
u c
an u
se �
or
� fo
r th
e sa
me
com
par
iso
n: 6
� 4
, or
4 �
6.
–5–4
–3–2
–10
12
34
5
–5–4
–3–2
–10
12
34
5
–5–4
–3–2
–10
12
34
5
SK
ET
CH
IT
Dra
w a
nu
mb
er
line in
th
e s
pac
e
abo
ve. R
em
em
ber,
nu
mb
ers
decr
eas
e m
ovi
ng
left
.
Ⓑ
Ⓔ
9781609797652_MUSS_OH_Math_Gr6_ATE_Ch2.indd 849781609797652_MUSS_OH_Math_Gr6_ATE_Ch2.indd 84 1/25/2019 3:44:34 PM1/25/2019 3:44:34 PM
[ 85 ]Chapter 2 | Number and Operations | masteryeducation.comCopying is prohibited.
[ 128 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el F
Copyi
ng
is p
rohib
ited
.
Less
on 1
4
C
OM
PAR
E A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
IND
EPEN
DEN
T PR
ACTI
CEA
nsw
er
the q
uest
ions.
1.
The
table
show
s th
e poin
t bal
ance
s fo
r se
vera
l pla
yers
in a
mat
h g
ame.
Wri
te a
n ineq
ual
ity
to s
how
the
rela
tionsh
ip b
etw
een t
he
leas
t am
ount
of poin
ts a
nd t
he
grea
test
am
ount
of poin
ts.
W
rite
your
answ
er in t
he
box.
�
22.7
5 �
35.
11
2.
The
two t
her
mom
eter
s sh
ow
diff e
rent
tem
per
ature
s. U
se t
he
num
ber
s
in t
he
box t
o c
om
par
e th
e te
mper
ature
s.
T
he
num
ber
s ca
nnot
be
use
d m
ore
than
once
. W
rite
eac
h n
um
ber
in
the
appro
pri
ate
box.
5
10
1
5
20
�
5
�1
0
�1
5
�2
0
5
°C �
�
15
°C
3.
Gre
ta w
rite
s a
set
of ra
tional
num
ber
s in
ord
er fro
m lea
st t
o g
reat
est.
Whic
h c
ould
be
Gre
ta’s s
et o
f num
ber
s?
Ⓐ
0, �
16 1
__
4 ,
27, 59
Ⓑ
�18, �
5.5
, 5, 17
Ⓒ
�9, 0, �
13, 34
Ⓓ
7, 1
0
___
2 ,
�24, �
73
4.
In g
olf,
a low
er s
core
is
a bet
ter
score
. A
golfe
r sa
ys h
er s
core
is
wors
e
than
�5 b
ut
bet
ter
than
5. W
hat
mig
ht
her
sco
re h
ave
bee
n?
Pos
sibl
e an
swer
s: �
4, �
3, �
2, �
1, 0
, 1, 2
, 3, 4
Mat
h M
aze
Poin
ts
Per
son
Poin
ts
Dere
k3
5.1
1
Mar
ie�
22
.75
Xin
17
.09
Will
�6
.06
°C
50 40 30 20 10 0 �10
�30
�20
°C
50 40 30 20 10 0 �10
�30
�20
Ⓑ
[ 129 ]
Chap
ter
2 | N
um
ber
and O
per
atio
ns
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
CO
MPA
RE A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
Less
on 1
4
5.
The
table
show
s th
e el
evat
ions,
rel
ativ
e to
sea
lev
el, of se
vera
l pla
ces.
Dra
w a
lin
e to
show
eac
h p
lace
in o
rder
fro
m h
ighes
t to
low
est,
1–5.
Cit
y Ele
vati
on
Cit
yEle
vati
on (
ft)
Bo
sto
n,
MA
14
1
New
Orl
ean
s, L
A�
8
Was
hin
gto
n,
D.C
.1
Deat
h V
alle
y, C
A�
28
2
Den
ver,
CO
5,1
83
Bo
sto
n,
MA
1
New
Orl
ean
s, L
A2
Was
hin
gto
n,
D.C
.3
Deat
h V
alle
y, C
A4
Den
ver,
CO
5
6.
Cir
cle
the
num
ber
that
corr
ectl
y co
mple
tes
the
stat
emen
t.
�9
�
�1
1
�1
5
10
8 0
� 5
7.
Val
say
s it
was
0ºF
on M
onday
and �
12ºF
on W
ednes
day
. Sh
e sa
ys
Tues
day
was
war
mer
than
Wed
nes
day
but
cold
er t
han
Monday
. W
hat
mig
ht
the
tem
per
ature
hav
e bee
n o
n T
ues
day
?
Pos
sibl
e an
swer
s: �
1ºF,
�2º
F, �
3ºF,
�4º
F, �
5ºF,
�
6ºF,
�7º
F, �
8ºF,
�9º
F, �
10ºF
, �11
ºF
WO
RK
SPA
CE
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[ 131 ]
Chap
ter
2 | N
um
ber
and O
per
atio
ns
| m
aste
ryed
uca
tion.c
om
Copyi
ng
is p
rohib
ited
.
CO
MPA
RE A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
Less
on 1
4
EXIT
TIC
KET
Now
that
you h
ave
mas
tere
d c
om
par
ing
rati
onal
num
ber
s, let
’s s
olv
e th
e pro
ble
m in t
he
Rea
l-W
orl
d C
onnec
tion.
Five
fri
ends
pla
y in
a g
olf
tourn
amen
t. T
he
table
show
s ea
ch p
laye
r’s
score
. In
golf,
the
pla
yer
wit
h t
he
low
est
score
win
s th
e ga
me. W
ho w
on t
he
tourn
amen
t? E
xpla
in h
ow
you k
now
.
Golf
Tourn
amen
t
Pla
yer
Score
Ana
�4
Mar
cos
�2
Lily
�8
To
m�
6
Luci
ente
�1
6
Sam
ple
answ
er: A
num
ber l
ine
can
be u
sed
to s
how
and
com
pare
eac
h pl
ayer
's s
core
.Th
e sc
ores
in o
rder
from
leas
t to
grea
test
: �16
, �8,
�2,
�4,
�6
In g
olf,
the
low
est s
core
win
s th
e ga
me.
Luc
ient
e’s
scor
e of
�16
is lo
wes
t.Lu
cien
te w
ins
the
tour
nam
ent.
6.N
S.C
.7, 6
.NS.
C.7
a, 6
.NS.
C.7
b
[ 130 ]
mas
tery
educa
tion.c
om
| M
athem
atic
s | Lev
el F
Copyi
ng
is p
rohib
ited
.
Less
on 1
4
C
OM
PAR
E A
ND
OR
DE
R R
AT
ION
AL N
UM
BE
RS
8. P
art
AW
rite
an ineq
ual
ity
to c
om
par
e �
7 a
nd 0
. W
rite
anoth
er ineq
ual
ity
to
com
par
e 33 a
nd 0
.
Sam
ple
answ
ers:
�7
� 0
33 �
0
Par
t B
Wri
te a
rea
l-w
orl
d s
ituat
ion in w
hic
h t
hes
e th
ree
num
ber
s
(�7, 33, an
d 0
) ar
e ord
ered
fro
m lea
st t
o g
reat
est.
Expla
in h
ow
you o
rder
ed t
he
num
ber
s.
Sam
ple
answ
er: O
n on
e da
y in
Feb
ruar
y, C
ity
A ha
s a
high
tem
pera
ture
of �
7ºF,
City
B h
as a
hi
gh te
mpe
ratu
re o
f 33º
F, a
nd C
ity C
has
a h
igh
tem
pera
ture
of 0
ºF. I
n or
der f
rom
leas
t to
grea
test
, th
e ci
ties
are
A, C
, and
B. F
rom
left
to ri
ght o
n a
num
ber l
ine,
thes
e nu
mbe
rs w
ould
be:
�7,
0, 3
3.
8.
WO
RK
SPA
CE
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COMPARE AND ORDER RATIONAL NUMBERS Lesson 14
TEACHER NOTESREAL-WORLD GOALS FOR STUDENTS
• Students will understand how to compare rational numbers using inequalities.
• Students will order rational numbers.
TIPS FOR THE STRUGGLING LEARNER
• Students may think that �6 �� �4, since 6 �� 4. The number line tool is important and
keeps the concept simple: the further left, the lesser the number. This has been true
for students since number lines were introduced in fi rst grade, so remind them that it
continues to be true.
TIPS FOR THE ENGLISH LANGUAGE LEARNER
• English learners may have diffi culty with word problems and deciphering what is being
asked. Review unfamiliar terms such as elevation, warmer/colder, better/worse. Use visuals
to help convey the meanings.
• Explain that although 6 �� 5 and 5 �� 6 sound diff erent when read aloud, they have very
similar meanings. Stress that the inequality symbol always opens toward the greater
number. Have students practice reading inequalities to reinforce the terminology and link
the symbols to the words greater than and less than.
ACTIVITIES FOR THE ADVANCED LEARNER
• Students can compare numbers by their distance from zero: �8 is further from zero
than 5. This is the start of the concept of absolute value, which students will see soon.
• Students can order rational numbers that include decimals and fractions, as well as integers.
They will need to think about how to compare numbers such as 3
_ 4 and 0.8.
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