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.



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.




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.




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




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




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




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


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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


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


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


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


[ 339 ][ 339 ]Correlation to the Ohio Learning Standards | masteryeducation.com


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


[ 341 ][ 341 ]Correlation to the Ohio Learning Standards | masteryeducation.com


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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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


[ 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

.

Ⓑ

Ⓔ



[ 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



[ 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




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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