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Attention Students and Families This packet is designed to be used only if there is not consistent access to technology to complete work online. If a student can interact with Google Classroom, this packet does not take the place of those assignments and it is not a requirement to be
completed in addition to Google Classroom work assigned by teachers.
6th Grade
Instructional Packet
May 4, 2020
English Teachers can tell you the pages that your child should complete each week. Your child should complete only the pages that they can. These packets will not be collected. Please contact your child’s teacher if you have questions or would like help. Spanish Los maestros pueden decirle las páginas que su hijo debe completar cada semana. Su hijo solo debe completar las páginas que pueda. Estos paquetes no serán recolectados. Comuníquese con el maestro de su hijo si tiene preguntas o desea ayuda. Russian Учителя могут рассказать вам страницы, которые ваш ребенок должен заполнять каждую неделю. Ваш ребенок должен заполнять только те страницы, которые он может. Эти пакеты не будут собраны. Пожалуйста, свяжитесь с учителем вашего ребенка, если у вас есть вопросы или вы хотели бы помочь. Vietnamese Giáo viên có thể cho bạn biết các trang mà con bạn nên hoàn thành mỗi tuần. Con bạn chỉ nên hoàn thành những trang mà chúng có thể. Những gói này sẽ không được thu thập. Vui lòng liên hệ với giáo viên dạy con của bạn nếu bạn có thắc mắc hoặc muốn được giúp đỡ. Arabic
یمكن للمعلمین إخبارك بالصفحات التي یجب أن یكملها طفلك كل أسبوع. یجب أن یكمل طفلك الصفحات التي یمكنهها فقط. لن یتم جمع هذه الحزم. یرجى االتصال بمعلم طفلك إذا كانت لدیك أسئلة أو ترید المساعدة.
Ukranian Вчителі можуть розповісти вам сторінки, які ваша дитина повинна завершувати щотижня. Ваша дитина повинна заповнити лише ті сторінки, які вона може. Ці пакети не збиратимуться. Якщо у вас є питання або хочете допомогти, зв’яжіться зі вчителем вашої дитини. Chinese 老师可以告诉您您的孩子每周应完成的页面。您的孩子应该只填写他们能完成的页面。这些数据包将不会被收集。如有疑问或需要帮助，请与您孩子的老师联系。 Romanian Profesorii îți pot spune paginile pe care copilul tău ar trebui să le completeze în fiecare săptămână. Copilul tău ar trebui să completeze doar paginile pe care le poate. Aceste pachete nu vor fi colectate. Vă rugăm să contactați profesorul copilului dvs. dacă aveți întrebări sau doriți ajutor.
Somali Macallimiintu waxay kuu sheegi karaan boggaga ay tahay inuu ilmahaagu dhammaystiro toddobaad kasta. Ilmahaagu waa inuu dhammaystiro oo keliya bogagga ay awoodaan. Xirmooyinkan lama ururin doono. Fadlan la xiriir macallinka cunuggaaga haddii aad wax su'aalo ah qabtid ama aad jeclaan lahayd caawimaad. Hmong Cov kws qhia tuaj yeem tuaj yeem qhia koj cov nplooj ntawv uas koj tus menyuam yuav tsum ua tiav txhua lub lim tiam. Koj tus menyuam yuav tsum tau ua kom tiav cov nplooj ntawv uas lawv muaj peev xwm ua tau. Cov pob no yuav tsis sau. Thov hu rau koj tus menyuam tus xibfwb yog tias koj muaj lus nug lossis xav tau kev pab. Napali �श�कह�ले तपा�लाई प�ृठह� बताउन स�छन ्जनु तपा�को ब�चाले ��येक ह�तामा पूरा गनु�पद�छ। तपा�को ब�चाले उनीह�ले गन� स�ने प�ृठह� मा� पूण� गनु� पछ�। यी �याकेटह� स be◌्कलन ग�रने छैन। कृपया तपा�को ब�चाको �श�कलाई स�पक� गनु�होस ्य�द तपा�सँग ��नह� छन ्वा म�दत चाहनुहु�छ भने। Burmese သင��က�လ�ကအပတ�တ��င���ဖည��စ�က�သင��သည��စ�မ�က����မ���က��ဆရ�မ���က��ပ��ပ���င�သည�။ သင�၏က�လ�သည�သ�တ�� �တတ����င��သ�စ�မ�က����မ���က��သ��ဖည��စ�က�သင��သည�။ ဒ� packets �တ�က��စ��ဆ�င��မ��မဟ�တ�ပ�ဘ�� သင��တ�င��မ�ခ�န��မ���ရ��ပ�ကသ�� �မဟ�တ�အက�အည�လ��ပ�ကသင��က�လ�၏ဆရ�က��ဆက�သ�ယ�ပ�။ Amharic ልጅዎ በየሳምንቱ መሙላት ያለባቸውን ገጾች መምህራን ሊነግሩዎት ይችላሉ። ልጅዎ መቻል የሚችሏቸውን ገጾች ብቻ መሙላት አለበት ፡፡ እነዚህ ፓኬጆች አይሰበሰቡም ፡፡ እባክዎ ጥያቄዎች ካሉዎት ወይም እገዛ ከፈለጉ የልጅዎን መምህር ያነጋግሩ።
6th5/4-5/8WordWorkLessonfocus:U20GreekandLatinRoots(elements)forTimeandFamily:chron,
mat/matr,pat/patr,onym,doc
Monday:1. Readwordstudyvocabularyposter.
2. Readthroughthefirstsetofwordcardsandhighlightanyroots(elements)you
recognizefromthewordstudyposter.
3. CompleteFormingWordsFromGreekandLatinElementsactivity.
Tuesday:1. Readthroughthesecondsetofwordcardsandhighlightanyroots(elements)
yourecognizefromthewordstudyposter.
2. CompletethefirstChoosetheWordactivity.
Wednesday:1. Readthrough“Unlockingthepast,Hollywood-Style”andhighlightanywords
containingchron,mat/matr,pat/patr,onym,ordoc.
2. CompletethesecondChoosetheWordactivity.Thursday:
1. Pickout5wordsyouhighlightedin“Unlockingthepast,HollywoodStyle”andtry
usingtheminanoralorwrittensentenceyoumakeup.
2. Findsomeonewhocanpickninewordsfromyourwordcardsthisweekandgive
youtheSpellingPeerCheck.
Friday:1. CompletetheU20Quick-Check.Centennialisproudofyouforworkingsohard
fromhome!Keepupthegoodwork.
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4 ExtendW
ordS
TUDY
VO
CABU
LARY
UNIT
20 Gre
ek a
nd L
atin
Ele
men
ts f
or T
ime
and
Fam
ily
chro
n, m
at/m
atr,
pat/
patr
, ony
m, d
ocEl
emen
tM
eani
ngEx
ampl
e
chro
ntim
ean
achr
onis
m: a
nyth
ing
that
see
ms
to b
e ou
t of i
ts p
rope
r tim
e in
his
tory
mat
/mat
rm
othe
rm
ater
nal:
like
a m
othe
r or c
hara
cter
istic
of
mot
herh
ood
pat/
patr
fath
erpa
tern
al: l
ike
a fa
ther
or p
rote
ctor
onym
nam
eac
rony
m: a
wor
d fo
rmed
from
the
first
le
tters
of a
ser
ies
of w
ords
doc
teac
hdo
ctor
ate:
hig
hest
deg
ree
awar
ded
by a
gr
adua
te s
choo
l
The
Gre
ek o
r Lat
in e
lem
ent m
ay b
e at
the
begi
nnin
g of
a w
ord:
mat
erna
l
The
Gre
ek o
r Lat
in e
lem
ent m
ay b
e in
the
mid
dle
of a
wor
d:an
achr
onis
m
The
Gre
ek o
r Lat
in e
lem
ent m
ay b
e at
the
end
of a
wor
d:ac
rony
m
Kit 4
_Anc
hor P
oste
rs.in
dd
206/
14/1
0 3
:02:
29 P
M
Word Study & Vocabulary 4: Unit 20: Greek and Latin elements chron, mat/matr, pat/patr, onym, doc ©2010 Benchmark Education Company, LLC
Name ___________________________________ Date _______________________________________
Unit 20 Quick-Check: Greek and Latin Elements for Time and Family
Answer QuestionsDirections: Choose the correct word to complete each sentence.
1. With her constant sneezing and sniffling, it seems like Felicity has a ____________ cold.
chronicle chronic doctored
2. Adam’s parents are ____________ of the local theater company and have good seats
for the company’s shows.
doctrines matrons patrons
3. Ali didn’t want anyone to know she wrote the poem, so she used a ____________.
pseudonym homonym anonymous
4. The old horse is easy to ride because she’s sweet and ____________.
docent docile matron
ApplyDirections: In the space below, list three to five words you know that have one of the Greek or Latin elements chron, mat/matr, pat/patr, onym, or doc.
____________ ____________ ____________ ____________ ____________
Directions: Using the words from the word bank, complete the following sort by writing the words in the appropriate category.
Words Related to “Teach” Words Related to “Father” Word Bank documentary, indoctrinate, patriarch, patronize, patriotic, docile, paternal, document
Think and Write about Greek and Latin Elements for Time and Family chron, mat/matr, pat/patr, onym, docDirections: In the space below, explain how understanding Greek and Latin elements for time and family helps you as a reader, speller, and writer.
_____________________________________________________________________________
Kit 4_Unit 20_TG.indd 8 6/8/10 5:12:24 PM
6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Lesson 1: The Relationship of Addition and Subtraction
Classwork Opening Exercise
a. Draw a tape diagram to represent the following expression: 5 + 4.
b. Write an expression for each tape diagram.i.
ii.
Exercises
1. Predict what will happen when a tape diagram has a large number of squares, some squares are removed, and thenthe same amount of squares are added back on.
2. Build a tape diagram with 10 squares.a. Remove six squares. Write an expression to represent the tape diagram.
b. Add six squares onto the tape diagram. Alter the original expression to represent the current tape diagram.
A STORY OF RATIOS
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka- math.orgG6-M4-SE-1.3.0-07.2015
S.1
6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
c. Evaluate the expression.
3. Write an equation, using variables, to represent the identities we demonstrated with tape diagrams.
4. Using your knowledge of identities, fill in each of the blanks.
a. 4 + 5 − _____ = 4
b. 25 − _____ + 10 = 25
c. _____ + 16 − 16 = 45
d. 56 − 20 + 20 = _____
5. Using your knowledge of identities, fill in each of the blanks.
a. 𝑎𝑎 + 𝑏𝑏 − _____ = 𝑎𝑎
b. 𝑐𝑐 − 𝑑𝑑 + 𝑑𝑑 = _____
c. 𝑒𝑒 + _____ − 𝑓𝑓 = 𝑒𝑒
d. _____ − ℎ + ℎ = 𝑔𝑔
A STORY OF RATIOS
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka- math.orgG6-M4-SE-1.3.0-07.2015
S.2
6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Problem Set 1. Fill in each blank.
a. _____ + 15 − 15 = 21
b. 450 − 230 + 230 = _____
c. 1289 − ______ + 856 = 1289
2. Why are the equations 𝑤𝑤 − 𝑥𝑥 + 𝑥𝑥 = 𝑤𝑤 and 𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥 = 𝑤𝑤 called identities?
A STORY OF RATIOS
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka- math.orgG6-M4-SE-1.3.0-07.2015
S.3
6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Lesson 2: The Relationship of Multiplication and Division
Classwork Opening Exercise
Draw a pictorial representation of the division and multiplication problems using a tape diagram.
a. 8 ÷ 2
b. 3 × 2
Exploratory Challenge
Work in pairs or small groups to determine equations to show the relationship between multiplication and division. Use tape diagrams to provide support for your findings.
1. Create two equations to show the relationship between multiplication and division. These equations should be identities and include variables. Use the squares to develop these equations.
2. Write your equations on large paper. Show a series of tape diagrams to defend each of your equations.
Use the following rubric to critique other posters. 1. Name of the group you are critiquing 2. Equation you are critiquing 3. Whether or not you believe the equations are true and reasons why
A STORY OF RATIOS
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka- math.orgG6-M4-SE-1.3.0-07.2015
S.4
6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Problem Set 1. Fill in each blank to make the equation true.
a. 132 ÷ 3 × 3 = _____
b. _____ ÷ 25 × 25 = 225
c. 56 × _____ ÷ 8 = 56
d. 452 × 12 ÷ _____ = 452
2. How is the relationship of addition and subtraction similar to the relationship of multiplication and division?
A STORY OF RATIOS
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka- math.orgG6-M4-SE-1.3.0-07.2015
S.5
6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
Lesson 3: The Relationship of Multiplication and Addition
Classwork Opening Exercise
Write two different expressions that can be depicted by the tape diagram shown. One expression should include addition, while the other should include multiplication.
a.
b.
c.
Exercises
1. Write the addition sentence that describes the model and the multiplication sentence that describes the model.
A STORY OF RATIOS
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S.6
6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
2. Write an equivalent expression to demonstrate the relationship of multiplication and addition. a. 6 + 6
b. 3 + 3 + 3 + 3 + 3 + 3
c. 4 + 4 + 4 + 4 + 4
d. 6 × 2
e. 4 × 6
f. 3 × 9
g. ℎ + ℎ + ℎ + ℎ + ℎ
h. 6
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S.7
6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
3. Roberto is not familiar with tape diagrams and believes that he can show the relationship of multiplication and addition on a number line. Help Roberto demonstrate that the expression 3 × 2 is equivalent to 2 + 2 + 2 on a number line.
4. Tell whether the following equations are true or false. Then, explain your reasoning. a. 𝑥𝑥 + 6𝑔𝑔 − 6𝑔𝑔 = 𝑥𝑥
b. 2𝑓𝑓 − 4𝑒𝑒 + 4𝑒𝑒 = 2𝑓𝑓
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S.8
6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
5. Write an equivalent expression to demonstrate the relationship between addition and multiplication. a. 6 + 6 + 6 + 6 + 4 + 4 + 4
b. 𝑑𝑑 + 𝑑𝑑 + 𝑑𝑑 + 𝑤𝑤 + 𝑤𝑤 + 𝑤𝑤 + 𝑤𝑤 + 𝑤𝑤
c. 𝑎𝑎 + 𝑎𝑎 + 𝑏𝑏 + 𝑏𝑏 + 𝑏𝑏 + 𝑐𝑐 + 𝑐𝑐 + 𝑐𝑐 + 𝑐𝑐
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S.9
6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
Problem Set Write an equivalent expression to show the relationship of multiplication and addition.
1. 10 + 10 + 10
2. 4 + 4 + 4 + 4 + 4 + 4 + 4
3. 8 × 2
4. 3 × 9
5. 6
6. 𝑑𝑑 + 𝑑𝑑 + 𝑑𝑑 + 𝑑𝑑 + 𝑑𝑑
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S.10
6•4 4
4: The Relationship of Division and Subtraction
4: The Relationship of Division and Subtraction
Classwork Exercise 1
Build subtraction equations using the indicated equations. The first example has been completed for you.
Division Equation
Divisor Indicates the Size of the Unit Tape Diagram What is
, , ?
12 ÷ 𝑥𝑥 = 4 12 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 = 0
𝑥𝑥 = 3
18 ÷ 𝑥𝑥 = 3
35 ÷ = 5
42 ÷ = 6
Division Equation
Divisor Indicates the Number of Units Tape Diagram What is
, , ?
12 ÷ 𝑥𝑥 = 4 12 − 4 − 4 − 4 = 0
𝑥𝑥 = 3
18 ÷ 𝑥𝑥 = 3
35 ÷ = 5
42 ÷ = 6
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S.11
6•4 4
4: The Relationship of Division and Subtraction
Exercise 2
Answer each question using what you have learned about the relationship of division and subtraction.
a. If 12 ÷ 𝑥𝑥 = 3, how many times would 𝑥𝑥 have to be subtracted from 12 in order for the answer to be zero? What is the value of 𝑥𝑥?
b. 36 − 𝑓𝑓 − 𝑓𝑓 − 𝑓𝑓 − 𝑓𝑓 = 0. Write a division sentence for this repeated subtraction sentence. What is the value of 𝑓𝑓?
c. If 24 ÷ 𝑏𝑏 = 12, which number is being subtracted 12 times in order for the answer to be zero?
A STORY OF RATIOS
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S.12
6•4 4
4: The Relationship of Division and Subtraction
Problem Set Build subtraction equations using the indicated equations.
Division Equation
Divisor Indicates the Size of the Unit Tape Diagram What is
, , ?
1. 24 ÷ 𝑥𝑥 = 4
2. 36 ÷ 𝑥𝑥 = 6
3. 28 ÷ = 7
4. 30 ÷ = 5
5. 16 ÷ = 4
Division Equation
Divisor Indicates the Number of Units Tape Diagram What is
, , ?
1. 24 ÷ 𝑥𝑥 = 4
2. 36 ÷ 𝑥𝑥 = 6
3. 28 ÷ = 7
4. 30 ÷ = 5
5. 16 ÷ = 4
A STORY OF RATIOS
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S.13
6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Lesson 1: The Relationship of Addition and Subtraction
Student Outcomes
� Students build and clarify the relationship of addition and subtraction by evaluating identities such as 𝑤𝑤 − 𝑥𝑥 + 𝑥𝑥 = 𝑤𝑤 and 𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥 = 𝑤𝑤.
Lesson Notes Teachers need to create square pieces of paper in order for students to build tape diagrams. Each pair of students needs 10 squares to complete the activities. If the teacher has square tiles, these can be used in place of paper squares.
The template for the squares and other shapes used in the lesson are provided at the end of the lesson. Teachers need to cut out the shapes.
Classwork Fluency Exercise (5 minutes): Multiplication of Decimals
RWBE: Refer to the Rapid White Board Exchanges sections in the Module Overview for directions to administer an RWBE.
Opening Exercise (5 minutes)
Opening Exercise
a. Draw a tape diagram to represent the following expression: 𝟓𝟓 + 𝟒𝟒.
b. Write an expression for each tape diagram. i.
ii.
Discuss the answers with the class. If students struggled with the Opening Exercise, provide more examples before moving into the Discussion.
𝟓𝟓 𝟒𝟒 +
𝟐𝟐 𝟐𝟐 +
𝟑𝟑 𝟒𝟒 +
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Discussion (15 minutes)
Provide each pair of students with a collection of 10 squares, so they can use these squares to create tape diagrams throughout the lesson.
� If each of the squares represents 1 unit, represent the number 3 using the squares provided. à
� Add two more squares to your tape diagram. à
� Write an expression to represent how we created a tape diagram with five squares. à
� Remove two squares from the tape diagram.
à � Alter our original expression 3 + 2 to create an expression that represents what we did with the tape diagram.
à 3 + 2 − 2 � Evaluate the expression.
à 3 � Let’s start a new diagram. This time, create a tape diagram with six squares.
à � Use your squares to demonstrate the expression 6 + 4.
à � Remove four squares from the tape diagram.
à � Alter the expression 6 + 4 to create an expression to represent the tape diagram.
à 6 + 4 − 4 � How many squares are left on your desk?
à 6 � Evaluate the expression.
à 6 � How many squares did we start with?
à 6 � What effect did adding four squares and then subtracting the four squares have on the number of squares?
à Adding and then subtracting the same number of squares resulted in the same number that we started with.
� What if I asked you to add 215 squares to the six squares we started with and then subtract 215 squares? Do you need to actually add and remove these squares to know what the result will be? Why is that? à We do not actually need to do the addition and subtraction because we now know that it will result in
the same amount of squares that we started with; when you add and then subtract the same number, the results will be the original number.
3 2 +
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
� What do you notice about the expressions we created with the tape diagrams? à Possible answer: When we add one number and then subtract the same number, we get our original
number. � Write an equation, using variables, to represent what we just demonstrated with tape diagrams. Remember
that a variable is a letter that represents a number. Use the shapes provided to create tape diagrams to demonstrate this equation.
Provide students time to work with their partners to write an equation.
à Possible answer: 𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥 = 𝑤𝑤. Emphasize that both 𝑤𝑤’s represent the same number, and the same rule applies to the 𝑥𝑥’s.
� Why is the equation 𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥 = 𝑤𝑤 called an identity? à Possible answer: The equation is called an identity because the variables can be replaced with any
numbers, and after completing the operations, I returned to the original value.
Exercises (12 minutes)
Students use their knowledge gained in the Discussion to create another equation using identities. Allow students to continue to work with their partners and 10 squares.
Exercises
1. Predict what will happen when a tape diagram has a large number of squares, some squares are removed, and then the same amount of squares are added back on.
Possible answer: When some squares are removed from a tape diagram, and then the same amount of squares are added back on, the tape diagram will end up with the same amount of squares that it started with.
2. Build a tape diagram with 𝟏𝟏𝟏𝟏 squares. a. Remove six squares. Write an expression to represent the tape diagram.
𝟏𝟏𝟏𝟏 − 𝟔𝟔
b. Add six squares onto the tape diagram. Alter the original expression to represent the current tape diagram.
𝟏𝟏𝟏𝟏 − 𝟔𝟔 + 𝟔𝟔
Scaffolding: The exercise could be completed as a class if students are struggling with the concept.
𝑤𝑤
𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥
𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥 = 𝑤𝑤
𝑤𝑤 + 𝑥𝑥
MP.7
MP.2
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
c. Evaluate the expression.
𝟏𝟏𝟏𝟏
3. Write an equation, using variables, to represent the identities we demonstrated with tape diagrams.
Possible answer: 𝒘𝒘− 𝒙𝒙 + 𝒙𝒙 = 𝒘𝒘
4. Using your knowledge of identities, fill in each of the blanks.
a. 𝟒𝟒 + 𝟓𝟓 − ____ = 𝟒𝟒
𝟓𝟓
b. 𝟐𝟐𝟓𝟓 − ____ + 𝟏𝟏𝟏𝟏 = 𝟐𝟐𝟓𝟓
𝟏𝟏𝟏𝟏
c. ____ +𝟏𝟏𝟔𝟔 − 𝟏𝟏𝟔𝟔 = 𝟒𝟒𝟓𝟓
𝟒𝟒𝟓𝟓
d. 𝟓𝟓𝟔𝟔 − 𝟐𝟐𝟏𝟏 + 𝟐𝟐𝟏𝟏 = _____
𝟓𝟓𝟔𝟔
5. Using your knowledge of identities, fill in each of the blanks.
a. 𝒂𝒂 + 𝒃𝒃 − _____ = 𝒂𝒂
𝒃𝒃
b. 𝒄𝒄 − 𝒅𝒅 + 𝒅𝒅 = _____
𝒄𝒄
c. 𝒆𝒆 + _____ − 𝒇𝒇 = 𝒆𝒆
𝒇𝒇
d. _____ − 𝒉𝒉 + 𝒉𝒉 = 𝒈𝒈
𝒈𝒈
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Closing (3 minutes)
� In every problem we did today, why did the final value of the expression equal the initial expression? à The overall change to the expression was 0.
� Initially, we added an amount and then subtracted the same amount. Later in the lesson, we subtracted an amount and then added the same amount. Did this alter the outcome? à This did not alter the outcome; in both cases, we still ended with our initial value.
� Why were we able to evaluate the final expression even when we did not know the amount we were adding and subtracting? à If we add and subtract the same value, it is similar to adding 0 to an expression because the two
numbers are opposites, which have a sum of 0.
Exit Ticket (5 minutes)
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Name Date
Lesson 1: The Relationship of Addition and Subtraction
Exit Ticket 1. Draw tape diagrams to represent each of the following number sentences.
a. 3 + 5 − 5 = 3
b. 8 − 2 + 2 = 8
2. Fill in each blank. a. 65 + _____ −15 = 65
b. _____ + 𝑔𝑔 − 𝑔𝑔 = 𝑘𝑘
c. 𝑎𝑎 + 𝑏𝑏 − _____ = 𝑎𝑎
d. 367 − 93 + 93 = _____
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Exit Ticket Sample Solutions
1. Draw a series of tape diagrams to represent the following number sentences. a. 𝟑𝟑 + 𝟓𝟓 − 𝟓𝟓 = 𝟑𝟑
b. 𝟖𝟖 − 𝟐𝟐 + 𝟐𝟐 = 𝟖𝟖
2. Fill in each blank. a. 𝟔𝟔𝟓𝟓+ _____ − 𝟏𝟏𝟓𝟓 = 𝟔𝟔𝟓𝟓
𝟏𝟏𝟓𝟓
b. ____ + 𝒈𝒈−𝒈𝒈 = 𝒌𝒌
𝒌𝒌
c. 𝒂𝒂 + 𝒃𝒃 − _____ = 𝒂𝒂
𝒃𝒃
d. 𝟑𝟑𝟔𝟔𝟑𝟑 − 𝟗𝟗𝟑𝟑+ 𝟗𝟗𝟑𝟑 = _____
𝟑𝟑𝟔𝟔𝟑𝟑
Problem Set Sample Solutions
1. Fill in each blank.
a. _____ + 𝟏𝟏𝟓𝟓 − 𝟏𝟏𝟓𝟓 = 𝟐𝟐𝟏𝟏
𝟐𝟐𝟏𝟏
b. 𝟒𝟒𝟓𝟓𝟏𝟏 − 𝟐𝟐𝟑𝟑𝟏𝟏+ 𝟐𝟐𝟑𝟑𝟏𝟏 = _____
𝟒𝟒𝟓𝟓𝟏𝟏
c. 𝟏𝟏𝟐𝟐𝟖𝟖𝟗𝟗 − _____ + 𝟖𝟖𝟓𝟓𝟔𝟔 = 𝟏𝟏𝟐𝟐𝟖𝟖𝟗𝟗
𝟖𝟖𝟓𝟓𝟔𝟔
2. Why are the equations 𝒘𝒘− 𝒙𝒙 + 𝒙𝒙 = 𝒘𝒘 and 𝒘𝒘 + 𝒙𝒙 − 𝒙𝒙 = 𝒘𝒘 called identities?
Possible answer: These equations are called identities because the variables can be replaced with any numbers, and after completing the operations, I returned to the original value.
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
Multiplication of Decimals Progression of Exercises
1. 0.5 × 0.5 =
𝟏𝟏.𝟐𝟐𝟓𝟓
2. 0.6 × 0.6 =
𝟏𝟏.𝟑𝟑𝟔𝟔
3. 0.7 × 0.7 =
𝟏𝟏.𝟒𝟒𝟗𝟗
4. 0.5 × 0.6 =
𝟏𝟏.𝟑𝟑
5. 1.5 × 1.5 =
𝟐𝟐.𝟐𝟐𝟓𝟓
6. 2.5 × 2.5 =
𝟔𝟔.𝟐𝟐𝟓𝟓
7. 0.25 × 0.25 =
𝟏𝟏.𝟏𝟏𝟔𝟔𝟐𝟐𝟓𝟓
8. 0.1 × 0.1 =
𝟏𝟏.𝟏𝟏𝟏𝟏
9. 0.1 × 123.4 =
𝟏𝟏𝟐𝟐.𝟑𝟑𝟒𝟒
10. 0.01 × 123.4 =
𝟏𝟏.𝟐𝟐𝟑𝟑𝟒𝟒
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
𝑤𝑤 + 𝑥𝑥
𝑤𝑤 𝑥𝑥
𝑤𝑤 𝑥𝑥
𝑤𝑤 + 𝑥𝑥
𝑤𝑤 𝑥𝑥
𝑤𝑤 𝑥𝑥
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6•4 Lesson 1
Lesson 1: The Relationship of Addition and Subtraction
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Lesson 2: The Relationship of Multiplication and Division
Student Outcomes
� Students build and clarify the relationship of multiplication and division by evaluating identities such as 𝑎𝑎 ÷ 𝑏𝑏 𝑏𝑏 = 𝑎𝑎 and 𝑎𝑎 𝑏𝑏 ÷ 𝑏𝑏 = 𝑎𝑎.
Lesson Notes Students use the squares that were used in Lesson 1; however, each pair of students should receive 20 squares for this lesson. Also, students need large paper to complete the Exploratory Challenge.
Classwork Fluency Exercise (5 minutes): Division of Fractions I
Sprint: Refer to the Sprints and Sprint Delivery Script sections in the Module Overview for directions to administer a Sprint.
Opening (2 minutes)
Remind students of the identities they learned the previous day. Discuss the relationship between addition and subtraction. Inform students that the relationship between multiplication and division is discussed today. Have students make predictions about this relationship using their knowledge gained in the previous lesson.
Opening Exercise (5 minutes) Opening Exercise
Draw a pictorial representation of the division and multiplication problems using a tape diagram.
a. 𝟖𝟖÷ 𝟐𝟐
b. 𝟑𝟑 × 𝟐𝟐
𝟑𝟑 𝟑𝟑
𝟔𝟔
MP.2
𝟒𝟒 𝟒𝟒
𝟖𝟖
𝟐𝟐
𝟖𝟖
𝟐𝟐 𝟐𝟐 𝟐𝟐
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Discussion (optional—see Scaffolding notes)
Provide each pair of students with a collection of 20 squares, which they use to create tape diagrams throughout the lesson.
� Build a tape diagram to represent 9 units. à
� Divide the 9 units into three equal groups. à
� Write an expression to represent the process you modeled with the tape diagram. à 9 ÷ 3
� Evaluate the expression. à 3
� Use your squares to demonstrate what it would look like to multiply 3 by 3. à
� Alter our original expression, 9 ÷ 3, to create an expression that represents what we did with the tape diagram. à 9 ÷ 3 × 3
� Evaluate the expression. à 9
� What do you notice about the expression of the tape diagram? à Possible answer: When we divide by one number and then multiply by the same number, we end up
with our original number. � Write an equation, using variables, to represent the identities we demonstrated with tape diagrams. Draw a
series of tape diagrams to demonstrate this equation. à Provide students time to work in pairs. à Possible answer: 𝑎𝑎 ÷ 𝑏𝑏 × 𝑏𝑏 = 𝑎𝑎. Emphasize that both 𝑎𝑎’s represent the same number, and the same
rule applies to the 𝑏𝑏’s.
Scaffolding: The Discussion is provided if students struggled during Lesson 1. If the Discussion is included in the lesson, the Exploratory Challenge is shortened because students only develop one number sentence.
MP.7
𝑎𝑎
𝑏𝑏
𝑎𝑎 ÷ 𝑏𝑏
𝑎𝑎 ÷ 𝑏𝑏 × 𝑏𝑏
𝑎𝑎 ÷ 𝑏𝑏 × 𝑏𝑏
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Exploratory Challenge (23 minutes)
Students work in pairs or small groups to determine equations to show the relationship between multiplication and division. They use tape diagrams to provide support for their findings.
Exploratory Challenge
Work in pairs or small groups to determine equations to show the relationship between multiplication and division. Use tape diagrams to provide support for your findings.
1. Create two equations to show the relationship between multiplication and division. These equations should be identities and include variables. Use the squares to develop these equations.
2. Write your equations on large paper. Show a series of tape diagrams to defend each of your equations.
Only one number sentence is shown there; the second number sentence and series of tape diagrams are included in the optional Discussion.
Possible answer: 𝒂𝒂 × 𝒃𝒃 ÷ 𝒃𝒃 = 𝒂𝒂
Possible answer: 𝒂𝒂 ÷ 𝒃𝒃 × 𝒃𝒃 = 𝒂𝒂
When students complete their work on the large paper, hang the papers around the room. Provide time for students to walk around and critique their peers’ work. While examining the other posters, students should be comparing the equations and tape diagrams to their own.
Use the following rubric to critique other posters.
1. Name of the group you are critiquing 2. Equation you are critiquing 3. Whether or not you believe the equations are true and reasons why
Closing (5 minutes)
� What did you determine about the relationship of multiplication and division? à When a number is multiplied and divided by the same number, the result is the original number.
� What equations can be used to show the relationship of multiplication and division? à 𝑎𝑎 ÷ 𝑏𝑏 𝑏𝑏 = 𝑎𝑎 and 𝑎𝑎 𝑏𝑏 ÷ 𝑏𝑏 = 𝑎𝑎
Exit Ticket (5 minutes)
𝒂𝒂
𝒂𝒂 × 𝒃𝒃
𝒂𝒂 𝒂𝒂 𝒂𝒂
𝒂𝒂 × 𝒃𝒃 ÷ 𝒃𝒃
Scaffolding: If students struggle with getting started, show them the identity equations for addition and subtraction learned in Lesson 1.
MP.7
MP.3
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Name Date
Lesson 2: The Relationship of Multiplication and Division
Exit Ticket 1. Fill in the blanks to make each equation true.
a. 12 ÷ 3 × ______ = 12
b. ݂ × ݄ ÷ ݄ = ______
c. 45 × ______ ÷ 15 = 45
d. ______ ÷ ݎ × ݎ =
2. Draw a series of tape diagrams to represent the following number sentences. a. 12 ÷ 3 × 3 = 12
b. 4 × 5 ÷ 5 = 4
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Exit Ticket Sample Solutions
1. Fill in the blanks to make each equation true. a. 𝟏𝟏𝟐𝟐÷ 𝟑𝟑 × ____ = 𝟏𝟏𝟐𝟐
𝟑𝟑
b. 𝒇𝒇 × 𝒉𝒉 ÷ 𝒉𝒉 = _____
𝒇𝒇
c. 𝟒𝟒𝟓𝟓× _____ ÷ 𝟏𝟏𝟓𝟓 = 𝟒𝟒𝟓𝟓
𝟏𝟏𝟓𝟓
d. _____ ÷ × =
2. Draw a series of tape diagrams to represent the following number sentences.
a. 𝟏𝟏𝟐𝟐÷ 𝟑𝟑 × 𝟑𝟑 = 𝟏𝟏𝟐𝟐
b. 𝟒𝟒 × 𝟓𝟓 ÷ 𝟓𝟓 = 𝟒𝟒
Problem Set Sample Solutions
1. Fill in each blank to make each equation true.
a. 𝟏𝟏𝟑𝟑𝟐𝟐÷ 𝟑𝟑 × 𝟑𝟑 = _____
𝟏𝟏𝟑𝟑𝟐𝟐
b. _____ ÷ 𝟐𝟐𝟓𝟓× 𝟐𝟐𝟓𝟓 = 𝟐𝟐𝟐𝟐𝟓𝟓
𝟐𝟐𝟐𝟐𝟓𝟓
c. 𝟓𝟓𝟔𝟔× _____ ÷ 𝟖𝟖 = 𝟓𝟓𝟔𝟔
𝟖𝟖
d. 𝟒𝟒𝟓𝟓𝟐𝟐× 𝟏𝟏𝟐𝟐÷ ______ = 𝟒𝟒𝟓𝟓𝟐𝟐
𝟏𝟏𝟐𝟐
2. How is the relationship of addition and subtraction similar to the relationship of multiplication and division?
Possible answer: Both relationships create identities.
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Number Correct: ______ Division of Fractions—Round 1
Directions: Evaluate each expression and simplify. Use blank spaces to create like units, where applicable.
1. 9 ones ÷ 3 ones 23. 610 ÷
410
2. 9 ÷ 3 24. 610 ÷
25 =
610 ÷ 10
3. 9 tens ÷ 3 tens 25. 1012 ÷
512
4. 90 ÷ 30 26. 56 ÷
512 = 12 ÷
512
5. 9 hundreds ÷ 3 hundreds 27. 1012 ÷
312
6. 900 ÷ 300 28. 1012 ÷
14 =
1012 ÷ 12
7. 9 halves ÷ 3 halves 29. 56 ÷
312 = 12 ÷
312
8. 92 ÷
32 30.
510 ÷
210
9. 9 fourths ÷ 3 fourths 31. 510 ÷
15 =
510 ÷ 10
10. 94 ÷
34 32. 1
2 ÷210 = 10 ÷
210
11. 98 ÷
38 33. 1
2 ÷24
12. 23 ÷
13 34.
34 ÷
28
13. 13 ÷
23 35.
12 ÷
38
14. 67 ÷
27 36. 1
2 ÷15 = 10 ÷ 10
15. 57 ÷
27 37.
24 ÷
13
16. 37 ÷
47 38.
14 ÷
46
17. 610 ÷
210 39.
34 ÷
26
18. 610 ÷
410 40. 5
6 ÷14
19. 610 ÷
810 41. 2
9 ÷56
20. 712 ÷
212 42.
59 ÷
16
21. 612 ÷
912 43.
12 ÷
17
22. 412 ÷
1112 44. 5
7 ÷12
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Division of Fractions—Round 1 [KEY]
Directions: Evaluate each expression and simplify. Use blank spaces to create like units, where applicable.
1. 9 ones ÷ 3 ones 𝟗𝟗𝟑𝟑 = 𝟑𝟑 23.
610 ÷
410
𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐
2. 9 ÷ 3 𝟗𝟗𝟑𝟑 = 𝟑𝟑 24. 6
10 ÷25 =
610 ÷ 10
𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐
3. 9 tens ÷ 3 tens 𝟗𝟗𝟑𝟑 = 𝟑𝟑 25. 10
12 ÷5
12 𝟏𝟏𝟏𝟏𝟓𝟓 = 𝟐𝟐
4. 90 ÷ 30 𝟗𝟗𝟑𝟑 = 𝟑𝟑 26. 5
6 ÷5
12 = 12 ÷5
12 𝟏𝟏𝟏𝟏𝟓𝟓 = 𝟐𝟐
5. 9 hundreds ÷ 3 hundreds 𝟗𝟗𝟑𝟑 = 𝟑𝟑 27. 10
12 ÷3
12 𝟏𝟏𝟏𝟏𝟑𝟑 = 𝟑𝟑
𝟏𝟏𝟑𝟑
6. 900 ÷ 300 𝟗𝟗𝟑𝟑 = 𝟑𝟑 28. 10
12 ÷14 =
1012 ÷ 12
𝟏𝟏𝟏𝟏𝟑𝟑 = 𝟑𝟑
𝟏𝟏𝟑𝟑
7. 9 halves ÷ 3 halves 𝟗𝟗𝟑𝟑 = 𝟑𝟑 29. 5
6 ÷3
12 = 12 ÷3
12 𝟏𝟏𝟏𝟏𝟑𝟑 = 𝟑𝟑
𝟏𝟏𝟑𝟑
8. 92 ÷
32
𝟗𝟗𝟑𝟑 = 𝟑𝟑 30.
510 ÷
210
𝟓𝟓𝟐𝟐 = 𝟐𝟐
𝟏𝟏𝟐𝟐
9. 9 fourths ÷ 3 fourths 𝟗𝟗𝟑𝟑 = 𝟑𝟑 31. 5
10 ÷15 =
510 ÷ 10
𝟓𝟓𝟐𝟐 = 𝟐𝟐
𝟏𝟏𝟐𝟐
10. 94 ÷
34
𝟗𝟗𝟑𝟑 = 𝟑𝟑 32. 1
2 ÷2
10 = 10 ÷2
10 𝟓𝟓𝟐𝟐 = 𝟐𝟐
𝟏𝟏𝟐𝟐
11. 98 ÷
38
𝟗𝟗𝟑𝟑 = 𝟑𝟑 33. 1
2 ÷24
𝟐𝟐𝟐𝟐 = 𝟏𝟏
12. 23 ÷
13
𝟐𝟐𝟏𝟏 = 𝟐𝟐 34.
34 ÷
28 𝟑𝟑
13. 13 ÷
23
𝟏𝟏𝟐𝟐 35.
12 ÷
38
𝟒𝟒𝟑𝟑 = 𝟏𝟏
𝟏𝟏𝟑𝟑
14. 67 ÷
27
𝟔𝟔𝟐𝟐 = 𝟑𝟑 36. 1
2 ÷15 = 10 ÷ 10
𝟓𝟓𝟐𝟐 = 𝟐𝟐
𝟏𝟏𝟐𝟐
15. 57 ÷
27
𝟓𝟓𝟐𝟐 = 𝟐𝟐
𝟏𝟏𝟐𝟐 37.
24 ÷
13
𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐
16. 37 ÷
47
𝟑𝟑𝟒𝟒 38.
14 ÷
46
𝟑𝟑𝟖𝟖
17. 6
10 ÷2
10 𝟔𝟔𝟐𝟐 = 𝟑𝟑 39.
34 ÷
26
𝟗𝟗𝟒𝟒 = 𝟐𝟐
𝟏𝟏𝟒𝟒
18. 6
10 ÷4
10 𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐 40. 5
6 ÷14
𝟏𝟏𝟏𝟏𝟑𝟑 = 𝟑𝟑
𝟏𝟏𝟑𝟑
19. 6
10 ÷8
10 𝟔𝟔𝟖𝟖 =
𝟑𝟑𝟒𝟒 41. 2
9 ÷56
𝟒𝟒𝟏𝟏𝟓𝟓
20. 712 ÷
212
𝟑𝟑𝟐𝟐 = 𝟑𝟑
𝟏𝟏𝟐𝟐 42.
59 ÷
16
𝟏𝟏𝟓𝟓𝟑𝟑 = 𝟓𝟓
21. 612 ÷
912
𝟔𝟔𝟗𝟗 =
𝟐𝟐𝟑𝟑 43.
12 ÷
17
𝟑𝟑𝟐𝟐 = 𝟑𝟑
𝟏𝟏𝟐𝟐
22. 412 ÷
1112
𝟒𝟒𝟏𝟏𝟏𝟏 44. 5
7 ÷12
𝟏𝟏𝟏𝟏𝟑𝟑 = 𝟏𝟏
𝟑𝟑𝟑𝟑
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Number Correct: ______ Improvement: ______
Division of Fractions—Round 2
Directions: Evaluate each expression and simplify. Use blank spaces to create like units, where applicable.
1. 12 ones ÷ 2 ones 23. 612 ÷
412
2. 12 ÷ 2 24. 612 ÷
26 =
612 ÷ 12
3. 12 tens ÷ 2 tens 25. 814 ÷
714
4. 120 ÷ 20 26. 814 ÷
12 =
814 ÷ 14
5. 12 hundreds ÷ 2 hundreds 27. 1114 ÷
214
6. 1,200 ÷ 200 28. 1114 ÷
17 =
1114 ÷ 14
7. 12 halves ÷ 2 halves 29. 17 ÷
614 = 14 ÷
614
8. 122 ÷
22 30.
718 ÷
318
9. 12 fourths ÷ 3 fourths 31. 718 ÷
16 =
718 ÷ 18
10. 124 ÷
34 32. 1
3 ÷1218 = 18 ÷
1218
11. 128 ÷
38 33.
16 ÷
418
12. 24 ÷
14 34.
412 ÷
86
13. 14 ÷
24 35.
13 ÷
315
14. 45 ÷
25 36. 2
6 ÷19 = 18 ÷ 18
15. 25 ÷
45 37.
16 ÷
49
16. 35 ÷
45 38.
23 ÷
34
17. 68 ÷
28 39.
13 ÷
35
18. 68 ÷
48 40.
17 ÷
12
19. 68 ÷
58 41. 5
6 ÷29
20. 6
10 ÷2
10 42. 59 ÷
26
21. 7
10 ÷8
10 43. 56 ÷
49
22. 4
10 ÷7
10 44. 12 ÷
45
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6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Division of Fractions—Round 2 [KEY]
Directions: Evaluate each expression and simplify. Use blank spaces to create like units, where applicable.
1. 12 ones ÷ 2 ones 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 23. 6
12 ÷4
12 𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐
2. 12 ÷ 2 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 24. 6
12 ÷26 =
612 ÷ 12
𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐
3. 12 tens ÷ 2 tens 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 25. 8
14 ÷7
14 𝟖𝟖𝟑𝟑 = 𝟏𝟏
𝟏𝟏𝟑𝟑
4. 120 ÷ 20 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 26. 8
14 ÷12 =
814 ÷ 14
𝟖𝟖𝟑𝟑 = 𝟏𝟏
𝟏𝟏𝟑𝟑
5. 12 hundreds ÷ 2 hundreds 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 27. 11
14 ÷2
14 𝟏𝟏𝟏𝟏𝟐𝟐 = 𝟓𝟓
𝟏𝟏𝟐𝟐
6. 1,200 ÷ 200 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 28. 11
14 ÷17 =
1114 ÷ 14
𝟏𝟏𝟏𝟏𝟐𝟐 = 𝟓𝟓
𝟏𝟏𝟐𝟐
7. 12 halves ÷ 2 halves 𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 29. 1
7 ÷6
14 = 14 ÷6
14 𝟐𝟐𝟔𝟔 =
𝟏𝟏𝟑𝟑
8. 122 ÷
22
𝟏𝟏𝟐𝟐𝟐𝟐 = 𝟔𝟔 30.
718 ÷
318
𝟑𝟑𝟑𝟑 = 𝟐𝟐
𝟏𝟏𝟑𝟑
9. 12 fourths ÷ 3 fourths 𝟏𝟏𝟐𝟐𝟑𝟑 = 𝟒𝟒 31. 7
18 ÷16 =
718 ÷ 18
𝟑𝟑𝟑𝟑 = 𝟐𝟐
𝟏𝟏𝟑𝟑
10. 124 ÷
34
𝟏𝟏𝟐𝟐𝟑𝟑 = 𝟒𝟒 32. 1
3 ÷1218 = 18 ÷
1218
𝟔𝟔𝟏𝟏𝟐𝟐 =
𝟏𝟏𝟐𝟐
11. 128 ÷
38
𝟏𝟏𝟐𝟐𝟑𝟑 = 𝟒𝟒 33.
16 ÷
418
𝟑𝟑𝟒𝟒
12. 24 ÷
14
𝟐𝟐𝟏𝟏 = 𝟐𝟐 34.
412 ÷
86
𝟒𝟒𝟏𝟏𝟔𝟔 =
𝟏𝟏𝟒𝟒
13. 14 ÷
24
𝟏𝟏𝟐𝟐 35.
13 ÷
315
𝟓𝟓𝟑𝟑 = 𝟏𝟏
𝟐𝟐𝟑𝟑
14. 45 ÷
25
𝟒𝟒𝟐𝟐 = 𝟐𝟐 36. 2
6 ÷19 = 18 ÷ 18
𝟔𝟔𝟐𝟐 = 𝟑𝟑
15. 25 ÷
45
𝟐𝟐𝟒𝟒 =
𝟏𝟏𝟐𝟐 37.
16 ÷
49
𝟑𝟑𝟖𝟖
16. 35 ÷
45
𝟑𝟑𝟒𝟒 38.
23 ÷
34
𝟖𝟖𝟗𝟗
17. 68 ÷
28
𝟔𝟔𝟐𝟐 = 𝟑𝟑 39.
13 ÷
35
𝟓𝟓𝟗𝟗
18. 68 ÷
48
𝟔𝟔𝟒𝟒 = 𝟏𝟏
𝟏𝟏𝟐𝟐 40.
17 ÷
12
𝟐𝟐𝟑𝟑
19. 68 ÷
58
𝟔𝟔𝟓𝟓 = 𝟏𝟏
𝟏𝟏𝟓𝟓 41. 5
6 ÷29
𝟏𝟏𝟓𝟓𝟒𝟒 = 𝟑𝟑
𝟑𝟑𝟒𝟒
20. 6
10 ÷2
10 𝟔𝟔𝟐𝟐 = 𝟑𝟑 42.
59 ÷
26
𝟏𝟏𝟏𝟏𝟔𝟔 = 𝟏𝟏
𝟐𝟐𝟑𝟑
21. 7
10 ÷8
10 𝟑𝟑𝟖𝟖 43. 5
6 ÷49
𝟏𝟏𝟓𝟓𝟖𝟖 = 𝟏𝟏
𝟑𝟑𝟖𝟖
22. 4
10 ÷7
10 𝟒𝟒𝟑𝟑 44.
12 ÷
45
𝟓𝟓𝟖𝟖
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6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
Lesson 3: The Relationship of Multiplication and Addition
Student Outcomes
� Students build and clarify the relationship of multiplication and addition by evaluating identities such as 3 𝑔𝑔 = 𝑔𝑔 + 𝑔𝑔 + 𝑔𝑔.
Lesson Notes Students continue to use the squares from Lessons 1 and 2 to create tape diagrams. Each pair of students needs 30 squares to complete the activities.
Classwork Opening Exercise (5 minutes)
Opening Exercise
Write two different expressions that can be depicted by the tape diagram shown. One expression should include addition, while the other should include multiplication.
a.
Possible answers: 𝟑𝟑 + 𝟑𝟑 + 𝟑𝟑 or 𝟑𝟑 × 𝟑𝟑
b.
Possible answers: 𝟖𝟖+ 𝟖𝟖 or 𝟐𝟐× 𝟖𝟖
c.
Possible answers: 𝟓𝟓 + 𝟓𝟓 + 𝟓𝟓 or 𝟑𝟑 × 𝟓𝟓
Discussion (17 minutes)
Provide each pair of students with a collection of 30 squares, which they use to create tape diagrams throughout the lesson.
� One partner builds a tape diagram to represent the expression 2 + 2 + 2 + 2, while the other partner builds a tape diagram to represent 4 × 2. à
à
2 2 2 2 + + +
4 4
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6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
� What do you notice about the two tape diagrams you created?
à Possible answer: Although the tape diagrams represent two different expressions, they each have the same number of squares.
� Why are the two tape diagrams the same? What does it say about the value of the expressions?
à The two tape diagrams are the same because the values of the expressions are equivalent. � If both expressions yield the same value, is there an advantage to using one over the other?
à Answers will vary. � Since each tape diagram has the same number of squares, can we say the two expressions are equivalent?
Why or why not?
à Possible answer: The two expressions are equivalent because they represent the same value. When evaluated, both expressions will equal 8.
� Therefore, 2 + 2 + 2 + 2 = 4 × 2. Let’s build a new set of tape diagrams. One partner builds a tape diagram
to represent the expression 3 × 4, while the other partner builds a tape diagram to represent the expression
4 + 4 + 4.
à
� Is 3 × 4 equivalent to 4 + 4 + 4? Why or why not?
à Possible answer: The two expressions are equivalent because when each of them is evaluated, they equal 12, as we can see with our tape diagrams.
� Using variables, write an equation to show the relationship of multiplication and addition.
Provide students with time to create an equation.
à Possible answer: 3𝑔𝑔 = 𝑔𝑔 + 𝑔𝑔 + 𝑔𝑔. Emphasize that each 𝑔𝑔 represents the same number.
� 3𝑔𝑔 is the same as writing 3 × 𝑔𝑔, but we no longer use the × for multiplication because it looks like a variable
and can become confusing. When a number is next to a variable with no sign, multiplication is implied.
� In the two previous lessons, we talked about identities. Is the equation 3𝑔𝑔 = 𝑔𝑔 + 𝑔𝑔 + 𝑔𝑔 also an identity? Why
or why not?
à Possible answer: The equation 3𝑔𝑔 = 𝑔𝑔 + 𝑔𝑔 + 𝑔𝑔 is an identity because we can replace 𝑔𝑔 with any number, and the equation will always be true.
𝑔𝑔 + 𝑔𝑔 + 𝑔𝑔
𝑔𝑔
4
1st group
2nd group
3rd group
MP.2
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6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
Exercises (15 minutes)
Students can continue to work with the given squares and with their partners to answer the following questions.
Exercises
1. Write the addition sentence that describes the model and the multiplication sentence that describes the model.
𝟓𝟓 + 𝟓𝟓 + 𝟓𝟓 and 𝟑𝟑× 𝟓𝟓
2. Write an equivalent expression to demonstrate the relationship of multiplication and addition.
a. 𝟔𝟔 + 𝟔𝟔
𝟐𝟐 × 𝟔𝟔
b. 𝟑𝟑 + 𝟑𝟑 + 𝟑𝟑 + 𝟑𝟑+ 𝟑𝟑 + 𝟑𝟑
𝟔𝟔 × 𝟑𝟑
c. 𝟒𝟒 + 𝟒𝟒 + 𝟒𝟒 + 𝟒𝟒+ 𝟒𝟒
𝟓𝟓 × 𝟒𝟒
d. 𝟔𝟔 × 𝟐𝟐
𝟐𝟐 + 𝟐𝟐 + 𝟐𝟐 + 𝟐𝟐+ 𝟐𝟐 + 𝟐𝟐
e. 𝟒𝟒 × 𝟔𝟔
𝟔𝟔 + 𝟔𝟔 + 𝟔𝟔 + 𝟔𝟔
f. 𝟑𝟑 × 𝟗𝟗
𝟗𝟗 + 𝟗𝟗 + 𝟗𝟗
g. 𝒉𝒉 + 𝒉𝒉 + 𝒉𝒉 + 𝒉𝒉+ 𝒉𝒉
𝟓𝟓𝒉𝒉
h. 𝟔𝟔
+ + + + +
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Lesson 3: The Relationship of Multiplication and Addition
3. Roberto is not familiar with tape diagrams and believes that he can show the relationship of multiplication and addition on a number line. Help Roberto demonstrate that the expression 𝟑𝟑 × 𝟐𝟐 is equivalent to 𝟐𝟐 + 𝟐𝟐 + 𝟐𝟐 on a number line.
Possible answer: The first number line shows that there are 𝟑𝟑 groups of 𝟐𝟐, resulting in 𝟔𝟔. The second number line shows the sum of 𝟐𝟐 + 𝟐𝟐 + 𝟐𝟐, resulting in 𝟔𝟔.
Since both number lines start at 𝟏𝟏 and end at 𝟔𝟔, the expressions are equivalent.
4. Tell whether the following equations are true or false. Then, explain your reasoning. a. 𝒙𝒙 + 𝟔𝟔𝒈𝒈 − 𝟔𝟔𝒈𝒈 = 𝒙𝒙
The equation is true because it demonstrates the addition identity.
b. 𝟐𝟐𝒇𝒇 − 𝟒𝟒𝒆𝒆 + 𝟒𝟒𝒆𝒆 = 𝟐𝟐𝒇𝒇
The equation is true because it demonstrates the subtraction identity. 5. Write an equivalent expression to demonstrate the relationship between addition and multiplication.
a. 𝟔𝟔 + 𝟔𝟔 + 𝟔𝟔 + 𝟔𝟔+ 𝟒𝟒 + 𝟒𝟒 + 𝟒𝟒
𝟒𝟒 × 𝟔𝟔 + 𝟑𝟑 × 𝟒𝟒
b. 𝒅𝒅 + 𝒅𝒅 + 𝒅𝒅+ 𝒘𝒘 + 𝒘𝒘 + 𝒘𝒘 + 𝒘𝒘 + 𝒘𝒘
𝟑𝟑𝒅𝒅+ 𝟓𝟓𝒘𝒘
c. 𝒂𝒂 + 𝒂𝒂 + 𝒃𝒃 + 𝒃𝒃 + 𝒃𝒃 + 𝒄𝒄 + 𝒄𝒄 + 𝒄𝒄 + 𝒄𝒄
𝟐𝟐𝒂𝒂 + 𝟑𝟑𝒃𝒃 + 𝟒𝟒𝒄𝒄
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
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Lesson 3: The Relationship of Multiplication and Addition
Closing 4 minutes)
� Create a diagram that models 3 groups of size 𝑏𝑏. à
� Write two equivalent expressions that represent this model. à Possible answers: 3𝑏𝑏, 𝑏𝑏 + 𝑏𝑏 + 𝑏𝑏
� Peter says that since the addition expression yields the same value as the multiplication expression, he will always choose to use the addition expression when solving these types of problems. Convince Peter that he may want to reconsider his position. à Answers will vary but should include the idea that when the group size is large, it is more advantageous
to multiply instead of add.
Exit Ticket 4 minutes)
𝑏𝑏 𝑏𝑏 𝑏𝑏
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6•4 Lesson 3
Lesson 3: The Relationship of Multiplication and Addition
Name Date
Lesson 3: The Relationship of Multiplication and Addition
Exit Ticket Write an equivalent expression to show the relationship of multiplication and addition. 1. 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 2. 4 × 9
3. 6 + 6 + 6 4. ݄ 5. ݆ + ݆ + ݆ + ݆ + ݆
ݑ .6 + ݑ + ݑ + ݑ + ݑ + ݑ + ݑ + ݑ + ݑ + ݑ
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Lesson 3: The Relationship of Multiplication and Addition
Exit Ticket Sample Solutions
Write an equivalent expression to show the relationship of multiplication and addition.
1. 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖+ 𝟖𝟖
𝟗𝟗 × 𝟖𝟖
2. 𝟒𝟒 × 𝟗𝟗
𝟗𝟗+ 𝟗𝟗+ 𝟗𝟗+ 𝟗𝟗
3. 𝟔𝟔+ 𝟔𝟔+ 𝟔𝟔
𝟑𝟑 × 𝟔𝟔
4. 𝟑𝟑𝒉𝒉
𝒉𝒉+ 𝒉𝒉+ 𝒉𝒉+ 𝒉𝒉+ 𝒉𝒉+ 𝒉𝒉+ 𝒉𝒉
5. + + + +
𝟓𝟓
6. + + + + + + + + +
𝟏𝟏𝟏𝟏
Problem Set Sample Solutions
Write an equivalent expression to show the relationship of multiplication and addition.
1. 𝟏𝟏𝟏𝟏+ 𝟏𝟏𝟏𝟏+ 𝟏𝟏𝟏𝟏
𝟑𝟑 × 𝟏𝟏𝟏𝟏
2. 𝟒𝟒+ 𝟒𝟒+ 𝟒𝟒+ 𝟒𝟒+ 𝟒𝟒+ 𝟒𝟒+ 𝟒𝟒
𝟑𝟑 × 𝟒𝟒
3. 𝟖𝟖 × 𝟐𝟐
𝟐𝟐+ 𝟐𝟐+ 𝟐𝟐+ 𝟐𝟐+ 𝟐𝟐+ 𝟐𝟐+ 𝟐𝟐+ 𝟐𝟐
4. 𝟑𝟑 × 𝟗𝟗
𝟗𝟗+ 𝟗𝟗+ 𝟗𝟗
5. 𝟔𝟔
+ + + + +
6. 𝒅𝒅+ 𝒅𝒅+ 𝒅𝒅+ 𝒅𝒅+ 𝒅𝒅
𝟓𝟓𝒅𝒅
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4: The Relationship of Division and Subtraction
Lesson 4: The Relationship of Division and Subtraction
Student Outcomes
� Students build and clarify the relationship of division and subtraction by determining that 12 ÷ 𝑥𝑥 = 4 means 12 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 = 0.
Lesson Notes Students continue to use the squares from Lessons 1–3 to create tape diagrams. Each pair of students needs 30 squares to complete the activities.
Classwork Discussion (20 minutes)
Provide each pair of students with a collection of 30 squares so they can use these squares to create tape diagrams throughout the lesson.
� Build a tape diagram that has 20 squares.
� Divide the tape diagram into 4 equal sections.
� How many squares are in each of the 4 sections?
à 5 � Write a number sentence to demonstrate what happened.
à 20 ÷ 4 = 5 � Combine your squares again to have a tape diagram with 20 squares.
� Now, subtract 4 squares from your tape diagram.
� Write an expression to demonstrate what happened.
à 20 − 4 � Subtract 4 more squares, and alter your expression to represent the new tape diagram.
à 20 − 4− 4
� Subtract 4 more squares, and alter your expression to represent the new tape diagram.
à 20 − 4− 4 − 4
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𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥
20 ÷ 𝑥𝑥
𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥
20− 𝑥𝑥
𝑥𝑥 𝑥𝑥 𝑥𝑥
20− 𝑥𝑥 − 𝑥𝑥
𝑥𝑥 𝑥𝑥
20− 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥
𝑥𝑥
20− 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥
20− 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥
� Subtract 4 more squares, and alter your expression to represent the new tape diagram.
à 20 − 4− 4 − 4 − 4
� Last time. Subtract 4 more squares, and alter your expression to an equation in order to represent a number sentence showing the complete transformation of the tape diagram. à No squares should remain. à 20 − 4− 4 − 4 − 4 − 4 = 0
� Let’s take a look at the process we took to determine the difference to be zero.
Discuss the process step-by-step to determine that the number of times the divisor was subtracted from the dividend is the same number as the quotient.
� Do you recognize a relationship between 20 ÷ 4 = 5 and 20 − 4 − 4 − 4− 4 − 4 = 0? If so, what is it? à Possible answer: If you subtract the divisor from the dividend 5 times (the quotient), there will be no
remaining squares. � Let’s take a look at a similar problem, 20 ÷ 5 = 4, to see if the quotient
is the number of times the divisor is subtracted from the dividend. � Let’s create a number sentence when we subtract the divisor.
à 20 − 5 − 5 − 5 − 5 = 0
Discuss the process to determine that the number of times the divisor is subtracted from the dividend is the same number as the quotient.
� Determine the relationship between 20 ÷ 5 = 4 and 20 − 5 − 5 − 5− 5 = 0. à 20 ÷ 5 = 4 can be interpreted as subtracting 4 fives from 20 is
0, or 20 − 5 − 5− 5 − 5 = 0. � Is this relationship always true? Let’s try to prove that it is.
Model the following set of tape diagrams with leading questions for discussion.
� 𝑥𝑥 is a number. What does 20 ÷ 𝑥𝑥 = 5 mean? à Exactly five 𝑥𝑥’s can be subtracted from twenty.
� What must 𝑥𝑥 be in this division sentence? à 4
MP.8
MP.8
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𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥
20 ÷ 𝑥𝑥 = 5
𝑥𝑥 𝑥𝑥 𝑥𝑥
20− 𝑥𝑥 or 20− 5
𝑥𝑥 𝑥𝑥
20− 𝑥𝑥 − 𝑥𝑥 or 20− 5 − 5
𝑥𝑥
20 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 or 20− 5 − 5− 5
20− 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 = 0 or 20− 5− 5 − 5 − 5 = 0
� Let’s keep taking 𝑥𝑥 away until we reach zero.
Model taking each 𝑥𝑥 away and creating subtraction expressions to record.
� Build a subtraction expression. à 20 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 = 0
� Is 20 − 4 − 4 − 4 − 4 − 4 = 0? à Yes
� Develop two equations using numbers and letters to show the relationship of division and subtraction.
à Possible answers: 20 ÷ 𝑥𝑥 = 5 and 20 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 = 0
� Or 20 ÷ 𝑥𝑥 = 5 means that 5 can be subtracted exactly 𝑥𝑥 number of times from 20. Is it true when 𝑥𝑥 = 4?
� To determine if 𝑥𝑥 = 4, let’s keep taking 𝑥𝑥 away until we reach zero.
Model taking each 𝑥𝑥 away and creating subtraction expressions to record by following the diagram to the right.
� Build a subtraction equation. à 20 − 5 − 5 − 5 − 5 = 0
� What two operations are we relating in the problems we completed? à Division and subtraction
Exercise ( minutes)
Students work in pairs to answer the following questions.
Build subtraction equations using the indicated equations. The first example has been completed for you.
Division Equation
Divisor Indicates the Size of the Unit Tape Diagram What is
𝒙𝒙, , ?
𝟏𝟏𝟐𝟐÷ 𝒙𝒙 = 𝟒𝟒 𝟏𝟏𝟐𝟐 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 = 𝟏𝟏
𝒙𝒙 = 𝟑𝟑
𝟏𝟏𝟖𝟖÷ 𝒙𝒙 = 𝟑𝟑 𝟏𝟏𝟖𝟖 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 = 𝟏𝟏
𝒙𝒙 = 𝟔𝟔
𝟑𝟑𝟓𝟓 ÷ = 𝟓𝟓 𝟑𝟑𝟓𝟓 − − − − − = 𝟏𝟏
= 𝟑𝟑
𝟒𝟒𝟐𝟐÷ = 𝟔𝟔 𝟒𝟒𝟐𝟐 − − − − − − = 𝟏𝟏
= 𝟑𝟑
MP.2
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4: The Relationship of Division and Subtraction
Division
Equation Divisor Indicates the Number of Units Tape Diagram
What is
𝒙𝒙, , ?
𝟏𝟏𝟐𝟐÷ 𝒙𝒙 = 𝟒𝟒 𝟏𝟏𝟐𝟐 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 = 𝟏𝟏
𝒙𝒙 = 𝟑𝟑
𝟏𝟏𝟖𝟖÷ 𝒙𝒙 = 𝟑𝟑 𝟏𝟏𝟖𝟖 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑− 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑 = 𝟏𝟏
𝒙𝒙 = 𝟔𝟔
𝟑𝟑𝟓𝟓÷ = 𝟓𝟓 𝟑𝟑𝟓𝟓 − 𝟓𝟓 − 𝟓𝟓− 𝟓𝟓 − 𝟓𝟓 − 𝟓𝟓− 𝟓𝟓 − 𝟓𝟓 = 𝟏𝟏
= 𝟑𝟑
𝟒𝟒𝟐𝟐÷ = 𝟔𝟔 𝟒𝟒𝟐𝟐 − 𝟔𝟔 − 𝟔𝟔− 𝟔𝟔 − 𝟔𝟔 − 𝟔𝟔− 𝟔𝟔 − 𝟔𝟔 = 𝟏𝟏
= 𝟑𝟑
Exercise 2 (5 minutes)
Exercise 2
Answer each question using what you have learned about the relationship of division and subtraction.
a. If 𝟏𝟏𝟐𝟐÷ 𝒙𝒙 = 𝟑𝟑, how many times would 𝒙𝒙 have to be subtracted from 𝟏𝟏𝟐𝟐 in order for the answer to be zero?
What is the value of 𝒙𝒙?
𝟑𝟑; 𝒙𝒙 = 𝟒𝟒
b. 𝟑𝟑𝟔𝟔 − 𝒇𝒇 − 𝒇𝒇 − 𝒇𝒇 − 𝒇𝒇 = 𝟏𝟏. Write a division sentence for this repeated subtraction sentence. What is the value
of 𝒇𝒇?
𝟑𝟑𝟔𝟔÷ 𝟒𝟒 = 𝒇𝒇 or 𝟑𝟑𝟔𝟔÷ 𝒇𝒇 = 𝟒𝟒; 𝒇𝒇 = 𝟗𝟗
c. If 𝟐𝟐𝟒𝟒÷ 𝒃𝒃 = 𝟏𝟏𝟐𝟐, which number is being subtracted 𝟏𝟏𝟐𝟐 times in order for the answer to be zero?
Two
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Closing (5 minutes)
Display the graphic organizer provided at the end of the lesson. Copies of the organizer can be made for students to follow along and record.
� In each of the circles, we can place an operation to satisfy the organizer. In the last four lessons, we have discovered that each operation has a relationship with other operations, whether they are inverse operations or they are repeats of another.
Place the addition symbol in the upper left-hand circle. � Let’s start with addition. What is the inverse operation of addition?
à Subtraction
Place the subtraction symbol in the upper right-hand circle.
� After our discussion today, repeated subtraction can be represented by which operation?
à Division
Place the division symbol in the lower right-hand circle.
� Which operation is the inverse of division?
à Multiplication
Place the multiplication symbol in the lower left-hand circle.
� Let’s see if this is correct. Is multiplication the repeat operation of addition?
à Yes
Understanding the relationships of operations is going to be instrumental when solving equations later in this unit.
Exit Ticket (5 minutes)
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4: The Relationship of Division and Subtraction
Name Date
Lesson 4: The Relationship of Division and Subtraction
Exit Ticket 1. Represent 56 ÷ 8 = 7 using subtraction. Explain your reasoning.
2. Explain why 30 ÷ 𝑥𝑥 = 6 is the same as 30− 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 − 𝑥𝑥 = 0. What is the value of 𝑥𝑥 in this example?
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Exit Ticket Sample Solutions
. Represent 𝟓𝟓𝟔𝟔 ÷ 𝟖𝟖 = 𝟑𝟑 using subtraction. Explain your reasoning.
𝟓𝟓𝟔𝟔 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑− 𝟑𝟑 − 𝟑𝟑 = 𝟏𝟏 because
𝟓𝟓𝟔𝟔 − 𝟑𝟑 = 𝟒𝟒𝟗𝟗; 𝟒𝟒𝟗𝟗 − 𝟑𝟑 = 𝟒𝟒𝟐𝟐; 𝟒𝟒𝟐𝟐 − 𝟑𝟑 = 𝟑𝟑𝟓𝟓; 𝟑𝟑𝟓𝟓 − 𝟑𝟑 = 𝟐𝟐𝟖𝟖; 𝟐𝟐𝟖𝟖 − 𝟑𝟑 = 𝟐𝟐𝟏𝟏; 𝟐𝟐𝟏𝟏 − 𝟑𝟑 = 𝟏𝟏𝟒𝟒; 𝟏𝟏𝟒𝟒 − 𝟑𝟑 = 𝟑𝟑; 𝟑𝟑 − 𝟑𝟑 = 𝟏𝟏.
OR
𝟓𝟓𝟔𝟔 − 𝟖𝟖 − 𝟖𝟖 − 𝟖𝟖 − 𝟖𝟖 − 𝟖𝟖 − 𝟖𝟖− 𝟖𝟖 = 𝟏𝟏 because
𝟓𝟓𝟔𝟔 − 𝟖𝟖 = 𝟒𝟒𝟖𝟖; 𝟒𝟒𝟖𝟖 − 𝟖𝟖 = 𝟒𝟒𝟏𝟏; 𝟒𝟒𝟏𝟏 − 𝟖𝟖 = 𝟑𝟑𝟐𝟐; 𝟑𝟑𝟐𝟐 − 𝟖𝟖 = 𝟐𝟐𝟒𝟒; 𝟐𝟐𝟒𝟒 − 𝟖𝟖 = 𝟏𝟏𝟔𝟔; 𝟏𝟏𝟔𝟔 − 𝟖𝟖 = 𝟖𝟖; 𝟖𝟖 − 𝟖𝟖 = 𝟏𝟏.
2. Explain why 𝟑𝟑𝟏𝟏÷ 𝒙𝒙 = 𝟔𝟔 is the same as 𝟑𝟑𝟏𝟏 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 = 𝟏𝟏. What is the value of 𝒙𝒙 in this example?
𝟑𝟑𝟏𝟏 ÷ 𝟓𝟓 = 𝟔𝟔, so 𝒙𝒙 = 𝟓𝟓. When I subtract 𝟓𝟓 from 𝟑𝟑𝟏𝟏 six times, the result is zero. Division is a repeat operation of subtraction.
Problem Set Sample Solutions
Build subtraction equations using the indicated equations.
Division Equation Divisor Indicates the Size of the Unit Tape Diagram
What is
𝒙𝒙, , ?
. 𝟐𝟐𝟒𝟒÷ 𝒙𝒙 = 𝟒𝟒 𝟐𝟐𝟒𝟒 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 = 𝟏𝟏
𝒙𝒙 = 𝟔𝟔
2. 𝟑𝟑𝟔𝟔÷ 𝒙𝒙 = 𝟔𝟔 𝟑𝟑𝟔𝟔 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 − 𝒙𝒙 = 𝟏𝟏
𝒙𝒙 = 𝟔𝟔
. 𝟐𝟐𝟖𝟖 ÷ = 𝟑𝟑 𝟐𝟐𝟖𝟖 − − − − − − − = 𝟏𝟏
= 𝟒𝟒
4. 𝟑𝟑𝟏𝟏 ÷ = 𝟓𝟓 𝟑𝟑𝟏𝟏 − − − − − = 𝟏𝟏 = 𝟔𝟔
5. 𝟏𝟏𝟔𝟔÷ = 𝟒𝟒 𝟏𝟏𝟔𝟔 − − − − = 𝟏𝟏 = 𝟒𝟒
A STORY OF RATIOS
47
©20 15 G re at Min ds. eureka-math.org G6-M4-TE-1.3.0-08.2015
6•4 4
4: The Relationship of Division and Subtraction
Division Equation
Divisor Indicates the Number of Units Tape Diagram
What is
𝒙𝒙, , ?
. 𝟐𝟐𝟒𝟒÷ 𝒙𝒙 = 𝟒𝟒 𝟐𝟐𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 = 𝟏𝟏
𝒙𝒙 = 𝟔𝟔
2. 𝟑𝟑𝟔𝟔÷ 𝒙𝒙 = 𝟔𝟔 𝟑𝟑𝟔𝟔 − 𝟔𝟔 − 𝟔𝟔 − 𝟔𝟔 − 𝟔𝟔 − 𝟔𝟔 − 𝟔𝟔 = 𝟏𝟏 𝒙𝒙 = 𝟔𝟔
. 𝟐𝟐𝟖𝟖÷ = 𝟑𝟑 𝟐𝟐𝟖𝟖 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑 − 𝟑𝟑 = 𝟏𝟏 = 𝟒𝟒
4. 𝟑𝟑𝟏𝟏÷ = 𝟓𝟓 𝟑𝟑𝟏𝟏 − 𝟓𝟓 − 𝟓𝟓 − 𝟓𝟓 − 𝟓𝟓 − 𝟓𝟓 − 𝟓𝟓 = 𝟏𝟏 = 𝟔𝟔
5. 𝟏𝟏𝟔𝟔÷ = 𝟒𝟒 𝟏𝟏𝟔𝟔 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 − 𝟒𝟒 = 𝟏𝟏
= 𝟒𝟒
A STORY OF RATIOS
48
©20 15 G re at Min ds. eureka-math.org G6-M4-TE-1.3.0-08.2015
6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Number Correct: ______
Division of Fractions—Round 1
Directions: Evaluate each expression and simplify. Use blank spaces to create like units, where applicable.
1. 9 ones ÷ 3 ones 23. 610 ÷
410
2. 9 ÷ 3 24. 610 ÷
25 =
610 ÷ 10
3. 9 tens ÷ 3 tens 25. 1012 ÷
512
4. 90 ÷ 30 26. 56 ÷
512 = 12 ÷
512
5. 9 hundreds ÷ 3 hundreds 27. 1012 ÷
312
6. 900 ÷ 300 28. 1012 ÷
14 =
1012 ÷ 12
7. 9 halves ÷ 3 halves 29. 56 ÷
312 = 12 ÷
312
8. 92 ÷
32
30. 510 ÷
210
9. 9 fourths ÷ 3 fourths 31. 510 ÷
15 =
510 ÷ 10
10. 94 ÷
34
32. 12 ÷
210 = 10 ÷
210
11. 98 ÷
38
33. 12 ÷
24
12. 23 ÷
13
34. 34 ÷
28
13. 13 ÷
23
35. 12 ÷
38
14. 67 ÷
27
36. 12 ÷
15 = 10 ÷ 10
15. 57 ÷
27
37. 24 ÷
13
16. 37 ÷
47
38. 14 ÷
46
17. 610 ÷
210
39. 34 ÷
26
18. 610 ÷
410
40. 56 ÷
14
19. 610 ÷
810
41. 29 ÷
56
20. 712 ÷
212
42. 59 ÷
16
21. 612 ÷
912
43. 12 ÷
17
22. 412 ÷
1112
44. 57 ÷
12
A STORY OF RATIOS
©20 15 G re at Min ds. eureka-math.org G6-M4-TE-1.3.0-08.2015
1
6•4 Lesson 2
Lesson 2: The Relationship of Multiplication and Division
Number Correct: ______ Improvement: ______
Division of Fractions—Round 2
Directions: Evaluate each expression and simplify. Use blank spaces to create like units, where applicable.
1. 12 ones ÷ 2 ones 23. 612 ÷
412
2. 12 ÷ 2 24. 612 ÷
26 =
612 ÷ 12
3. 12 tens ÷ 2 tens 25. 814 ÷
714
4. 120 ÷ 20 26. 814 ÷
12 =
814 ÷ 14
5. 12 hundreds ÷ 2 hundreds 27. 1114 ÷
214
6. 1,200 ÷ 200 28. 1114 ÷
17 =
1114 ÷ 14
7. 12 halves ÷ 2 halves 29. 17 ÷
614 = 14 ÷
614
8. 122 ÷
22 30.
718 ÷
318
9. 12 fourths ÷ 3 fourths 31. 718 ÷
16 =
718 ÷ 18
10. 124 ÷
34 32. 1
3 ÷1218 = 18 ÷
1218
11. 128 ÷
38 33.
16 ÷
418
12. 24 ÷
14 34.
412 ÷
86
13. 14 ÷
24 35.
13 ÷
315
14. 45 ÷
25 36. 2
6 ÷19 = 18 ÷ 18
15. 25 ÷
45 37.
16 ÷
49
16. 35 ÷
45 38.
23 ÷
34
17. 68 ÷
28 39.
13 ÷
35
18. 68 ÷
48 40.
17 ÷
12
19. 68 ÷
58 41. 5
6 ÷29
20. 6
10 ÷2
10 42. 59 ÷
26
21. 7
10 ÷8
10 43. 56 ÷
49
22. 4
10 ÷7
10 44. 12 ÷
45
A STORY OF RATIOS
©20 15 G re at Min ds. eureka-math.org G6-M4-TE-1.3.0-08.2015
2
KEY CONCEPT OVERVIEW
(From Lessons 3-4)SAMPLE PROBLEMS
Write the addition and multiplication expressions that describe the model.
5 + 5 + 5 and 3 × 5
Using the equation 18 ÷ x = 3, write a related subtraction equation, and represent it as a tape diagram. Then, state the value of x.
18 − x − x − x = 0
x = 6
In Topic A, students use a tape diagram to examine relationships between operations. They begin by exploring the relationship between addition and subtraction. Next, they explore the relationships between multiplication and division and multiplication and addition. Students conclude the topic by exploring how subtraction and division are related.
You can expect to see homework that asks your child to do the following: ▪ Fill in the missing part of a number sentence or equation. ▪ Explain why the equations w − x + x = w and w + x − x = w are called identities. ▪ Examine and describe the relationships between operations. ▪ Write an equivalent expression to show a specific relationship. For example, 3 × 9 is equivalent to
9 + 9 + 9, or 3d is equivalent to d + d + d. ▪ From a division equation, write the related subtraction equation, draw the tape diagram, and determine the
value of the variable. (See the Sample Problem.)
G R A D E 6 | M O D U L E 4 | T O P I C A | L E S S O N S 1–4
Additional sample problems with detailed answer steps are found in the Eureka Math Homework Helpers books. Learn more at GreatMinds.org.
For more resources, visit » Eureka.support
TERMS
Equation: A statement indicating that two expressions are equal (e.g., 3 × 4 = 6 × 2 and 5 + x = 20).Equivalent expressions: Expressions that have the same value (e.g., 2 × 6 is equivalent to 4a if a = 3).Expression: A group of numbers, symbols, and operators such as + and − with no equal sign that evaluates to a number (e.g., 2 × 4 and 9n + 7).Identity: An equation that is true no matter what values are substituted for the variables (e.g., w − x + x = w because w and x can be replaced with any numbers, and the equation would remain true).Number sentence: A statement indicating that two numerical expressions are equal (e.g., 8 − 2 = 5 + 1).Variable: A symbol, such as a letter, that is a placeholder for a number.
HOW YOU CAN HELP AT HOME
You can help at home in many ways. Here are some tips to help you get started. ▪ Read this statement with your child: “When a number is multiplied and divided by the same number, the
result is the original number.” For example, 11 × 5 ÷ 5 = 11. Ask your child to write a few examples to show this. Discuss with your child why the equation 3 × 9 ÷ 3 = 9 does not represent this statement. (A number is not multiplied and then divided by the same number. The 3 is multiplied by 9 and then divided by 3, not 9.)
▪ With your child, create a few examples of real-life money situations where the result is the original number. For example, say that you have $10. You spend $5 at the store. Then you find $5 on the sidewalk. How do your examples relate to the identities w − x + x = w or w + x − x = w? (10 – 5 + 5 = 10)
G R A D E 6 | M O D U L E 4 | T O P I C A | L E S S O N S 1–4
For more resources, visit» Eureka.support © 2016, GREAT MINDS®
MUESTRAS DE PROBLEMAS (Tomados de las Lecciones 3 y 4)
RESUMEN DE CONCEPTOS CLAVE
Escribe las expresiones de suma y multiplicación que describen la representación.
5 + 5 + 5 y 3 × 5
Usando la ecuación 18 ÷ x = 3, escribe una ecuación relacionada de resta y represéntala como un diagrama de cinta. Después expresa el valor de x.
18 − x − x − x = 0
x = 6
En el Tema A, los estudiantes usan un diagrama de cinta para examinar la relación entre las operaciones. Empiezan explorando la relación entre la suma y la resta. Después exploran las relaciones entre la multiplicación y la división y la multiplicación y la suma. Los estudiantes concluyen el tema explorando cómo se relacionan la división y la resta. Espere ver tareas que le pidan a su hijo/a que haga lo siguiente:
Llenar la parte faltante de un enunciado numérico o ecuación. ▪ Explicar por qué las ecuaciones w − x + x = w y w + x − x = w se llaman identidades. ▪ Examinar y describir las relaciones entre operaciones. ▪ Escribir una expresión equivalente para mostrar una relación específica. Por ejemplo, 3 × 9 es
equivalente a 9 + 9 + 9 o 3d es equivalente a d + d + d . ▪ De una ecuación de división, escribir la ecuación de resta relacionada, dibujar el diagrama de cinta y
determinar el valor de la variable. (Vea las Muestras de problemas).
G R A D O 6 | M Ó D U L O 4 | T E M A A | L E C C I O N E S 1–4
Puede encontrar ejemplos adicionales de problemas con pasos de respuesta detallados en los libros de Eureka Math Homework Helpers. Obtenga más información en GreatMinds.org.
Para obtener más recursos, visite » es.eureka.support
VOCABULARIO
Ecuación: un enunciado que indica que dos expresiones son iguales (p. ej., 3 × 4 = 6 × 2 y 5 + x = 20).Expresiones equivalentes: expresiones que tienen el mismo valor (p. ej., 2 × 6 es equivalente a 4a si a = 3).Expresión: un grupo de números, símbolos y operadores como + y − sin signo igual que se resuelve en un número (p. ej., 2 × 4 y 9n + 7).Identidad: una ecuación que es verdadera sin importar qué valores se sustituyan por las variables (p. ej., w − x + x = w porque w y x se pueden reemplazar con cualquier número y la ecuación seguiría siendo verdadera).Enunciado numérico: una declaración que indica que dos expresiones numéricas son iguales (p. ej., 8 – 2 = 5 + 1).Variable: un símbolo, como una letra, que es el marcador de posición de un número.
Usted puede ayudar en casa de muchas maneras. Aquí hay algunos consejos para comenzar: ▪ Lea este enunciado con su hijo/a: “Cuando un número se multiplica y divide por el mismo número, el resultado
es el número original”. Por ejemplo, 11 × 5 ÷ 5 = 11. Pídale a su hijo/a que escriba algunos ejemplos para mostrar esto. Discuta con su hijo/a por qué la ecuación 3 × 9 ÷ 3 = 9 no representa este enunciado. (Un número no se multiplica y después divide por el mismo número. El 3 se multiplica por 9 y después se divide por 3, no 9).
▪ Con su hijo/a, desarrolle algunos ejemplos de situaciones de dinero de la vida real en las que el resultado es el número original. Por ejemplo, digamos que usted tiene $10. Se gasta $5 en la tienda. Después se encuentra $5 en la acera. ¿Cómo es que sus ejemplos se relacionan con las identidades w − x + x = w o w + x − x = w? (10 – 5 + 5 = 10)
G R A D O 6 | M Ó D U L O 4 | T E M A A | L E C C I O N E S 1–4
CÓMO PUEDE AYUDAR EN CASA
Para obtener más recursos, visite» es.eureka.support © 2017, GREAT MINDS®
When adding or subtracting fractions with common denominators, simply complete the operation with the numerators. Example: + = 8
281
83
Solve. Simplify, if possible.
1. - =54
51 2. + =8
385
3. + =516
316 4. + =4
543
5. - =714
614 6. - =9
893
When adding or subtracting fractions with common denominators, simply complete the operation with the numerators. Example: + = 8
281
83
Solve. Simplify, if possible.
1. - =54
51
53 2. + = = 18
385
88
3. + = =516
316
816 2
1 4. + = = 245
43
48
5. - =714
614
114 6. - =9
893
95
Solve each problem.
1. 478.89 + 147.09 = 2. 1004 + 236.09 =
3. 59.84 - 18.33 = 4. 12785.06 - 1.47 =
5. 8.007 + 14.52 = 6. 347 - 289.3 =
7. 1400 + 784.01 = 8. 7356.24 - 2567.09 =
9. 240.01 + 367.5 = 10. 17.859 + 27.01 =
Solve each problem.
1. 478.89 + 147.09 = 625.98 2. 1004 + 236.09 = 1240.09
3. 59.84 - 18.33 = 41.51 4. 12785.06 - 1.47 = 12,783.59
5. 8.007 + 14.52 = 22.527 6. 347 - 289.3 = 57.7
7. 1400 + 784.01 = 2,184.01 8. 7356.24 - 2567.09 = 4789.15
9. 240.01 + 367.5 = 607.51 10. 17.859 + 27.01 = 44.869
A mixed number has a whole number and a fraction piece. An improper fraction has a numerator that is larger than the denominator. Example: 1 = 3
235
Convert each mixed number to an improper fraction.
Example: 1 = 32
35
I multiplied the denominator of my fraction piece, (which is 3) by my 1 whole. I then added the remaining 2 pieces to that, which gave me 5. My denominator stays the same.
5 =95 10 =7
3
8 =32 4 =7
10
Convert each improper fraction into a mixed number.
Example: = 5316
31
I divided my numerator (16) by my denominator (3) and it divided evenly 5 whole times (3 x 5=15), with one remaining piece. This remaining piece represents that I have only 1 out of 3 pieces. Therefore I have
5 whole pieces and piece.31
=312 =7
22
=522 =5
32
ANSWER KEY: Convert each mixed number to an improper fraction.
5 =95
950 10 =7
3773
8 =32
326 4 =7
10 1047
Convert each improper fraction into a mixed number.
=312 4 =37
2271
=522 4 5
2 = 6 532
52
Divide. Use a multiplication menu to support your thinking. Examples:
1. 484,692 ÷ 13 =37,284 1 x 13=13 2 x 13=26 3 x 13=30 4 x 13=52 5 x 13=65 6 x 13=78 7 x 13=9`
2. 281,886 ÷ 33 =8542 1 x 33=33 2 x 33=66 3 x 33=99 4 x 33=132 5 x 33=165 6 x 33=198 7 x 33=231 8 x 33=264
Practice
1. 1,653 ÷ 19 = 2. 115,785 ÷ 31 =
3. 2,475 ÷ 25 = 4. 21,402 ÷ 41 =
Divide. Use a multiplication menu to support your thinking. Examples:
1. 484,692 ÷ 13 =37,284
2. 281,886 ÷ 33 =8542
Practice
1. 1,653 ÷ 19 = 87 2. 115,785 ÷ 31 =3735
3. 2,475 ÷ 25 = 99 4. 21,402 ÷ 41 =522
Divide. Use a multiplication menu to support your thinking. Examples:
1. 484,692 ÷ 13 =37,284
2. 281,886 ÷ 33 =8542
Practice
1. 1,653 ÷ 19 = 87 2. 115,785 ÷ 31 =3735
3. 2,475 ÷ 25 = 99 4. 21,402 ÷ 41 =522
Read“OnBecomingaScribe.”
1. Summarizethetext,inoneparagraph(approximately5
sentences.)Includethemainidea,themostimportantdetails,
andaconclusion.
2. Writeanopinionpiece,onetotwoparagraphslong:Wouldyou
haveenjoyedlearningtobecomeascribe?Whyorwhynot?
Supportyouropinionwithdetailsfromthetext.
______________________________________________________________________
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©2014 Benchm
ark Education Company, LLC
43
Unit 3
I am a fortunate young m
an. Not only have I
been born into an elite family in M
esopotamia, but
tomorrow
I begin my studies to becom
e a scribe. It is hum
bling to think that someday I shall be able to
write stories and poem
s like those of Enheduanna
(en-heh-doo-AH
-nuh), King Sargon’s daughter. She
is the high priestess of the moon god, and she has
written m
any beautiful hymns. I hope to help preserve
her words by w
riting them dow
n. For tonight, I am
too excited to sleep. O
f course I shall begin slowly. I w
ill learn how to
make a stylus, w
ith a proper edge for writing, from
a reed of grass. T
hen I will begin to practice pressing the
stylus into tablets made w
ith soft clay from the river
valley. It will take years to know
how to read, w
rite, and com
bine all the symbols and m
arks.
When at last m
y studies are completed, I w
ill be able to w
rite contracts and read letters for those who
are unable to do so for themselves. A
nd who can say
how m
any more hym
ns Enheduanna m
ay have written
by then?T
he career of a scribe will suit m
e well. I am
blessed to be chosen to learn this im
portant profession. It dates back to the ancient tim
es, but it has been greatly m
odernized for today’s society.
On Becom
ing a
Scribe
Read“FreeFallFromSpace.”
1. Summarizethetext,inoneparagraph(approximately5
sentences.)Includethemainidea,themostimportantdetails,
andaconclusion.
2. Writeanopinionpiece,onetotwoparagraphslong:Wouldyou
liketohavejoinedJosephKittingerJronhisrecord-setting
parachutejump?Whyorwhynot?Supportyouropinionwith
detailsfromthetext.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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©2014 Benchm
ark Education Company, LLC
41
Unit 3
Free Fall from
Spa
ce Joseph K
ittinger Jr. was a U
.S. Air Force captain
who flew
experimental jet fighters and participated
in aerospace medical research. O
n August 16, 1960,
Kittinger m
ade his mark in history. R
iding in the basket of a large helium
balloon, he reached an altitude of 31,333 m
eters (102,800 feet)—three tim
es higher than m
ost comm
ercial airplanes fly—rem
ained there for about tw
elve minutes, and then jum
ped into the darkness of space. W
ith his first parachute deploying after thirteen seconds and his second parachute about five m
inutes later, he floated safely to Earth.
Wearing layers of clothing and a pressure suit,
Kittinger w
as able to withstand tem
peratures as low as
–70°C (–94°F) and speeds approaching that of sound.
In addition to setting a record for the longest parachute free fall, K
ittinger demonstrated that, properly
protected, a human could survive a jum
p from the
edge of space. T
he results of this and other high-altitude experim
ents have helped scientists design and build pressure and life-support system
s used by astronauts on space m
issions.
Sentence Starters for Opinion Writing
Opinion: In my opinion___________
In my opinion we should ______ For example in my experience _______. I agree/disagree because _________.
I think this because __________. Please consider _____. My position is ____. My opinion is based on __________.
R eason and Evidence:
The greatest part about ____________ is ______________ I prefer________ In addition, ____.
Another example can be found in _____. This example explains _______. To better understand my position ____
Opinion:
I am convinced that ____. It is essential to recognize _______. It is my strongest belief ____. In closing, ______.
On a final note, _______. The facts clearly indicate _. It cannot be denied that __. Let’s remember that ____. Finally, _______.
Opinion Writing Checklist
__I stated a strong opinion, position, or point of view.
__ I used well-organized reasons to support my opinion.
__ I linked my opinions and reasons using words, phrases, and clauses.
__ I wrote a conclusion that supports my position.
__ I reviewed my writing for good grammar.
__ I reviewed my writing for capitalization, punctuation, and spelling.
4/24/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 1/4
AnswersTeacher Copy
p. 211
EmbeddedAssessment1:ResearchingandDebatingaControversy
ACTIVITY
3.9
PreviewingEmbeddedAssessment2:Preparingfor
ArgumentativeWriting
LearningTargets
Analyze and summarize the skills and knowledge needed to complete Embedded Assessment2 successfully.
Explore rhetorical appeals used in argumentative writing.
GraphicOrganizer(LearningStrategy)
Definition
Using a visual representation for the organization of information from the text
Purpose
To facilitate increased comprehension and discussion
CloseReading(LearningStrategy)
Definition
Accessing small chunks of text to read, reread, mark, and annotate key passages, word-for-word,sentence-by-sentence, and line-by-line
Purpose
To develop comprehensive understanding by engaging in one or more focused readings of a text
LearningStrategies
Graphic Organizer, Close Reading
MakingConnections
In the first part of this unit, you learned about elements essential to argumentative writing: claims,reasons, and evidence. In this part of the unit you will expand on your writing skills by writing anargumentative letter to persuade an audience to agree with your position on an issue.
EssentialQuestions
Reflect on your increased understanding of the Essential Questions. Based on your currentunderstanding, how would you answer these questions now?
Why do we have controversy in society?
4/24/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 2/4
p. 212
p. 213
DevelopingVocabulary
In your Reader/Writer Notebook, look at the new vocabulary you learned as you were introduced toargumentative writing in the first half of this unit. Re-sort the words below in the graphic organizer,once again using the QHT strategy. Notice which words have moved from one column to another.
UnpackingEmbeddedAssessment2
Read the assignment for Embedded Assessment 2: Writing an Argumentative Letter.
Think about a topic (subject, event, idea, or controversy) that you truly care about andtake a position on it. Write an argumentative letter to convince an audience to supportyour position on the topic.
In your own words, summarize what you will need to know to complete this assessmentsuccessfully. With your class, create a graphic organizer to represent the skills and knowledge youwill need to complete the tasks identified in the Embedded Assessment.
ThinkingAboutPersuasion
IndependentReadingLink
To support your learning in the second half of the unit, you might think about reading a book,magazine articles, or news articles that explore a current “hot topic” or controversial issue.
How do we communicate in order to convince others?
Academic Vocabulary
controversy
argument
claim
reasons
evidence
research
citation
textual evidenceplagiarism
credible
Literary Terms
editorial
tone
formal style
Q H T
4/24/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 3/4
ACTIVITY3.10:LookingataModelArgumentativeLetter
Think about times in the past when you tried to convince someone to believe or to dosomething. Were you successful? Write down at least 4–5 examples of times you tried to bepersuasive and the outcome of each.
Times I Was Persuasive Outcome
1.
For each successful outcome listed above, write down the reasons that you gave thatpersuaded the other person. Try to list four or five examples of supporting reasons.
2.
Which of the examples given in the previous question were appeals to the emotions of yourlistener? Which were appeals to your listener’s logic—intellectual appeals?
3.
With a group of classmates, discuss the examples you each recorded and whether thoseexamples were appeals to emotion or to logic. Based on your examples, were emotionalappeals or logical appeals more effective?
4.
©2014CollegeBoard.Allrightsreserved.
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 1/14
AnswersTeacher Copy
EmbeddedAssessment1:ResearchingandDebatingaControversy
ACTIVITY
3.9
PreviewingEmbeddedAssessment2:Preparingfor
ArgumentativeWriting
CommonCoreStateStandards
FocusStandards
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
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After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
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Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
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Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Sincethis is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
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For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
CommonCoreStateStandards
FocusStandards
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
4/26/2020 Springboard - English Language Arts Grade 6
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Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
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Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
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Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Sincethis is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
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Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
CommonCoreStateStandards
FocusStandards
SL.6.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led)with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing theirown clearly.
SL.6.1a: Come to discussions prepared, having read or studied required material; explicitly draw on thatpreparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas underdiscussion.
AdditionalStandardsAddressed
RI.6.10; SL.6.1c
Plan
Suggested Pacing: 1 50-minute class period
Teach
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Step 1:
Use think-pair-share to have students discuss connections to the learning in the first part of the unit andto respond to the Essential Questions.
Step 2:
Have students re-sort the word lists using the graphic organizer. Then ask students to share their “T” wordswith each other, giving explanations and examples so that peers’ “Q” words can be moved to the “H”category.
Step 3:
Unpack the Embedded Assessment by first asking students to read the assignment and Scoring Guide ontheir own and to think about a topic they might like to write about.
Step 4:
Lead the class in a discussion to paraphrase and create a graphic organizer of the required concepts andskills for Embedded Assessment 2.
DifferentiatingInstruction
To support students’ unpacking and to guide their understanding of “beginning with the end in mind,” usea think aloud. To extend this step for students, ask partners to do the paraphrasing and to create a graphicorganizer in a small group before collaborating to create a classroom display of the unpacked assessment.
Step 5:
Ask students to fill in the graphic organizer, giving examples of times they times have used persuasion intheir own lives and the outcome of each case listed. Students will then answer the questions following thegraphic organizer to reflect on persuasive reasoning and on the effectiveness of emotional vs. intellectualappeals.
Step 6:
For independent reading, students may continue reading the text they started in the first half of the unit orselect a new one. Define what you want students to do while reading. For example, create or revise areading calendar and any active reading/note-taking method you may have set up. Use the skills andconcepts of the Embedded Assessment to guide the look-fors of independent reading. You might thinkabout asking students to read recently published works on controversial topics as a way to prime theirthinking about persuasive writing.
Assess
In looking at students’ QHT sorts and unpacking of the Embedded Assessment, check to see what termsthey are confident and less confident in. Use this data to guide instruction during the unit.
Adapt
Reinforce the concepts and vocabulary as students complete each activity to ensure that they understandand can use the concepts/vocabulary correctly.
LearningTargets
Analyze and summarize the skills and knowledge needed to complete Embedded Assessment2 successfully.
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Explore rhetorical appeals used in argumentative writing.
GraphicOrganizer(LearningStrategy)
Definition
Using a visual representation for the organization of information from the text
Purpose
To facilitate increased comprehension and discussion
CloseReading(LearningStrategy)
Definition
Accessing small chunks of text to read, reread, mark, and annotate key passages, word-for-word,sentence-by-sentence, and line-by-line
Purpose
To develop comprehensive understanding by engaging in one or more focused readings of a text
LearningStrategies
Graphic Organizer, Close Reading
MakingConnections
In the first part of this unit, you learned about elements essential to argumentative writing: claims,reasons, and evidence. In this part of the unit you will expand on your writing skills by writing anargumentative letter to persuade an audience to agree with your position on an issue.
EssentialQuestions
DevelopingVocabulary
In your Reader/Writer Notebook, look at the new vocabulary you learned as you were introduced toargumentative writing in the first half of this unit. Re-sort the words below in the graphic organizer,once again using the QHT strategy. Notice which words have moved from one column to another.
Reflect on your increased understanding of the Essential Questions. Based on your currentunderstanding, how would you answer these questions now?
Why do we have controversy in society?
How do we communicate in order to convince others?
Academic Vocabulary
controversy
argument
Literary Terms
editorial
tone
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p. 213
UnpackingEmbeddedAssessment2
Read the assignment for Embedded Assessment 2: Writing an Argumentative Letter.
Think about a topic (subject, event, idea, or controversy) that you truly care about andtake a position on it. Write an argumentative letter to convince an audience to supportyour position on the topic.
In your own words, summarize what you will need to know to complete this assessmentsuccessfully. With your class, create a graphic organizer to represent the skills and knowledge youwill need to complete the tasks identified in the Embedded Assessment.
ThinkingAboutPersuasion
IndependentReadingLink
To support your learning in the second half of the unit, you might think about reading a book,magazine articles, or news articles that explore a current “hot topic” or controversial issue.
claim
reasons
evidence
research
citation
textual evidenceplagiarism
credible
formal style
Q H T
Think about times in the past when you tried to convince someone to believe or to dosomething. Were you successful? Write down at least 4–5 examples of times you tried to bepersuasive and the outcome of each.
Times I Was Persuasive Outcome
1.
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ACTIVITY3.10:LookingataModelArgumentativeLetter
For each successful outcome listed above, write down the reasons that you gave thatpersuaded the other person. Try to list four or five examples of supporting reasons.
2.
Which of the examples given in the previous question were appeals to the emotions of yourlistener? Which were appeals to your listener’s logic—intellectual appeals?
3.
With a group of classmates, discuss the examples you each recorded and whether thoseexamples were appeals to emotion or to logic. Based on your examples, were emotionalappeals or logical appeals more effective?
4.
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AnswersTeacher Copy
p. 214
ACTIVITY3.9:PreviewingEmbeddedAssessment2:PreparingforArgumentative
Writing
ACTIVITY3.10 LookingataModelArgumentativeLetter
LearningTargets
Read closely to identify claim, reasons, and evidence.
Generate ideas and apply an organizational pattern to write an argumentative paragraph.
MarkingtheText(LearningStrategy)
Definition
Selecting text by highlighting, underlining, and/or annotating for specific components, such as mainidea, imagery, literary devices, and so on
Purpose
To focus reading for specific purposes, such as author’s craft, and to organize information fromselections; to facilitate reexamination of a text
Webbing(LearningStrategy)
Definition
Developing a graphic organizer that consists of a series of circles connected with lines to indicaterelationships among ideas
Purpose
To generate ideas, concepts, or key words that provide a focus and/or establish organization prior towriting an initial draft and/or during the revision process
Writer’sChecklist(LearningStrategy)
Definition
Using a co-constructed checklist (that could be written on a bookmark and/or displayed on the wall)in order to look for specific features of a writing text and check for accuracy
Purpose
To focus on key areas of the writing process so that the writer can effectively revise a draft andcorrect mistakes
LearningStrategies
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Marking the Text, Brainstorming, Webbing, Writer’s Checklist
BeforeReading
DuringReading
Draft
StudentLetter
Dear Legislator,
We live in the 21st century and see technology all around us. Americans have access to the Internetalmost everywhere, at home, on cell phones, and even at school. For some students, school is theonly access they have to the Internet. The Web also provides many more learning opportunities andprepares us students for high school and the real world. Internet access for students in schoollibraries is crucial for our success.
KeyIdeasandDetails
What do you notice about the formatting of this letter?
KeyIdeasandDetails
Where is the commentary in paragraph number 3? What does it do for the paragraph?
Unpack the prompt by underlining the sentence that is the “task.” What is the prompt askingyou to do? Circle the verbs and highlight the nouns.
Argumentative Prompt: Some state legislators believe that school libraries should notprovide Internet access for students. Decide whether you agree or disagree with thisposition. Write a letter to convince state legislators to support your position.
1.
Scan the letter below and mark these parts of the letter: salutation, body, closing.2.
Mark the text and take notes in the margin to identify the claim, reasoning, and evidenceprovided in the letter.
3.
00:00 / 02:19
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Students need school access to the Internet because computers and the price for Internet service cansometimes be too costly for a family. Internet service providers, such as Quest, charge an average offifty dollars a month. Many times teachers assign projects that students need access to computers tocomplete. Internet access in the school library is sometimes the only option for numerous pupils. Ifthat only option is taken away, innocent students will be penalized for not being able to fulfill aschool project.
When we get to high school, we will be getting prepared for the real world that is coming to ussooner than we think. In the technology-filled society that we are about to embark on, we will haveto know many skills on how to best utilize a computer and the Internet. My cousin is a goodexample of someone who is utilizing the technology skills he learned as a teenager. He is in collegeand takes courses online. Taking online courses allows him to have a job and go to college at thesame time. He says he spends close to 10 hours a week studying, mostly at night after his job.Knowing how to use the Internet is helping build a successful future. Students spend most of theirtime in school around adults that are here to teach them life skills. I believe that we can learn themost in preparation for the real world in school!
In conclusion, the best solution is to continue allowing school libraries to provide Internet access forstudents. For many, that provides the only access they have. It not only provides gateways for betterlearning experiences, but also readies us for the big journey that is ahead of us once we leave thecomfort of middle and high school. Can you even imagine what kind of struggles would come ourway if state legislators choose to terminate school Internet access?
Sincerely,
A Concerned Student
AfterReading
Draftingabodyparagraph:Prewriting
Brainstorm evidence for the main idea (reason) of the paragraph.
Research:
What questions will guide your research?
Where will you gather evidence?
What sources will you consult?
Drafting
Return to the letter to mark the text for formal style. Annotate the text to identify the author’stone.
4.
With the guidance of your teacher, conduct research as needed and draft another bodyparagraph as a new third paragraph. You will return to this body paragraph to practicerevision strategies and refine your writing skills. Follow the steps below to research anddraft a paragraph.
5.
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After conducting initial research, generate an outline for the body paragraph and then write yourdraft. Remember, each body paragraph should consist of:
A topic sentence: a sentence that consists of a subject and an opinion that works directly tosupport the claim (thesis)
Transitions: words used to connect ideas (e.g., for example, for instance)
Supporting information: specific evidence and details (What facts and details are mostappropriate? Do you accurately synthesize information from a variety of sources?)
Reflective commentary: sentences that explain how the information is relevant to theclaim/thesis. (Use reflective commentary to also bring a sense of closure to the paragraph.)
CheckYourUnderstanding
Create a Writer’s Checklist based on what you already know you should “be sure to” do to create asuccessful argument.
ACTIVITY3.11:FactsandFeelings:RhetoricalAppealsinArgumentativeWriting
Draft your body paragraph in the space below.6.
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AnswersTeacher Copy
ACTIVITY3.9:PreviewingEmbeddedAssessment2:PreparingforArgumentative
Writing
ACTIVITY3.10 LookingataModelArgumentativeLetter
CommonCoreStateStandards
FocusStandards
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
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After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
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Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
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Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Sincethis is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
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p. 214
For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
LearningTargets
Read closely to identify claim, reasons, and evidence.
Generate ideas and apply an organizational pattern to write an argumentative paragraph.
MarkingtheText(LearningStrategy)
Definition
Selecting text by highlighting, underlining, and/or annotating for specific components, such as mainidea, imagery, literary devices, and so on
Purpose
To focus reading for specific purposes, such as author’s craft, and to organize information fromselections; to facilitate reexamination of a text
Webbing(LearningStrategy)
Definition
Developing a graphic organizer that consists of a series of circles connected with lines to indicaterelationships among ideas
Purpose
To generate ideas, concepts, or key words that provide a focus and/or establish organization prior towriting an initial draft and/or during the revision process
Writer’sChecklist(LearningStrategy)
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Definition
Using a co-constructed checklist (that could be written on a bookmark and/or displayed on the wall)in order to look for specific features of a writing text and check for accuracy
Purpose
To focus on key areas of the writing process so that the writer can effectively revise a draft andcorrect mistakes
LearningStrategies
Marking the Text, Brainstorming, Webbing, Writer’s Checklist
BeforeReading
DuringReading
Draft
StudentLetter
Dear Legislator,
We live in the 21st century and see technology all around us. Americans have access to the Internetalmost everywhere, at home, on cell phones, and even at school. For some students, school is theonly access they have to the Internet. The Web also provides many more learning opportunities andprepares us students for high school and the real world. Internet access for students in schoollibraries is crucial for our success.
KeyIdeasandDetails
What do you notice about the formatting of this letter?
Unpack the prompt by underlining the sentence that is the “task.” What is the prompt askingyou to do? Circle the verbs and highlight the nouns.
Argumentative Prompt: Some state legislators believe that school libraries should notprovide Internet access for students. Decide whether you agree or disagree with thisposition. Write a letter to convince state legislators to support your position.
1.
Scan the letter below and mark these parts of the letter: salutation, body, closing.2.
Mark the text and take notes in the margin to identify the claim, reasoning, and evidenceprovided in the letter.
3.
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KeyIdeasandDetails
Where is the commentary in paragraph number 3? What does it do for the paragraph?
Students need school access to the Internet because computers and the price for Internet service cansometimes be too costly for a family. Internet service providers, such as Quest, charge an average offifty dollars a month. Many times teachers assign projects that students need access to computers tocomplete. Internet access in the school library is sometimes the only option for numerous pupils. Ifthat only option is taken away, innocent students will be penalized for not being able to fulfill aschool project.
When we get to high school, we will be getting prepared for the real world that is coming to ussooner than we think. In the technology-filled society that we are about to embark on, we will haveto know many skills on how to best utilize a computer and the Internet. My cousin is a goodexample of someone who is utilizing the technology skills he learned as a teenager. He is in collegeand takes courses online. Taking online courses allows him to have a job and go to college at thesame time. He says he spends close to 10 hours a week studying, mostly at night after his job.Knowing how to use the Internet is helping build a successful future. Students spend most of theirtime in school around adults that are here to teach them life skills. I believe that we can learn themost in preparation for the real world in school!
In conclusion, the best solution is to continue allowing school libraries to provide Internet access forstudents. For many, that provides the only access they have. It not only provides gateways for betterlearning experiences, but also readies us for the big journey that is ahead of us once we leave thecomfort of middle and high school. Can you even imagine what kind of struggles would come ourway if state legislators choose to terminate school Internet access?
Sincerely,
A Concerned Student
AfterReading
Draftingabodyparagraph:Prewriting
Brainstorm evidence for the main idea (reason) of the paragraph.
Return to the letter to mark the text for formal style. Annotate the text to identify the author’stone.
4.
With the guidance of your teacher, conduct research as needed and draft another bodyparagraph as a new third paragraph. You will return to this body paragraph to practicerevision strategies and refine your writing skills. Follow the steps below to research anddraft a paragraph.
5.
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Research:
What questions will guide your research?
Where will you gather evidence?
What sources will you consult?
Drafting
After conducting initial research, generate an outline for the body paragraph and then write yourdraft. Remember, each body paragraph should consist of:
A topic sentence: a sentence that consists of a subject and an opinion that works directly tosupport the claim (thesis)
Transitions: words used to connect ideas (e.g., for example, for instance)
Supporting information: specific evidence and details (What facts and details are mostappropriate? Do you accurately synthesize information from a variety of sources?)
Reflective commentary: sentences that explain how the information is relevant to theclaim/thesis. (Use reflective commentary to also bring a sense of closure to the paragraph.)
Since the World Wide Web is a widely used form of communication and research, it provides manymore practical opportunities for learning. Having that privilege at school makes the jobs of teachersand students so much easier! Students have the luxury of doing research at school or maybe typingup a paper. Teachers can also send students to certain sites that can teach lessons interactively or thatcan help better explain a lesson. The math teachers at our school encourage students who want morepractice to go to the Internet to practice. This is a win-win situation.
CheckYourUnderstanding
Create a Writer’s Checklist based on what you already know you should “be sure to” do to create asuccessful argument.
Provide a clear claim (thesis).
Have a topic sentence that relates to the claim.
Use reasons and evidence.
Maintain a formal style.
ACTIVITY3.11:FactsandFeelings:RhetoricalAppealsinArgumentativeWriting
Draft your body paragraph in the space below.6.
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AnswersTeacher Copy
p. 217
ACTIVITY3.10:LookingataModelArgumentativeLetter
ACTIVITY
3.11
FactsandFeelings:RhetoricalAppealsinArgumentative
Writing
LearningTargets
Identify logos and pathos used in an argument.
Explain how evidence is relevant and sufficient to support a claim.
MarkingtheText(LearningStrategy)
Definition
Selecting text by highlighting, underlining, and/or annotating for specific components, such as mainidea, imagery, literary devices, and so on
Purpose
To focus reading for specific purposes, such as author’s craft, and to organize information fromselections; to facilitate reexamination of a text
Rereading(LearningStrategy)
Definition
Encountering the same text with more than one reading
Purpose
To identify additional details; to clarify meaning and/or reinforce comprehension of texts
LearningStrategies
Marking the Text, Rereading
RhetoricandRhetoricalAppeals
LiteraryTerms
Rhetorical appeals, or persuasive strategies, are used in arguments to support claims.
Logos is a rhetorical appeal that uses logical reasoning and evidence.
Pathos is a rhetorical appeal to feelings.
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Rhetoric is the art of using words to persuade in writing and speaking. Writers use different types ofrhetoric depending on their purpose and audience.
Writers of argumentative texts appeal to their audience using sound reasoning and evidence. Writerswho use logical thinking that makes sense and is backed up with valid evidence (such as statistics,examples) are appealing to reason. This rhetorical appeal is known as logos.
At times, writers of argumentative texts also use evidence that appeals to feelings. When appealingto feelings, a writer uses emotional language or talks about basic values such as kindness, justice,and responsibility. This rhetorical appeal is known as pathos. Pathos should be used sparingly in anargument since relevant evidence is required to support a claim, but an emotional appeal typicallydoes not include evidence.
BeforeReading
DuringReading
Letter
AbouttheAuthor
The Grand Council Fire of American Indians was a Native American organization whose memberscame from many different tribes. The organization worked for better treatment of and policies forthe American Indian populations. In 1927 a political campaigner (William Hale Thompson ofChicago) used a slogan of “America First” to claim that the history taught in textbooks was biasedin favor of the British. Thompson won re-election as the mayor of Chicago, and he then demandedthat the city’s textbooks be replaced with books that focused on the accomplishments of the ethnicgroups in the United States. Members of the Grand Council Fire of American Indians used the“America First” program as an opportunity to describe how Native Americans also weremisrepresented in textbooks. The president of the Council, Scott H. Peters (of the Chippewa Tribe)wrote the following letter to Chicago’s newly elected mayor asking that the contributions andaccomplishments of Native Americans also be included in the textbooks.Marking the Text,Rereading, Graphic Organizer
TheFirstAmericans
KeyIdeasandDetails
What is the speaker’s tone?
How do you think people choose issues to support?1.
As you read the letter that follows, highlight the claim. Mark the text for specific evidencethat appeals to logic (logos, L) and to emotion (pathos, P).
2.
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KeyIdeasandDetails
What is the purpose of this speech? Who is the audience?
by Scott H. Peters, Grand Council Fire of American Indians
December 1, 1927
To the mayor of Chicago:
You tell all white men “America First.” We believe in that. We are the only ones, truly, that are onehundred percent. We therefore ask you, while you are teaching schoolchildren about America First,teach them truth about the First Americans.
We do not know if school histories are pro-British, but we do know that they are unjust to the life ofour people—the American Indian. They call all white victories battles and all Indian victoriesmassacres. The battle with Custer has been taught to schoolchildren as a fearful massacre on ourpart. We ask that this, as well as other incidents, be told fairly. If the Custer battle was a massacre,what was Wounded Knee?
History books teach that Indians were murderers—is it murder to fight in self-defense? Indianskilled white men because white men took their lands, ruined their hunting grounds, burned theirforests, destroyed their buffalo. White men penned our people on reservations, then took away thereservations. White men who rise to protect their property are called patriots—Indians who do thesame are called murderers.
White men call Indians treacherous—but no mention is made of broken treaties on the part of thewhite man. White men say that Indians were always fighting. It was only our lack of skill in whiteman’s warfare that led to our defeat. An Indian mother prayed that her boy be a great medicine manrather than a great warrior. It is true that we had our own small battles, but in the main we werepeace loving and home loving.
White men called Indians thieves—and yet we lived in frail skin lodges and needed no locks or ironbars. White men call Indians savages. What is civilization? Its marks are a noble religion andphilosophy, original arts, stirring music, rich story and legend. We had these. Then we were notsavages, but a civilized race.
We made blankets that were beautiful, that the white man with all his machinery has never been ableto duplicate. We made baskets that were beautiful. We wove in beads and colored quills designs thatwere not just decorative motifs but were the outward expression of our very thoughts. We madepottery—pottery that was useful, and beautiful as well. Why not make schoolchildren acquaintedwith the beautiful handicrafts in which we were skilled? Put in every school Indian blankets,baskets, pottery.
We sang songs that carried in their melodies all the sounds of nature—the running of waters, thesighing of winds, and the calls of the animals. Teach these to your children that they may come tolove nature as we love it.
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We had our statesmen—and their oratory1 has never been equaled. Teach the children some of thesespeeches of our people, remarkable for their brilliant oratory.
We played games—games that brought good health and sound bodies. Why not put these in yourschools? We told stories. Why not teach schoolchildren more of the wholesome proverbs andlegends of our people? Tell them how we loved all that was beautiful. That we killed game only forfood, not for fun. Indians think white men who kill for fun are murderers.
Tell your children of the friendly acts of Indians to the white people who first settled here. Tell themof our leaders and heroes and their deeds. Tell them of Indians such as Black Partridge, Shabbona,and others who many times saved the people of Chicago at great danger to themselves. Put in yourhistory books the Indian’s part in the World War. Tell how the Indian fought for a country of whichhe was not a citizen, for a flag to which he had no claim, and for a people that have treated himunjustly.
The Indian has long been hurt by these unfair books. We ask only that our story be told in fairness.We do not ask you to overlook what we did, but we do ask you to understand it. A true program ofAmerica First will give a generous place to the culture and history of the American Indian.
We ask this, Chief, to keep sacred the memory of our people.
AfterReading
AcademicVocabulary
In order to be convincing, evidence must be both relevant or closely connected to the matter athand, and sufficient, or enough for the purpose of supporting a claim or reason.
Reread the letter. Use the graphic organizer to record examples of the writer’s use ofrhetorical appeals.
Title: "The First Americans"
Appeals to Reason: logos (facts, statistics, examples, observations, quotations, and expert opinion)
Examples:
Appeals to Feelings: pathos(emotional language, mention of basic values)
Examples:
3.
Choose one piece of evidence and discuss how it is both relevant and sufficient to supportthe claim of the letter.
4.
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CheckYourUnderstanding
Which text do you find most convincing? Explain how that author incorporated rhetorical appeals tocreate the argument. Did the argument of that text use one kind of appeal—logos or pathos—morethan the other?
ACTIVITY3.12:CitingEvidence
Revisit and reread another text you have previously read in this unit. Analyze that text forrhetorical appeals. Then, complete the graphic organizer on the next page.
Title:
Appeals to Reason: logos (facts, statistics, examples, observations, quotations, and expert opinion)
Examples:
Appeals to Feelings: pathos (emotional language, mention of basic values)
Examples:
5.
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AnswersTeacher Copy
ACTIVITY3.10:LookingataModelArgumentativeLetter
ACTIVITY
3.11
FactsandFeelings:RhetoricalAppealsinArgumentative
Writing
CommonCoreStateStandards
FocusStandards
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
4/26/2020 Springboard - English Language Arts Grade 6
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After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
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Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 4/26
Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Sincethis is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 5/26
For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
CommonCoreStateStandards
FocusStandards
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 6/26
Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 7/26
Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 8/26
Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Sincethis is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 9/26
Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
CommonCoreStateStandards
FocusStandards
SL.6.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led)with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing theirown clearly.
SL.6.1a: Come to discussions prepared, having read or studied required material; explicitly draw on thatpreparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas underdiscussion.
AdditionalStandardsAddressed
RI.6.10; SL.6.1c
Plan
Suggested Pacing: 1 50-minute class period
Teach
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 10/26
Step 1:
Use think-pair-share to have students discuss connections to the learning in the first part of the unit andto respond to the Essential Questions.
Step 2:
Have students re-sort the word lists using the graphic organizer. Then ask students to share their “T” wordswith each other, giving explanations and examples so that peers’ “Q” words can be moved to the “H”category.
Step 3:
Unpack the Embedded Assessment by first asking students to read the assignment and Scoring Guide ontheir own and to think about a topic they might like to write about.
Step 4:
Lead the class in a discussion to paraphrase and create a graphic organizer of the required concepts andskills for Embedded Assessment 2.
DifferentiatingInstruction
To support students’ unpacking and to guide their understanding of “beginning with the end in mind,” usea think aloud. To extend this step for students, ask partners to do the paraphrasing and to create a graphicorganizer in a small group before collaborating to create a classroom display of the unpacked assessment.
Step 5:
Ask students to fill in the graphic organizer, giving examples of times they times have used persuasion intheir own lives and the outcome of each case listed. Students will then answer the questions following thegraphic organizer to reflect on persuasive reasoning and on the effectiveness of emotional vs. intellectualappeals.
Step 6:
For independent reading, students may continue reading the text they started in the first half of the unit orselect a new one. Define what you want students to do while reading. For example, create or revise areading calendar and any active reading/note-taking method you may have set up. Use the skills andconcepts of the Embedded Assessment to guide the look-fors of independent reading. You might thinkabout asking students to read recently published works on controversial topics as a way to prime theirthinking about persuasive writing.
Assess
In looking at students’ QHT sorts and unpacking of the Embedded Assessment, check to see what termsthey are confident and less confident in. Use this data to guide instruction during the unit.
Adapt
Reinforce the concepts and vocabulary as students complete each activity to ensure that they understandand can use the concepts/vocabulary correctly.
CommonCoreStateStandards
FocusStandards
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 11/26
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 12/26
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 13/26
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Since
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 14/26
this is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 15/26
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
CommonCoreStateStandards
FocusStandards
SL.6.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led)with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing theirown clearly.
SL.6.1a: Come to discussions prepared, having read or studied required material; explicitly draw on thatpreparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas underdiscussion.
AdditionalStandardsAddressed
RI.6.10; SL.6.1c
Plan
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Use think-pair-share to have students discuss connections to the learning in the first part of the unit andto respond to the Essential Questions.
Step 2:
Have students re-sort the word lists using the graphic organizer. Then ask students to share their “T” wordswith each other, giving explanations and examples so that peers’ “Q” words can be moved to the “H”category.
Step 3:
Unpack the Embedded Assessment by first asking students to read the assignment and Scoring Guide ontheir own and to think about a topic they might like to write about.
Step 4:
Lead the class in a discussion to paraphrase and create a graphic organizer of the required concepts andskills for Embedded Assessment 2.
DifferentiatingInstruction
To support students’ unpacking and to guide their understanding of “beginning with the end in mind,” usea think aloud. To extend this step for students, ask partners to do the paraphrasing and to create a graphic
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 16/26
organizer in a small group before collaborating to create a classroom display of the unpacked assessment.
Step 5:
Ask students to fill in the graphic organizer, giving examples of times they times have used persuasion intheir own lives and the outcome of each case listed. Students will then answer the questions following thegraphic organizer to reflect on persuasive reasoning and on the effectiveness of emotional vs. intellectualappeals.
Step 6:
For independent reading, students may continue reading the text they started in the first half of the unit orselect a new one. Define what you want students to do while reading. For example, create or revise areading calendar and any active reading/note-taking method you may have set up. Use the skills andconcepts of the Embedded Assessment to guide the look-fors of independent reading. You might thinkabout asking students to read recently published works on controversial topics as a way to prime theirthinking about persuasive writing.
Assess
In looking at students’ QHT sorts and unpacking of the Embedded Assessment, check to see what termsthey are confident and less confident in. Use this data to guide instruction during the unit.
Adapt
Reinforce the concepts and vocabulary as students complete each activity to ensure that they understandand can use the concepts/vocabulary correctly.
CommonCoreStateStandards
FocusStandards
RI.6.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferencesdrawn from the text.
AdditionalStandardsAddressed
RI.6.2; RI.6.3; RI.6.5; W.6.1a; W.6.1b; W.6.1e; W.6.4; W.6.7; W.6.10
Plan
Materials: highlighters; access to sources
Suggested Pacing: 2 50-minute class periods
Teach
Step 1:
Begin by unpacking the argumentative prompt with students. Next, ask students to access prior
knowledge to label the parts of the student letter. You might also ask them where a date would go andwhat type of letter it is.
Step 2:
Decide on the format/type of letter you will require for EA2 and use this letter to adapt for the model. Thisis a modified business/block style letter.
4/26/2020 Springboard - English Language Arts Grade 6
https://centennialor.springboardonline.org/ebook/book/110074257/E55DF8C7E42545B9AF2C06195DBB5E30 17/26
Step 3:
A second body paragraph is intentionally omitted from this student sample. Students will be drafting thisparagraph as practice and will use it to practice revising for rhetorical appeals in the next three activities.
Step 4:
Conduct a shared reading of the student text while marking. At this point, students should be able tolook for many components of an argument. Use think aloud and pair-share after each paragraph. Sincethis is student writing and incomplete, no text complexity is included.
Key Ideas and Details: The letter is in modified block format, which uses single spacing, indentedparagraphs, and a line space between paragraphs. The formatting clearly separates the paragraphs.
Key Ideas and Details: The commentary explains the information about the writer’s cousin. It helpssupport the argument by showing why the information was included.
Step 5:
Assign small groups of students one of the paragraphs to reread, marking the text for formal style andidentify tone. Asking groups to share while others mark so that all students have examples in eachparagraph.
Step 6:
Guide students to begin the writing and research process in order to draft the missing body paragraph. Themain idea of the paragraph is given in the center of the web. Use webbing to brainstorm evidence thatstudents can think of off the top of their heads as support.
Step 7:
You might want to support students in writing a topic sentence together before the research step.
Step 8:
Have students consider the research they will need to do. Consider either bringing in resources orscheduling time outside of class for research.
DifferentiatingInstruction
Decide if you want this to be a class-constructed paragraph or an independent paragraph, based on yourstudents’ needs. Have students read the information on a body paragraph as a reminder. Return to themodel letter to locate/mark and analyze the sentence of reflective commentary.
Step 9:
Use the students’ experience with evidence from the first half of the unit to decide what evidence and howmuch evidence to include in the paragraph. Before drafting, have pairs of students write their own Writer’sChecklists, share with the class, and refine to arrive at a checklist agreed on by the entire class.
Step 10:
For the Check Your Understanding, ask students to write the skills from the Writer’s Checklist in a verticallist according to how confident they are with each skill. This will serve as a self-assessment and providediagnostic information that will help you differentiate during the rest of the unit.
Assess
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Make sure students are reading the prompt accurately and marking what they need to do for the task.
Check that students understand the role of research in writing an argument. Also check how successfullythey are able to draft an argumentative body paragraph; for this lesson, ensure that their topic sentencerelates directly to the claim.
Adapt
You may want to provide specific, guided writing instruction on a target skill for students who need help.Students will be revising for logos (focusing on evidence as support) and pathos (focusing on persuasivediction).
You might access Writing Workshop 10 to support the skill of letter writing. This is also a good time toextend the task by introducing the concept of the “counterargument” and how writers address it inargumentative writing. While this is not a grade-level expectation, it is where students will need to moveas they become more sophisticated argumentative writers. Use the Writing Workshop to provide directinstruction.
CommonCoreStateStandards
FocusStandards
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of atext and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in thetext.
AdditionalStandardsAddressed
RI.6.1; RI.6.2; RI.6.3; RI.6.4; RI.6.8; RI.6.10; L.6.6
Plan
Materials: Highlighters
Suggested Pacing: 1 50-minute class period
Teach
Step 1:
Begin by asking students what the word “appeal” means to them. Have students read “Rhetoric andRhetorical Appeals,” which includes information to connect what they already know about argumentationto the concepts of logos and pathos.
Step 2:
Add Rhetorical Appeals: Logos and Pathos to the Word Wall.
Exlpain the following:
Think = logos = logic
Pathos = reminds me of “passion,” which is an emotion
BackgroundInformationonGrandCouncilFireofAmericanIndians
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In 1927, while running for a third term as mayor of Chicago, William Hale Thompson campaigned on thetheme of “America First.” Thompson claimed that textbooks used in Chicago schools were biased in favorof the British; he wanted them to be revised to be “100 percent American.” Thompson’s anti-Britishprogram was intended to win the votes of immigrants from Ireland and Germany, nations that had troubledrelations with England.
After he won the election, Thompson attacked the city’s superintendent of schools for using pro-Britishtextbooks and demanded that they be replaced with books that recognized the historical contributions ofGerman, Irish, and other European ethnic groups.
Members of the Grand Council Fire of American Indians used Thompson’s “America First” program as anopportunity to point out that Native Americans were often either overlooked or misrepresented in schooltextbooks. The president of the Grand Council, Scott H. Peters, a Chippewa Indian, wrote a letter to themayor asking that textbooks also feature the accomplishments of Native Americans.
TextComplexity
Overall: Complex
Lexile: 890L
Qualitative: Moderate Difficulty
Task: Challenging (Evaluate)
Step 3:
Students will read the letter twice. The first time, conduct a read-aloud (you or students reading). Assignhalf of the class to mark the text for logos and half to mark it for pathos. Discuss to analyze as you read.
TeachertoTeacher
This text has many examples of both logos and pathos. Students will learn in the following activity that aneffective argument is supported primarily with logos and enhanced with pathos.
Step 4:
Next, assign small groups to reread a designated portion (a specific paragraph or chunk); they shouldcompare their markings and discuss what they can identify.
Key Ideas and Details: The tone of the letter is firm and demanding. There is also an element of angerover the way history books portray Native Americans.
Key Ideas and Details: The purpose of the letter is to convince those who write and buy history books forschool children to provide a fair portrayal of Native American history and interactions with white people.The audience is first the mayor of Chicago (to whom the letter is addressed), but also to all citizens whovalue accuracy and fairness in textbooks.
Step 5:
Ask groups to share their findings as the class records the examples of logos in the graphic organizer.
Step 6:
Have groups continue to share their findings as the class records the examples of pathos in thegraphicorganizer.
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p. 217
Step 7:
Have students practice identifying rhetorical appeals by assigning one of the opinion texts from earlier inthe unit. Consider using “Don't ban peanuts at school, but teach about the dangers” or “Letter on ThomasJefferson” or even the I Wanna Iquana picture book. You might also consider using historical speeches orletters (e.g., authored by Martin Luther King, John F. Kennedy, George Washington, Abigail Adams).
Step 8:
For this analysis, you could use a jigsaw by first making “expert” groups in which students have the sametext. They could read their assigned text one time through individually, then work together for five minutesto analyze and record examples of appeals in the graphic organizer.
Step 9:
Then, to create jigsaw groups, ask each person in the expert group to go form a new group of other“experts” who had different texts. Allow jigsaw groups to work together to share information and discussthe types of appeals each text used.
DifferentiatingInstruction
As a way for each group to share the text they evaluated as most convincing, prompt them to write anddeliver a short letter or speech using appeals. Have students share their letters or speeches.
Step 10:
Use think-pair-share to check for understanding.
Assess
The key look-for is centered on students’ ability to identify examples of logos and pathos. Check to seethat students can differentiate between the two types of appeals.
Pay attention to students’ ability to complete the graphic organizer collaboratively and independently.
Adapt
You might consider generating personal examples by asking students when they use the two types ofappeals in their lives.
LearningTargets
Identify logos and pathos used in an argument.
Explain how evidence is relevant and sufficient to support a claim.
MarkingtheText(LearningStrategy)
Definition
Selecting text by highlighting, underlining, and/or annotating for specific components, such as mainidea, imagery, literary devices, and so on
Purpose
To focus reading for specific purposes, such as author’s craft, and to organize information fromselections; to facilitate reexamination of a text
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Rereading(LearningStrategy)
Definition
Encountering the same text with more than one reading
Purpose
To identify additional details; to clarify meaning and/or reinforce comprehension of texts
LearningStrategies
Marking the Text, Rereading
RhetoricandRhetoricalAppeals
LiteraryTerms
Rhetorical appeals, or persuasive strategies, are used in arguments to support claims.
Logos is a rhetorical appeal that uses logical reasoning and evidence.
Pathos is a rhetorical appeal to feelings.
Rhetoric is the art of using words to persuade in writing and speaking. Writers use different types ofrhetoric depending on their purpose and audience.
Writers of argumentative texts appeal to their audience using sound reasoning and evidence. Writerswho use logical thinking that makes sense and is backed up with valid evidence (such as statistics,examples) are appealing to reason. This rhetorical appeal is known as logos.
At times, writers of argumentative texts also use evidence that appeals to feelings. When appealingto feelings, a writer uses emotional language or talks about basic values such as kindness, justice,and responsibility. This rhetorical appeal is known as pathos. Pathos should be used sparingly in anargument since relevant evidence is required to support a claim, but an emotional appeal typicallydoes not include evidence.
BeforeReading
DuringReading
How do you think people choose issues to support?1.
As you read the letter that follows, highlight the claim. Mark the text for specific evidencethat appeals to logic (logos, L) and to emotion (pathos, P).
2.
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p. 218p. 219Letter
AbouttheAuthor
The Grand Council Fire of American Indians was a Native American organization whose memberscame from many different tribes. The organization worked for better treatment of and policies forthe American Indian populations. In 1927 a political campaigner (William Hale Thompson ofChicago) used a slogan of “America First” to claim that the history taught in textbooks was biasedin favor of the British. Thompson won re-election as the mayor of Chicago, and he then demandedthat the city’s textbooks be replaced with books that focused on the accomplishments of the ethnicgroups in the United States. Members of the Grand Council Fire of American Indians used the“America First” program as an opportunity to describe how Native Americans also weremisrepresented in textbooks. The president of the Council, Scott H. Peters (of the Chippewa Tribe)wrote the following letter to Chicago’s newly elected mayor asking that the contributions andaccomplishments of Native Americans also be included in the textbooks.Marking the Text,Rereading, Graphic Organizer
TheFirstAmericans
KeyIdeasandDetails
What is the speaker’s tone?
KeyIdeasandDetails
What is the purpose of this speech? Who is the audience?
by Scott H. Peters, Grand Council Fire of American Indians
December 1, 1927
To the mayor of Chicago:
You tell all white men “America First.” We believe in that. We are the only ones, truly, that are onehundred percent. We therefore ask you, while you are teaching schoolchildren about America First,teach them truth about the First Americans.
We do not know if school histories are pro-British, but we do know that they are unjust to the life ofour people—the American Indian. They call all white victories battles and all Indian victoriesmassacres. The battle with Custer has been taught to schoolchildren as a fearful massacre on ourpart. We ask that this, as well as other incidents, be told fairly. If the Custer battle was a massacre,what was Wounded Knee?
00:00 / 05:08
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History books teach that Indians were murderers—is it murder to fight in self-defense? Indianskilled white men because white men took their lands, ruined their hunting grounds, burned theirforests, destroyed their buffalo. White men penned our people on reservations, then took away thereservations. White men who rise to protect their property are called patriots—Indians who do thesame are called murderers.
White men call Indians treacherous—but no mention is made of broken treaties on the part of thewhite man. White men say that Indians were always fighting. It was only our lack of skill in whiteman’s warfare that led to our defeat. An Indian mother prayed that her boy be a great medicine manrather than a great warrior. It is true that we had our own small battles, but in the main we werepeace loving and home loving.
White men called Indians thieves—and yet we lived in frail skin lodges and needed no locks or ironbars. White men call Indians savages. What is civilization? Its marks are a noble religion andphilosophy, original arts, stirring music, rich story and legend. We had these. Then we were notsavages, but a civilized race.
We made blankets that were beautiful, that the white man with all his machinery has never been ableto duplicate. We made baskets that were beautiful. We wove in beads and colored quills designs thatwere not just decorative motifs but were the outward expression of our very thoughts. We madepottery—pottery that was useful, and beautiful as well. Why not make schoolchildren acquaintedwith the beautiful handicrafts in which we were skilled? Put in every school Indian blankets,baskets, pottery.
We sang songs that carried in their melodies all the sounds of nature—the running of waters, thesighing of winds, and the calls of the animals. Teach these to your children that they may come tolove nature as we love it.
We had our statesmen—and their oratory1 has never been equaled. Teach the children some of thesespeeches of our people, remarkable for their brilliant oratory.
We played games—games that brought good health and sound bodies. Why not put these in yourschools? We told stories. Why not teach schoolchildren more of the wholesome proverbs andlegends of our people? Tell them how we loved all that was beautiful. That we killed game only forfood, not for fun. Indians think white men who kill for fun are murderers.
Tell your children of the friendly acts of Indians to the white people who first settled here. Tell themof our leaders and heroes and their deeds. Tell them of Indians such as Black Partridge, Shabbona,and others who many times saved the people of Chicago at great danger to themselves. Put in yourhistory books the Indian’s part in the World War. Tell how the Indian fought for a country of whichhe was not a citizen, for a flag to which he had no claim, and for a people that have treated himunjustly.
The Indian has long been hurt by these unfair books. We ask only that our story be told in fairness.We do not ask you to overlook what we did, but we do ask you to understand it. A true program ofAmerica First will give a generous place to the culture and history of the American Indian.
We ask this, Chief, to keep sacred the memory of our people.
AfterReading
Reread the letter. Use the graphic organizer to record examples of the writer’s use ofrhetorical appeals.
3.
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AcademicVocabulary
In order to be convincing, evidence must be both relevant or closely connected to the matter athand, and sufficient, or enough for the purpose of supporting a claim or reason.
Title: "The First Americans"
Appeals to Reason: logos (facts, statistics, examples, observations, quotations, and expert opinion)
Examples:
"It was only our lack of skill in white man’s warfare that led to our defeat."
"What is civilization? Its marks are a noble religion and philosophy, original arts, stirring music, rich storyand legend. We had these. Then we were not savages, but a civilized race."
"Put in your history books the Indian’s part in the World War. Tell how the Indian fought for a country ofwhich he was not a citizen, for a flag to which he had no claim, and for a people that have treated himunjustly."
Appeals to Feelings: pathos(emotional language, mention of basic values)
Examples:
“They call all white victories battles and all Indian victories massacres.”
“... Indians were murderers—is it murder to fight in self-defense?”
“We sang songs that carried in their melodies all the sounds of nature—the running of waters, the sighingof winds, and the calls of the animals. Teach these to your children that they may come to love nature aswe love it.”
“Tell them how we loved all that was beautiful. That we killed game only for food …”
Choose one piece of evidence and discuss how it is both relevant and sufficient to supportthe claim of the letter.
4.
Revisit and reread another text you have previously read in this unit. Analyze that text forrhetorical appeals. Then, complete the graphic organizer on the next page.
Title:
Appeals to Reason: logos (facts, statistics, examples, observations, quotations, and expert opinion)
5.
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CheckYourUnderstanding
Which text do you find most convincing? Explain how that author incorporated rhetorical appeals tocreate the argument. Did the argument of that text use one kind of appeal—logos or pathos—morethan the other?
ACTIVITY3.12:CitingEvidence
Examples:
Appeals to Feelings: pathos (emotional language, mention of basic values)
Examples:
©2014CollegeBoard.Allrightsreserved.
If there was a movie about your life right now,which songs would it include?
Title: ________________________________________________ Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________ Title: ________________________________________________Artist:________________________________________________
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InstrumentsoftheOrchestra TheseinstrumentsbelongtotheStringFamily.Traceeachword.
Nowdrawalinefromeachinstrumenttoitsname.
guitar banjo
cello harp violin
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Use materials around your home to make a musicalinstrument.If your instrument had a name, what would it be? What materials did you use to make it? How do you play it? What kind of music does it play? Draw a picture of your instrument below!
Directions: Identify the notes on the staff. Use the key as your practice guide for identification.
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Music Appreciation
Scavenger Hunt
Spring Rhythms
Directions: Write the words from the word bank in the box with the matching rhythm.
q q q n
n q n n
Word Bank
Bees Buzzing
Birds Chirping
Blooming Flowers
Butterfly
Cherry Blossom
Cloudy Weather
Daffodil
Flourishing
Flower Bed
Gardening
Green Grass
Planting Flowers
Plants Sprouting
Rain Boots
Rainbow
Rain Coat
Rainy Weather
Springtime
Sun Shining
Tulips
Draw your favorite part below:
Why was that your favorite part?________________________________________________________________________________________________________________
With the help of your family, choose a movie to watch!
Write about what happened:________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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ANSWER KEY
Spring Rhythms Answer Key
Directions: Write the words from the word bank in the box with the matching rhythm.
q q
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! Rain Boots
! Rainbow
! Rain Coat
! Springtime
! Tulips
q n
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! Birds Chirping
! Plants Sprouting
! Sun Shining
n q
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! Daffodil
! Flourishing
! Flower Bed
! Gardening
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! Cherry Blossom
! Cloudy Weather
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! Rainy Weather
Word Bank
Bees Buzzing
Birds Chirping
Blooming Flowers
Butterfly
Cherry Blossom
Cloudy Weather
Daffodil
Flourishing
Flower Bed
Gardening
Green Grass
Planting Flowers
Plants Sprouting
Rain Boots
Rainbow
Rain Coat
Rainy Weather
Springtime
Sun Shining
Tulips
