G6 m4-f-lesson 19-t

Lesson 19: Substituting to EvaluateAddition and SubtractionExpressions
Date: 4/1/15 190
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 19
Lesson 19: Substituting to Evaluate Addition and
Subtraction Expressions
Student Outcomes
 Students develop expressions involvingaddition and subtraction fromreal -world problems.
 Students evaluate these expressions for given values.
Lesson Notes
In this lesson,students begin by fillingin data tables to help them organizedata and see patterns; then, they move to
drawingtheir own tables. Encourage students to label the columns completely.
FluencyExercise (10 minutes)
Subtraction of Decimals Sprint
Classwork
OpeningExercise (3 minutes)
Opening Exercise
My older sister isexactly two yearsolder than I am. Sharing abirthday is both fun and annoying. Every year on our
birthday we have aparty, which is fun, but she alwaysbragsthat she istwo yearsolder than I am, which isannoying.
Shown below isatable ofour ages, starting when I wasborn:
My Age (in years) My Sister’sAge (in years)
𝟎 𝟐
𝟏 𝟑
𝟐 𝟒
𝟑 𝟓
𝟒 𝟔
Make surestudents understand the context of the story problem. It should be clear thatthe day I was born was my
sister’s second birthday. My firstbirthday was her third birthday;my second birthday was her fourth birthday;etc.
Scaffolding:
Some students will benefit
from havingblank tables
prepared ahead of time.

Date: 4/1/15 191
Discussion(5 minutes)
 Today in class wewill usedata tables. They help us organize data and see patterns. We can use variables to
make generalizations aboutthe patterns we see.
1. Looking at the table, what patternsdo you see? Tell apartner.
My sister’s ageis always two years morethan my age.
2. On the day I turned 𝟖yearsold, how old wasmy sister?
𝟏𝟎years old
3. How do you know?
Since my sister’s ageis always two years morethan my age, wejust add 𝟐. 𝟖 + 𝟐 = 𝟏𝟎
4. On the day I turned 𝟏𝟔yearsold, how old wasmy sister?
𝟏𝟖years old
5. How do you know?
Sincemy sister’s ageis always two years morethan my age, wejust add 𝟐. 𝟏𝟔+ 𝟐 = 𝟏𝟖.
6. Do we need to extend thetableto calculatethese answers?
No; thepattern is to add 𝟐 to your age to calculate your sister’s age.
Example 1 (10 minutes)
Example 1
𝟎 𝟐
𝟏 𝟑
𝟐 𝟒
𝟑 𝟓
𝟒 𝟔
𝒀 𝒀 + 𝟐
a. What ifyou don’t know how old I am? Let’suse avariable for my age. Let 𝒀 =my age in years. Can you
develop an expression to describe how old my sister is?
Your sister is 𝒀 + 𝟐 years old.
b. Please add that to the last row ofthe table.
 My age is 𝑌 years. My sister is 𝑌 + 2 years old. So,no matter what my age is,or was,my sister’s agein years
will alwaysbetwo greater than mine.
Scaffolding:
A number linein the classroom
can providean additional
reference for students. A
cardboard sheet with two
windows cut to reveal 𝑌 and
𝑌 + 2 works with Examples 1
and 2.
MP.6

Date: 4/1/15 192
Example 2 (5 minutes)
Example 2
𝟎 𝟐
𝟏 𝟑
𝟐 𝟒
𝟑 𝟓
𝟒 𝟔
𝑮 − 𝟐 𝑮
a. How old wasI when my sister was 𝟔 yearsold?
𝟒years old
b. How old wasI when my sister was 𝟏𝟓 yearsold?
𝟏𝟑years old
c. How do you know?
My ageis always 𝟐years less than my sister’s age.
d. Look at the table in Example 2. Ifyou know my sister’s age, can you determinemy age?
Wecan subtract two fromyour sister’s age, and that willequalyour age.
e. If we use the variable 𝑮for my sister’sage in years, what expressionwould describe my age in years?
𝑮 − 𝟐
f. Fill in the last row ofthe table with theexpressions.
My ageis 𝑮 − 𝟐years. My sister is 𝑮years old.
g. With apartner, calculate how old I waswhen my sister was 𝟐𝟐, 𝟐𝟑, and 𝟐𝟒yearsold.
You were 𝟐𝟎, 𝟐𝟏, and 𝟐𝟐years old, respectively.

Date: 4/1/15 193
Exercise 1–3 (15 minutes)
Exercises1–3
1. Noah and Carter are collecting box topsfor their school. They eachbring in 𝟏per day starting on thefirst day of
school. However, Carter had ahead start because hisaunt senthim 𝟏𝟓box topsbefore school began. Noah’s
grandmasaved 𝟏𝟎box tops, and Noah added those on hisfirst day.
a. Fill in the missing valuesthat indicate thetotalnumber ofbox topseachboy brought to school.
School Day
Number ofBox Tops
Noah Has
Number ofBox Tops
Carter Has
𝟏 𝟏𝟏 𝟏𝟔
𝟐 𝟏𝟐 𝟏𝟕
𝟑 𝟏𝟑 𝟏𝟖
𝟒 𝟏𝟒 𝟏𝟗
𝟓 𝟏𝟓 𝟐𝟎
b. If we let 𝑫 be the number ofdayssince the new school year began, on day 𝑫 ofschool, how many box tops
will Noah have brought to school?
𝑫 + 𝟏𝟎box tops
c. On day 𝑫 of school, how many box topswill Carter have brought toschool?
𝑫 + 𝟏𝟓box tops
d. On day 𝟏𝟎of school, how many box topswill Noah have brought to school?
𝟐𝟎box tops
e. On day 𝟏𝟎of school, how many box topswill Carter have brought toschool?
𝟐𝟓box tops
2. Each week the Primary Schoolrecycles 𝟐𝟎𝟎poundsofpaper. The IntermediateSchool also recyclesthesame
amount but had another 𝟑𝟎𝟎poundsleft over from summer school. The IntermediateSchoolcustodian added this
extra 𝟑𝟎𝟎pounds to the first recycle week.
a. Number the weeksand recordthe amount ofpaper recycled by both schools.
Week
Total Amount ofPaper Recycled by the
Primary School ThisSchool Year in Pounds
Total Amount of Paper Recycled by the
IntermediateSchool ThisSchool Year in Pounds
𝟏 𝟐𝟎𝟎 𝟓𝟎𝟎
𝟐 𝟒𝟎𝟎 𝟕𝟎𝟎
𝟑 𝟔𝟎𝟎 𝟗𝟎𝟎
𝟒 𝟖𝟎𝟎 𝟏,𝟏𝟎𝟎
𝟓 𝟏, 𝟎𝟎𝟎 𝟏,𝟑𝟎𝟎
b. If thistrend continues, what willbe thetotal amount collectedfor each school on Week 𝟏𝟎?
The Primary School will havecollected 𝟐,𝟎𝟎𝟎pounds. TheIntermediateSchool willhavecollected
𝟐, 𝟑𝟎𝟎pounds.

Date: 4/1/15 194
3. Shelly and Kristen share abirthday, but Shelly is 𝟓yearsolder.
a. Make atable showing their ages every year, beginning whenKristen wasborn.
Kristen’s Age(in years) Shelly’s Age(in years)
𝟎 𝟓
𝟏 𝟔
𝟐 𝟕
𝟑 𝟖
b. If Kristen is 𝟏𝟔yearsold, how old isShelly?
If Kristen is 𝟏𝟔years old, Shelly is 𝟐𝟏years old.
c. If Kristen is 𝑲yearsold, how old isShelly?
If Kristen is 𝑲years old, Shelly is 𝑲 + 𝟓years old.
d. If Shelly is 𝑺 yearsold, how old isKristen?
If Shelly is 𝑺 years old, Kristen is 𝑺 − 𝟓years old.
Closing(2 minutes)
 Why were we ableto write these expressions?
 There was a relationship between the two quantities that we could identify.
 What is importantto remember about labelingcolumns in a table?
 The label should be complete, with units, so the reader understands precisely what is meant.
 How are addition and subtraction expression related to one another?
 They are inverse operations. One undoes the other.
Exit Ticket (5 minutes)

Date: 4/1/15 195
Name Date
Lesson 19: Substituting to Evaluate Addition and Subtraction
Expressions
Exit Ticket
1. Jenna and Alliework together at a piano factory. They both were hired on January 3, but Jenna was hired in 2005,
and Alliewas hired in 2009.
a. Fill in the tablebelow to summarize the two workers’ experience totals.
Year Allie’s Years of Experience Jenna’s Years of Experience
2010
2011
2012
2013
2014
b. If both workers continue workingat the piano factory,when Alliehas 𝐴 years of experience on the job,how
many years of experience will Jenna have on the job?
c. If both workers continue workingat the piano factory,when Alliehas 20 years of experience on the job,how
many years of experience will Jenna have on the job?

Date: 4/1/15 196
Exit Ticket Sample Solutions
1. Jennaand Allie work together at apiano factory. They both werehired on January 3, but Jennawashiredin 2005,
and Allie washired in 2009.
a. Fill in the table below to summarize the two workers’ experiencetotals.
Year Allie’sYearsofExperience Jenna’sYearsofExperience
2010 𝟏 𝟓
2011 𝟐 𝟔
2012 𝟑 𝟕
2013 𝟒 𝟖
2014 𝟓 𝟗
b. If both workers continueworking at thepiano factory, when Allie has 𝑨 yearsofexperience on the job, how
many years of experience will Jennahave on the job?
Jenna will havebeen on thejob for 𝑨 + 𝟒years.
c. If both workers continueworking at thepiano factory, when Allie has 𝟐𝟎yearsofexperienceon thejob, how
many years of experience will Jennahave on the job?
Jenna will havebeen on thejob for 𝟐𝟒years.
Problem Set Sample Solutions
1. Suellen and Tara are in 6th grade, and both take dance lessonsat Twinkle ToesDance Studio. ThisisSuellen’sfirst
year, while thisisTara’s fifth year. Both girlsplan to continue taking lessons throughouthigh school.
a. Complete the tableshowing thenumberofyearsthe girls willhave danced at thestudio.
Grade Suellen’sYearsofExperience Dancing Tara’s YearsofExperience Dancing
Sixth 𝟏 𝟓
Seventh 𝟐 𝟔
Eighth 𝟑 𝟕
Ninth 𝟒 𝟖
Tenth 𝟓 𝟗
Eleventh 𝟔 𝟏𝟎
Twelfth 𝟕 𝟏𝟏
b. If Suellen hasbeentaking dancelessons for 𝒀 years, how many yearshasTarabeen taking lessons?
Tara has been taking dancelessons for 𝒀 + 𝟒 years.

Date: 4/1/15 197
2. Daejoy and Damian collect fossils. Before they wenton afossil-hunting trip, Daejoy had 𝟐𝟓fossils in her collection,
and Damian had 𝟏𝟔fossils in hiscollection. On a 𝟏𝟎-day fossil hunting trip, they eachcollected 𝟐new fossilseach
day.
a. Make atable showing how many fossilseach person had at the end of each day.
Day Number ofFossils in Daejoy’s Collection Number ofFossils in Damian’s Collection
𝟏 𝟐𝟕 𝟏𝟖
𝟐 𝟐𝟗 𝟐𝟎
𝟑 𝟑𝟏 𝟐𝟐
𝟒 𝟑𝟑 𝟐𝟒
𝟓 𝟑𝟓 𝟐𝟔
𝟔 𝟑𝟕 𝟐𝟖
𝟕 𝟑𝟗 𝟑𝟎
𝟖 𝟒𝟏 𝟑𝟐
𝟗 𝟒𝟑 𝟑𝟒
𝟏𝟎 𝟒𝟓 𝟑𝟔
b. If thispattern offossil-finding continues, how many fossilswill Damian havewhen Daejoy has 𝑭 fossils?
When Daejoy has 𝑭 fossils, Damian willhave 𝑭 − 𝟗 fossils.
c. If thispattern offossil-finding continues, how many fossilswill Damian havewhen Daejoy has 𝟓𝟓fossils?
When Daejoy has 𝟓𝟓fossils, Damian willhave 𝟒𝟔fossils.
3. A train consistsof three typesofcars: box cars, an engine, and acaboose.
Number ofBox Cars Number ofCarsin the Train
𝟎 𝟐
𝟏 𝟑
𝟐 𝟒
𝟏𝟎 𝟏𝟐
𝟏𝟎𝟎 𝟏𝟎𝟐
a. Tom wrote an expression for the relationshipdepictedin thetable as 𝑩 + 𝟐. Theresawrotean expression
for the same relationship as 𝑪 − 𝟐. Isit possible to have twodifferent expressionsto represent one
relationship? Explain.
Both expressions can represent thesamerelationship, depending on thepointofview. Theexpression 𝑩 + 𝟐
represents thenumber ofbox cars plus an engineand a caboose. Theexpression 𝑪 − 𝟐represents thewhole
car length ofthetrain, less theengineand caboose.
b. What do you think the variable in each student’sexpression represents? How would you definethem?
The variable 𝑪 would represent thetotalcars in thetrain. Thevariable 𝑩 would represent thenumber ofbox
cars.

Date: 4/1/15 198
4. David was 𝟑when Mariekawasborn. Completethetable.
Marieka’sAge in Years David’sAge in Years
𝟓 𝟖
𝟔 𝟗
𝟕 𝟏𝟎
𝟖 𝟏𝟏
𝟏𝟎 𝟏𝟑
𝟏𝟕 𝟐𝟎
𝟑𝟐 𝟑𝟓
𝑴 𝑴 + 𝟑
𝑫 − 𝟑 𝑫
5. Caitlin and Michaelare playing acard game. In the first round, Caitlin scored 𝟐𝟎𝟎points, and Michael scored 𝟏𝟕𝟓
points. In each ofthe next few rounds, they each scored 𝟓𝟎points. Their scoresheet isbelow.
Caitlin’spoints Michael’spoints
𝟐𝟎𝟎 𝟏𝟕𝟓
𝟐𝟓𝟎 𝟐𝟐𝟓
𝟑𝟎𝟎 𝟐𝟕𝟓
𝟑𝟓𝟎 𝟑𝟐𝟓
a. If thistrend continues, how many pointswill Michaelhave whenCaitlin has 𝟔𝟎𝟎points?
Michael will have 𝟓𝟕𝟓points.
b. If thistrend continues, how many pointswill Michaelhave whenCaitlin has 𝑪points?
Michael will have 𝑪 − 𝟐𝟓points.
c. If thistrend continues, how many pointswill Caitlin have when Michael has 𝟗𝟕𝟓points?
Caitlin will have 𝟏, 𝟎𝟎𝟎points.
d. If thistrend continues, how many pointswill Caitlin have when Michael has 𝑴points?
Caitlin will have 𝑴 + 𝟐𝟓 points.
6. The high school marching band has 𝟏𝟓drummers thisyear. The band director insiststhat thereare to be 𝟓more
trumpet playersthan drummersat all times.
a. How many trumpet playersare in themarching band thisyear?
𝟏𝟓+ 𝟓 = 𝟐𝟎. Thereare 𝟐𝟎 trumpet players this year.
b. Write an expression that describesthe relationshipofthe number oftrumpet players(𝑻)and the number of
drummers(𝑫).
𝑻 = 𝑫 + 𝟓 or 𝑫 = 𝑻 − 𝟓
c. If there are only 𝟏𝟒trumpet playersinterested in joining the marching band nextyear, how many drummers
will the band director want inthe band?
The band director willwant 𝟗drummers.

Date: 4/1/15 199
Subtraction of Decimals – Round 1
Directions: Subtract the decimals to determine the difference.
1. 9.4 − 4.1 16. 41.72 − 33.9
2. 7.4 − 3.2 17. 354.65 − 67.5
3. 49.5 − 32.1 18. 448.9 − 329.18
4. 20.9 − 17.2 19. 8 − 5.38
5. 9.2 − 6.8 20. 94.21 − 8
6. 7.48 − 2.26 21. 134.25 − 103.17
7. 58.8 − 43.72 22. 25.8 − 0.42
8. 38.99 − 24.74 23. 115 − 1.65
9. 116.32 − 42.07 24. 187.49 − 21
10. 46.83 − 35.6 25. 345.77 − 248.69
11. 54.8 − 43.66 26. 108 − 54.7
12. 128.43 − 87.3 27. 336.91 − 243.38
13. 144.54 − 42.09 28. 264 − 0.742
14. 105.4 − 68.22 29. 174.38 − 5.9
15. 239.5 − 102.37 30. 323.2 − 38.74
NumberCorrect:______

Date: 4/1/15 200
Subtraction of Decimals – Round 1 [KEY]
1. 9.4 − 4.1 𝟓. 𝟑 16. 41.72 − 33.9 𝟕. 𝟖𝟐
2. 7.4 − 3.2 𝟒. 𝟐 17. 354.65 − 67.5 𝟐𝟖𝟕. 𝟏𝟓
3. 49.5 − 32.1 𝟏𝟕. 𝟒 18. 448.9 − 329.18 𝟏𝟏𝟗. 𝟕𝟐
4. 20.9 − 17.2 𝟑. 𝟕 19. 8 − 5.38 𝟐. 𝟔𝟐
5. 9.2 − 6.8 𝟐. 𝟒 20. 94.21 − 8 𝟖𝟔. 𝟐𝟏
6. 7.48 − 2.26 𝟓. 𝟐𝟐 21. 134.25 − 103.17 𝟑𝟏. 𝟎𝟖
7. 58.8 − 43.72 𝟏𝟓. 𝟎𝟖 22. 25.8 − 0.42 𝟐𝟓. 𝟑𝟖
8. 38.99 − 24.74 𝟏𝟒. 𝟐𝟓 23. 115 − 1.65 𝟏𝟏𝟑. 𝟑𝟓
9. 116.32 − 42.07 𝟕𝟒. 𝟐𝟓 24. 187.49 − 21 𝟏𝟔𝟔. 𝟒𝟗
10. 46.83 − 35.6 𝟏𝟏. 𝟐𝟑 25. 345.77 − 248.69 𝟗𝟕. 𝟎𝟖
11. 54.8 − 43.66 𝟏𝟏. 𝟏𝟒 26. 108 − 54.7 𝟓𝟑. 𝟑
12. 128.43 − 87.3 𝟒𝟏. 𝟏𝟑 27. 336.91 − 243.38 𝟗𝟑. 𝟓𝟑
13. 144.54 − 42.09 𝟏𝟎𝟐. 𝟒𝟓 28. 264 − 0.742 𝟐𝟔𝟑. 𝟐𝟓𝟖
14. 105.4 − 68.22 𝟑𝟕. 𝟏𝟖 29. 174.38 − 5.9 𝟏𝟔𝟖. 𝟒𝟖
15. 239.5 − 102.37 𝟏𝟑𝟕. 𝟏𝟑 30. 323.2 − 38.74 𝟐𝟖𝟒. 𝟒𝟔

Date: 4/1/15 201
Subtraction of Decimals – Round 2
1. 8.4 − 5.4 16. 14 − 10.32
2. 5.6 − 3.1 17. 43.37 − 28
3. 9.7 − 7.2 18. 24.56 − 18.88
4. 14.3 − 12.1 19. 33.55 − 11.66
5. 34.5 − 13.2 20. 329.56 − 284.49
6. 14.86 − 13.85 21 574.3 − 342.18
7. 43.27 − 32.14 22. 154 − 128.63
8. 48.48 − 27.27 23. 247.1 − 138.57
9. 64.74 − 31.03 24. 12 − 3.547
10. 98.36 − 24.09 25. 1.415 − 0.877
11. 33.54 − 24.4 26. 185.774 − 154.86
12. 114.7 − 73.42 27. 65.251 − 36.9
13. 45.2 − 32.7 28. 144.2 − 95.471
14. 74.8 − 53.9 29. 2.11 − 1.949
15. 238.4 − 114.36 30. 100 − 34.746
NumberCorrect:______
Improvement:______

Date: 4/1/15 202
Subtraction of Decimals – Round 2 [KEY]
1. 8.4 − 5.4 𝟑. 𝟎 16. 14 − 10.32 𝟑. 𝟔𝟖
2. 5.6 − 3.1 𝟐. 𝟓 17. 43.37 − 28 𝟏𝟓. 𝟑𝟕
3. 9.7 − 7.2 𝟐. 𝟓 18. 24.56 − 18.88 𝟓. 𝟔𝟖
4. 14.3 − 12.1 𝟐. 𝟐 19. 33.55 − 11.66 𝟐𝟏. 𝟖𝟗
5. 34.5 − 13.2 𝟐𝟏. 𝟑 20. 329.56 − 284.49 𝟒𝟓. 𝟎𝟕
6. 14.86 − 13.85 𝟏. 𝟎𝟏 21. 574.3 − 342.18 𝟐𝟑𝟐. 𝟏𝟐
7. 43.27 − 32.14 𝟏𝟏. 𝟏𝟑 22. 154 − 128.63 𝟐𝟓. 𝟑𝟕
8. 48.48 − 27.27 𝟐𝟏. 𝟐𝟏 23. 247.1 − 138.57 𝟏𝟎𝟖. 𝟓𝟑
9. 64.74 − 31.03 𝟑𝟑. 𝟕𝟏 24. 12 − 3.547 𝟖. 𝟒𝟓𝟑
10. 98.36 − 24.09 𝟕𝟒. 𝟐𝟕 25. 1.415 − 0.877 𝟎. 𝟓𝟑𝟖
11. 33.54 − 24.4 𝟗. 𝟏𝟒 26. 185.774 − 154.86 𝟑𝟎. 𝟗𝟏𝟒
12. 114.7 − 73.42 𝟒𝟏. 𝟐𝟖 27. 65.251 − 36.9 𝟐𝟖. 𝟑𝟓𝟏
13. 45.2 − 32.7 𝟏𝟐. 𝟓 28. 144.2 − 95.471 𝟒𝟖. 𝟕𝟐𝟗
14. 74.8 − 53.9 𝟐𝟎. 𝟗 29. 2.11 − 1.949 𝟎. 𝟏𝟔𝟏
15. 238.4 − 114.36 𝟏𝟐𝟒. 𝟎𝟒 30. 100 − 34.746 𝟔𝟓. 𝟐𝟓𝟒

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