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ESSENTIAL QUESTION
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Proportions and
Percent
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How can you use
proportions and percent to
solve real-world problems?
Math On the Spot
A store may have a sale with deep discounts on some items. They can still make a profit because they first markup the wholesale price by as much as 400%, then markdown the retail price.
LESSON 5.1
Percent Increase and
Decrease
7.RP.3 LESSON 5.2Rewriting Percent
Expressions
7.RP.3, 7.EE.2, 7.EE.3 LESSON 5.3Applications of
Percent
7.RP.3, 7.EE.3You can use percent and proportions to find the amount by which real-world quantities have increased or decreased.
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Personal Math Trainer Online Practice and Help my.hrw.com Completetheseexercisestoreviewskillsyou will needforthismodule.
Percents and Decimals EXAMPLE 147% = 100% + 47%
= 100___ 100 + ___ 10047
= 1 + 0.47 = 1.47
Writeeach percentasadecimal.
1. 22% 2. 75% 3. 6% 4. 189%
Writeeachdecimalasa percent.
5. 0.59 6. 0.98 7. 0.02 8. 1.33
Find the Percent of a Number EXAMPLE 30% of 45 = ? 30% = 0.30 4 5 ×0.3 _ 13.5
Findthe percentof each number.
9. 50% of64 10. 7% of30 11. 15% of160 12. 32% of62 13. 120% of 4 14. 6% of1,000
Write the percent as a decimal. Multiply.
Write the percent as the sum of 1 whole and a percent remainder.
Write the percents as fractions. Write the fractions as decimals. Simplify. 32 59% 0.22 19.84 2.1 98% 0.75 24 2% 0.06 133% 1.89 60 4.8 Unit 2 138 © H ough to n Miff l in H ar cour t Pu b l ishing Compan y Math Trainer Online Assessment and Intervention Personal my.hrw.com 1 2 3 Response to Intervention 1 2 3 Response to Intervention Professional Development
PROFESSIONAL DEVELOPMENT VIDEO
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Interactive Answers and Solutions
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Interactive Whiteboards
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Personal Math Trainer: Online Assessment and Intervention
Assign automatically graded homework, quizzes, tests, and intervention activities. Prepare your students with updated practice tests aligned with Common Core.
Author Juli Dixon models successful teaching practices as she explores percent problems in an actual seventh-grade classroom.
Are You Ready?
Assess Readiness
Use the assessment on this page to determine if students need intensive or strategic intervention for the module’s prerequisite skills.
Intervention Enrichment
Access Are You Ready? assessment online, and receive instant scoring, feedback, and customized intervention or enrichment.
Online and Print Resources
Skills Intervention worksheets • Skill 30 Percents and
Decimals
• Skill 46 Find the Percent of a Number
Differentiated Instruction • Challenge worksheets
PRE-AP
Extend the Math PRE-AP
Lesson Activities in TE
Real-World Video Viewing Guide
After students have watched the video, discuss the following: •What is a discount?
•How is the amount of the discount calculated? Multiply the original price by the discount expressed as a fraction or a decimal.
Reading
Start-Up
Active Reading
Tri-FoldBeforebeginningthemodule, create atri-foldtohelpyou learntheconceptsand
vocabularyinthismodule. Foldthepaperinto threesections. Label thecolumns “What I Know,” “What I Needto Know,” and “What I Learned.”
Completethefirsttwocolumnsbeforeyou read. Afterstudyingthemodule, completethethird.
Visualize Vocabulary
Usethe✔wordstocompletethetriangle. Writethereview wordthat fitsthedescription in eachsection of thetriangle.
Understand Vocabulary
Completethesentences using the previewwords.
1.Afixedpercentoftheprincipal is .
2.Theoriginal amountofmoneydepositedorborrowedisthe .
3.A istheamountofincreasedividedbytheoriginal amount. astatementthat
tworatiosareequivalent
Vocabulary Review Words ✔ proportion (proporción) ✔ percent (porcentaje) rate (tasa) ✔ ratio (razón) unit rate (tasa unitaria) Preview Words percent decrease
(porcen-taje de disminución) percent increase
(porcen-taje de aumento) principal (capital) simple interest (interés
simple)
comparesanumberto 100
acomparisonoftwonumbersbydivision
proportion percent ratio simpleinterest principal percentincrease 139 Module 5 © H ough to n Miff l in H ar cour t Pu b l ishing Compan y
Reading Start-Up
Have students complete the activities on this page by working alone or with others.
Strategies for English Learners
Each lesson in the TE contains specific strategies to help English Learners of all levels succeed.
Emerging: Students at this level typically progress very quickly, learning to use English for immediate needs as well as beginning to understand and use academic vocabulary and other features of academic language.
Expanding: Students at this level are challenged to increase their English skills in more contexts, and learn a greater variety of vocabulary and linguistic structures, applying their growing language skills in more sophisticated ways appropriate to their age and grade level.
Bridging: Students at this level continue to learn and apply a range of high-level English language skills in a wide variety of contexts, includ-ing comprehension and production of highly technical texts.
Active Reading
Integrating Language Arts
Students can use these reading and note-taking strategies to help them organize and understand new concepts and vocabulary.
Additional Resources Differentiated Instruction •Reading Strategies EL
EL
After Students will:•solve real-world problems using percent
In this module
Students represent and solve problems involving proportional relationships:
•solve problems involving percent increase, percent decrease, and percent of change
•solve markup and markdown problems
•use percents to find sales tax, tips, total cost, simple interest
Before
Students understand proportional relationships:
•convert units within a measurement system •solve real-world problems
involving percent
Tracking Your Learning Progression
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What It Means to You
You will findhelpful waystorewriteanexpression inanequivalentform.
What It Means to You
You will useproportionstosolveproblemsinvolvingratio and percent.
Understanding the Standards and the vocabulary terms in the Standards will help you know exactly what you are expected to learn in this module.
Findtheamountofsalestax ifthesalestax rateis5% andthe costoftheitemis $40.
5% = ___ 5 100 = __ 201
Multiply __ 1
20 timesthecosttofindthesalestax.
1
__ 20 × 40 = 2
Thesalestax is $2.
Astoreadvertisesthatall bicyclehelmetswill besoldat 10% off theregularprice. Findtwoexpressionsthatrepresentthe valueof thesalepricepforthehelmetsthatareonsale.
Saleprice = original priceminus 10% oftheprice
= p - 0.10p
Equivalently,
p - 0.10p = p(1 - 0.10) = 0.90p
GETTING READY FOR
Proportions and Percent
Useproportional relationships tosolvemultistepratioand percentproblems.
Key Vocabulary
proportion (proporción) An equation that states that two ratios are equivalent.
ratio (razón) A comparison of two quantities by division.
percent (porcentaje) A ratio that compares a part to the whole using 100.
Understandthatrewritingan expressionindifferentformsina problemcontextcanshed light ontheproblemandhowthe quantitiesinitarerelated.
Key Vocabulary
expression (expresión) A mathematical phrase containing variables, constants and operation symbols.
EXAMPLE 7.RP.3 EXAMPLE 7.EE.2 Visit my.hrw.com to see all CA Common Core Standards explained. 7.EE.2 7.RP.3 Unit 2 140 © H ough to n Miff l in H ar cour t Pu b l ishing Compan y • I mage Cr edits : © H emer a T echno l ogies /Al am y I mages
GETTING READY FOR
Proportions and Percent
Use the examples on the page to help students know exactly what they are expected to learn in this module.
my.hrw.com Go online to see a complete unpacking of the CA Common Core Standards.
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Content AreasRatios and Proportional Relationships—7.RP
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Expressions and Equations—7.EE
Cluster Use properties of operations to generate equivalent expressions.
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Lesson5.1
Lesson 5.2
Lesson 5.3
7.RP.3 Recognize and represent proportional relationships between quantities.
7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
80% 50% The first decimal square shows 30% more than the second decimal square.
Lesson Support
Content Objective
Students will learn to use percents to describe change.Language Objective
Students will show how to use percents to describe change.LESSON
5.1
Percent Increase and Decrease
Building Background
Visualize Math Have students work with a partner to shade
in two decimal squares each representing a different percent. Then have them compare the percents.
Learning Progressions
In this lesson, students continue to build their understanding of percents. They will use percent to describe change as percent increase and percent decrease. Some key understandings for students are the following:
• Percent change (increase or decrease) is always the amount of change divided by the original amount. • Percent increase describes how much a quantity
increases in comparison to the original amount. • Percent decrease describes how much a quantity
decreases in comparison to the original amount. • The original amount and the percent of change can be
used to determine the new amount.
The concepts of percent increase and percent decrease will be used to solve a variety of real-world problems, such as problems involving price markups and markdowns.
Cluster Connections
This lesson provides an excellent opportunity to connect ideas in this cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. Give students the following prompt: “One week a store
decreased the price of potatoes by 25%. The next week the price was increased by 25%. The original price of 5 pounds of
potatoes was $4.00. How does the final price compare with the original price?” Have students justify their answer.
The final price was less. 4 × 0.25 = 1.00, 4 - 1 = 3. The first week the price was $3.
Then 3 × 0.25 = 0.75, 3 + 0.75 = 3.75. The final price was $3.75, which is less than the original price, $4.00.
Focus | Coherence | Rigor
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7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.
Math Talk
Language Support
EL
PROFESSIONAL DEVELOPMENT
Linguistic Support
EL
Academic/Content Vocabulary
percent – The word percent may be familiar to speakers of Spanish and other Latin-based languages. The root word percent means one part out of each hundred. Point out that one cent is another word for one penny and that there are 100 pennies in a US dollar. In Spanish the meaning of the word for percent
porciento is much more evident because the word
ciento is also the word for hundred.
Multiple Meaning Words
change – Explain to students that the word change
can have different meanings in mathematics. When working with money, change can indicate an amount of money returned from a transaction, or it can indicate the coins. In this lesson, percent change
describes the percent of increase or decrease in an amount compared to the original amount. Review with students the words increase and decrease.
Leveled Strategies for English Learners
Emerging Have students select a problem from this lesson and demonstrate how to find the
percentage increase or the percentage decrease.
Expanding Pair students and have them select a problem from the lesson and explain it to each
other. Provide a sentence frame:
This problem is an example of percentage increase/decrease because ______________.
Bridging Have students write in their journal when they think showing a percent increase, rather
than an actual amount of increase, can be more useful.
Model for English learners how to begin their responses with a sentence frame.
Finding percentincrease and finding percentdecrease are alikebecause ______________. Finding percentincrease and finding percentdecrease are not alike
because ______________.
EL
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Emerging 2.I.6c. Reading/viewing closely – Use knowledge of morphology, context, reference materials, and visual cues to determine the meaning of unknown and multiple-meaning words on familiar topics.
Expanding 2.I.6c. Reading/viewing closely – Use knowledge of morphology, context, reference materials, and visual cues to determine the meaning of unknown and multiple-meaning words on familiar and new topics.
Bridging 2.I.6c. Reading/viewing closely – Use knowledge of morphology, context, reference materials, and visual cues to determine the meaning, including figurative and connotative meanings, of unknown and multiple-meaning words on a variety of new topics.
Engage
ESSENTIAL QUESTION
How do you use percents to describe change? Sample answer: Dividing the amount of the change by the original amount results in a percent increase or decrease.
Motivate the Lesson
Ask: What does it mean to have a 100% increase in something? Begin the lesson to find out.
Explore
Motivate the Lesson
A pen costs $1, and a jacket costs $199; both prices increase by $1. Have students discuss how they preceive both increases, and use this opportunity to introduce relative increases.
Explain
EXAMPLE 1
Focus on Communication
Make sure students can express in their own words that a percent increase is always the amount of change divided by the original amount.
Questioning Strategies Mathematical Practices
•How do you find the amount of change? Subtract the lesser value from the greater value.
YOUR TURN
Focus on Technology Mathematical Practices
If students are using a calculator, make sure parentheses are inputted to find (64 - 52) ÷ 52.
Talk About It
Check for Understanding
Ask: If you were not told a situation is a percent increase, how could you recognize that it is? The new amount is greater than the original amount.
EXAMPLE 2
Questioning Strategies Mathematical Practices
•How could you find 50% of 89? 50% of a number is half the number. 89 ÷ 2 is 44.5. Avoid Common Errors
Remind students that when changing a fraction to a decimal, the top number is divided by the bottom number. For example, __ 3889 means 38 ÷ 89 or 89 ⟌ ⎯ 38 .
YOUR TURN
Focus on Modeling Mathematical Practices
Have students show symbolically the connection between the original amount, 18, the new amount, 12, the amount of change, 6, and the percent decrease, 33%.
5.1
L E S S
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Percent Increase and Decrease
Interactive Whiteboard
Interactive example available online ADDITIONAL EXAMPLE 1
The number of people signed up for a bus trip increased from 32 to 45. What is the percent increase? Round to the nearest percent. 41%
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Interactive Whiteboard
Interactive example available online ADDITIONAL EXAMPLE 2
The regular price of a scooter is $65.50. It is on sale for $52.40. What is the percent decrease from the regular price to the sale price of the scooter?
20%
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Thestudentisexpectedto:
Ratio and Proportional Relationships—7.RP.3
Useproportional relationshipstosolvemultistepratioand percentproblems.
Mathematical Practices
My Notes Math Trainer Online Practice and Help Personal my.hrw.com
Math On the Spot
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Finding Percent Decrease
Whenthechangeintheamountdecreases, you can useasimilarapproach tofindpercentdecrease.Percent decreasedescribeshowmuchaquantity decreasesincomparisontotheoriginal amount.
Davidmoved fromahousethatis 89 milesaway fromhisworkplaceto ahousethatis 51 milesaway fromhisworkplace. Whatisthe percent decreasein thedistance fromhishometohisworkplace?
EXAMPLE 2
Findtheamountofchange.
AmountofChange = Greater Value - Lesser Value
= 89 - 51 = 38
Findthepercentdecrease. Roundtothenearestpercent. PercentChange = Amount of Change______________ Original Amount
= 38__ 89
≈ 0.427 = 43%
Reflect
3. CritiqueReasoningDavidconsideredmovingevenclosertohis workplace. Heclaimsthatifhehaddoneso, thepercentofdecrease wouldhavebeenmorethan 100%. IsDavidcorrect? Explainyour reasoning.
STEP 1
STEP 2
4. Thenumberofstudentsinachessclubdecreasedfrom 18 to 12. What is thepercentdecrease? Roundtothenearestpercent. 5. Officer Brimberrywrote 16 ticketsfortraffic violations lastweek, but
only 10 ticketsthisweek. Whatisthepercentdecrease? YOUR TURN
How is finding percent decrease the same as finding
percent increase? How is it different?
Itsthesamebecause you subtractthe
lesser valuefrom thegreater value tofindtheamount ofchangeandthen dividetheamount ofchangebythe original amountto findpercentchange.
Itsdifferentbecause theoriginal amount isgreaterthanthe newquantity.
Math TalkMathematical Practices
7.RP.3
Substitute values. Subtract.
Substitute values. Divide.
Write as a percent and round.
No; The leastdistanceDavidcould livefromhis workplaceis 0 miles, whichcorrespondstoa 100%
decrease.Adecreasegreaterthanthisisimpossible.
33% 37.5% © H ough to n Miff l in H ar cour t Pu b l ishing Compan y Unit 2 142
Howdoyou usepercentstodescribechange?
?
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Finding Percent Increase
Percentscanbe usedtodescribehowanamountchanges. PercentChange = Amount of Change______________ Original Amount
Thechangemaybeanincreaseoradecrease.Percent increasedescribeshow muchaquantityincreasesincomparisonto theoriginal amount.
Amber gotaraise, andherhourlywageincreased from $8 to $9.50. Whatis the percentincrease?
Findtheamountofchange.
AmountofChange = Greater Value - Lesser Value
= 9.50 - 8.00 = 1.50
Findthepercentincrease. Roundtothenearestpercent. PercentChange = Amount of Change______________ Original Amount
= ____ 18.5.000
= 0.1875
≈ 19%
Reflect
1. Whatdoesa 100% increasemean?
EXAMPL EXAMPLE 1
STEP 1
STEP 2
L E S SO N
5.
1
Percent Increase
and Decrease
ESSENTIAL QUESTION
2. Thepriceofapairofshoesincreasesfrom $52 to $64. Whatisthe percentincreasetothenearestpercent? YOUR TURN
7.RP.3
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Substitute values. Subtract. Substitute values. Divide. Write as apercent and round.
Theamountofchangeisequal totheoriginal amount;
the valuedoubles.
23%
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MathBackground
The percent of change compares the amount of change to the original amount. When there is a series of percent changes, the original amount changes with each additional percent increase or decrease. For example, the percent increase from 10 to 15, where 10 is the original amount, is a 50% increase
(
_____ 1510-10 = __ 105 = 50%)
, but the percent decrease of 15 back to 10 is a 33.3% decrease(
_____ 1515-10 = __ 155 = 33. _3 %)
because 15 is now the original amount.IntegrateMathematical Practices MP.2
This lesson provides an opportunity to address this Mathematical Practice standard. It calls for students to create and use representations to organize, record, and communicate mathemati-cal ideas. Students use verbal equations to model a relationship among the percent increase or decrease, the amount of change, and the original amount. Students use these equations
to then write numerical equations to find the percent of change.
EXAMPLE 3
Engage with the Whiteboard
Cover up the solution and have students read the Example a couple of times. Then invite a student to circle all the information needed to solve the problem and to draw a line through any extraneous information.
Questioning Strategies Mathematical Practices
•Why is 1.15 used as a factor for 115%? 1.15 is the decimal equivalent for 115%. To multiply by a percent, the percent must be represented by either a decimal or a fraction.
•How do you know whether to add or subtract the amount of change? Since the population increased, the amount of change is added to the original amount.
Focus on Critical Thinking Mathematical Practices
Be sure students understand how to change any percent to a decimal. Remind them that percents less than 100% will equal decimals less than 1.
YOUR TURN
Avoid Common Errors
When solving Exercises 8 and 9, students may skip Step 2 as shown in Example 3. Remind them that the new amount for a percent increase is found by adding the original amount to the amount of change. The new amount for a percent decrease is found by subtracting the amount of change from the original amount.
Elaborate
Talk About ItSummarizethe Lesson
Ask: How would you explain percent increase and percent decrease? Percent increase is a ratio of the amount of the increase to the original amount expressed as a percent. Percent decrease is a ratio of the amount of the decrease to the original amount expressed as a percent.
GUIDED PRACTICE
Engage with the Whiteboard
In the space under each of Exercises 1–6, invite volunteers to write the original amount (OM), the amount of change (AC), and the ratio they will simplify to find the percent increase or decrease (PI or PD). So, for Exercise 1 students would write OM = 5; AC = 8 - 5 or 3; PI = __ 35 .
Avoid Common Errors
Exercise 6 Remind students to use number sense to check their answers for reasonableness. 16 is more than 3 × 5, so the percent will be more than 200%.
Exercise 14 Students might question whether the 3 hours be changed to minutes or the
half hour be treated as a fraction or a decimal. Either approach will yield the correct answer. However, the math is much easier if the calculation is performed using hours as the unit of measure.
Interactive Whiteboard
Interactive example available online ADDITIONAL EXAMPLE 3
A shoe sales associate earned $300 in August. In September she earned 8% more than she did in August. How much did she earn in September? $324
Guided Practice
Find each percent increase. Round to the nearest percent. (Example 1)
1. From $5 to $8 2. From 20 students to 30 students
3. From 86 books to 150 books 4. From $3.49 to $3.89
5. From 13 friends to 14 friends 6. From 5 miles to 16 miles
7. Nathan usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day. If he starts drinking 64 ounces, what
is the percent increase? Round to the nearest percent. (Example 1)
Find each percent decrease. Round to the nearest percent. (Example 2)
8. From $80 to $64 9. From 95 °F to 68 °F
10. From 90 points to 45 points 11. From 145 pounds to 132 pounds
12. From 64 photos to 21 photos 13. From 16 bagels to 0 bagels
14. Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she was only allowed to play video games for half an hour per day. What is the percent decrease? Round to
the nearest percent. (Example 2)
Find the new amount given the original amount and the percent of change. (Example 3)
15. $9; 10% increase 16. 48 cookies; 25% decrease
17. 340 pages; 20% decrease 18. 28 members; 50% increase
19. $29,000; 4% decrease 20. 810 songs; 130% increase
21. Adam currently runs about 20 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run per week?(Example 3)
22. What process do you use to find the percent change of a quantity?
CHECK-IN ESSENTIAL QUESTION
?
60% 74% 8% 20% 78% $9.90 272 pages $27,840 26 milesDivide the amount of change in the quantity by the original amount, then express the answer as a percent.
36 cookies 42 members 1,863 songs 50% 67% 28% 9% 100% 50% 11% 220% 83% Unit 2 144 © Hough ton Mifflin Har cour t P ublishing Compan y
DO NOT EDIT--Changes must be made through “File info” CorrectionKey=A 7_MCAAESE202610_U2M05L1.indd 144 4/23/13 12:39 PM Math Trainer Online Practice and Help Personal my.hrw.com
Math On the Spot
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Using Percent of Change
Given an original amount and a percent increase or decrease, you can use the percent of change to find the new amount.
The grizzly bear population in Yellowstone National Park in 1970 was about 270. Over the next 35 years, it increased by about 115%. What was the population in 2005?
Find the amount of change. 1.15 × 270 = 310.5
≈ 311 Find the new amount.
New Amount = Original Amount + Amount of Change
= 270 + 311
= 581
The population in 2005 was about 581 grizzly bears.
Reflect
6. Why will the percent of change always be represented by a positive number?
7. Draw Conclusions If an amount of $100 in a savings account increases by 10%, then increases by 10% again, is that the same as increasing by 20%? Explain.
EXAMPL EXAMPLE 3
STEP 1
STEP 2
A TV has an original price of $499. Find the new price after the given percent of change.
8. 10% increase 9. 30% decrease
YOUR TURN
7.RP.3
Find 115% of 270. Write 115% as a decimal. Round to the nearest whole number.
Substitute values. Add.
Add the amount of change because the population increased.
No. An increase of 10% gives a balance of $110. Another 10% increase would give a balance of $121. One increase of 20% would give a balance of $120.
$548.90 $349.30
Sample answer: The amount of change is equal to the greater value minus the lesser value, which is always positive. 143 Lesson 5.1 © Hough ton M ifflin Har cour t P ublishing Compan y • Image Cr edits: ©C orbis
DO NOT EDIT--Changes must be made through “File info” CorrectionKey=B
7_MCABESE202610_U2M05L1.indd 143 30/10/13 2:42 AM
Cooperative Learning
Have students work in pairs to solve percent increase and decrease problems. Start with a problem, and have each person complete one step in the process. Have students exchange roles so each person has a chance to complete each step at least once. This helps emphasize that finding percent increase or decrease is a multi-step process.
Critical Thinking
Ask students to think about percent increase and decrease in the context of integers. For example, if a bank account increases from
-$100 to $100, can you use the formula to calculate percent increase? Does the answer make sense? The formula gives a percent increase of -200% in this context. This percent doesn’t make much intuitive sense, so percent increase may not be a useful tool for
understanding increases from negative to positive.
Additional Resources
Differentiated Instruction includes:
•Reading Strategies
•Success for English Learners EL
•Reteach
•Challenge PRE-AP
DIFFERENTIATE INSTRUCTION
DO NOT EDIT--Changes must be made through "File info"
CorrectionKey=B
Math Trainer Online Assessment and Intervention Personal Online homework assignment available my.hrw.com
Evaluate
GUIDED AND INDEPENDEN
T PRACTICE
Concepts & Skills Practice
Example 1
Finding Percent Increase
Exercises 1–7, 23, 25
Example 2
Finding Percent Decrease
Exercises 8–14, 24, 25
Example3
Using Percent of Change
Exercises 15–21, 26
Additional Resources Differentiated Instruction includes: •Leveled Practice Worksheets
Lesson Quiz available online
5.1 LESSON QUIZ
Find each percent increase or decrease to the nearest percent. 1. from 14 books to 40 books
2. from 72 points to 50 points
Find the new amount given the original amount and the percent of change.
3. $12; 20% increase
4. 36 grams; 45% decrease
5. If 48 eggs are used in the cafeteria today but the number expected to be used tomorrow is 30% less than that, how many eggs are expected to be used tomorrow?
6. Priscilla currently reads 10 pages in her book each night. She wants to increase the number of pages by 30%. How many pages will Priscilla read each night after the increase?
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Focus | Coherence | Rigor
7.RP.3
Exercise Depth of Knowledge (D.O.K.) Mathematical Practices
23 2 Skills/Concepts MP.2 Reasoning
24 2 Skills/Concepts MP.2 Reasoning
25 2 Skills/Concepts MP.4 Modeling
26 4 Extended Thinking MP.7 Using Structure
27 3 Strategic Thinking MP.7 Using Structure
28 3 Strategic Thinking MP.3 Logic
29 3 Strategic Thinking MP.4 Modeling
7.RP.3 Answers 1. 186% increase 2. 31% decrease 3. $14.40 4. 19.8 g 5. 34 6. 13
Work Area 26. Percent error calculations are used to determine how close to the true
values, or how accurate, experimental values really are. The formula is similar to finding percent of change.
Percent Error = |__________________________ Experimental Value Actual Value- Actual Value| × 100
In chemistry class, Charlie records the volume of a liquid as 13.3 milliliters. The actual volume is 13.6 milliliters. What is his percent error? Round to the nearest percent.
27. Look for a Pattern Leroi and Sylvia both put $100 in a savings account. Leroi decides he will put in an additional $10 each week. Sylvia decides to put in an additional 10% of the amount in the account each week.
a. Who has more money after the first additional deposit? Explain.
b. Who has more money after the second additional deposit? Explain.
c. How do you think the amounts in the two accounts will compare after a month? A year?
28. Critical Thinking Suppose an amount increases by 100%, then decreases by 100%. Find the final amount. Would the situation change if the original increase was 150%? Explain your reasoning.
29. Look for a Pattern Ariel deposited $100 into a bank account. Each Friday she will withdraw 10% of the money in the account to spend. Ariel thinks her account will be empty after 10 withdrawals. Do you agree? Explain.
FOCUS ON HIGHER ORDER THINKING
They have the same. $100 + $10 = $110 and $100 + 10%($100) = $110.
Sylvia has more. Leroi has $110 + $10 = $120 and Sylvia has $110 + 10%($110) = $121.
Because Sylvia will have more after the second additional deposit and she will be depositing increasing amounts, she will always have more in her account.
The final amount is always 0. A 100% decrease of any amount would leave 0.
No. Only the first withdrawal is $10. Each withdrawal after that is less than $10 because it is 10% of the remaining balance. There will be money left after 10 withdrawals.
2% Unit 2 146 © Hough ton Mifflin Har cour t P ublishing Compan y
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Atlantic Basin Hurricanes
Year Hurricanes Personal Math Trainer Online Practice and Help my.hrw.com
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Independent Practice
5.1
23. Complete the table.
Item Original Price New Price Percent Change Increase or Decrease
Bike $110 $96 Scooter $45 $56 Tennis
Racket $79 5% Increase Skis $580 25% Decrease
24. Multiple Representations The bar graph shows the number of hurricanes in the Atlantic Basin from 2006–2011.
a. Find the amount of change and the percent of decrease in the number of hurricanes from 2008 to 2009 and from 2010 to 2011. Compare the amounts of change and percents of decrease.
b. Between which two years was the percent of change the greatest? What was the percent of change during that period?
25. Represent Real-World Problems Cheese sticks that were previously priced at “5 for $1” are now “4 for $1”. Find each percent of change and show your work.
a. Find the percent decrease in the number of cheese sticks you can buy for $1.
b. Find the percent increase in the price per cheese stick.
7.RP.3
5; 5; 62.5%; 41.7%; the amount of change is the same, but the percent of change is less from 2010 to 2011.
2009 and 2010; 300% increase
Amount of change = 1; percent decrease = 1 _ 5 = 20%
$1.00
____ 5 = $0.20 each; $1.00____ 4 = $0.25 each. Amount of change = $0.05; percent increase = 0.05 ____ 0.20 = 25%
$82.95 ≈ 13% ≈ 24% $435 Decrease Increase 145 Lesson 5.1 © Hough ton Mifflin Har cour t P ublishing Compan y
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EXTEND THE MATH
PRE-APActivity On a grid draw a 4 × 4 square. Use the square and what you have learned about percent increase and percent decrease to determine what happens to the area of the square when the sides are increased by 50%. State by what percent the area increases. Then make a third square by decreasing the sides of the second square by 50%. State by what percent the area decreases. By what percent would you have had to change the sides of the 4 × 4 square to get the third square?
The area of the 4 × 4 square is 16 units2.
Increasing the sides by 50% makes a 6 × 6 square with an area of 36 units2. The area of the first
square is increased by 125%. Decreasing the second square’s sides by 50% makes a 3 × 3 square with an area of 9 units2. The area of the
second square is decreased by 75%. The sides of the original square could have been decreased by 25% to get the third square.
Activity available online my.hrw.com
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100% 300 75 75 75 75 75 75 25% 25% 25% 25% 25%
Lesson Support
Content Objective
Students will learn to rewrite percent expressions to solve markup and markdown problems.Language Objective
Students will demonstrate and explain how to rewrite expressions to help you solve markup andmarkdown problems.
LESSON
5.2
Rewriting Percent Expressions
Building Background
Visualize Math Knowledge Draw the bar model on the
board. Discuss with students what the model shows and how they could use the model to find the missing information. For example, the model shows that the amount 300 is equal to 100%. Four equal parts of the second bar are equal to 100%. So, each part is 300 ÷ 4 = 75. The fifth 25% is another 75. So, the total length of the top bar is 375, which is 125% of 300.
Learning Progressions
In this lesson, students extend their skill at using percents to solve problems by rewriting expressions for easier computation. Some key understandings for students are the following:
• A percent can be written as a decimal or as a fraction. Depending on the problem, one of the two forms may provide a more efficient solution than the other. • A markup is an example of a percent increase. The term
markup sometimes refers to a percent increase and sometimes to the amount of the increase. A markup of 20% on $150 is a markup of $30.
• A markdown is an example of a percent decrease. Concepts related to percent and the use of equivalent expressions will continue to be applied in everyday life and in the study of algebra.
Cluster Connections
This lesson provides an excellent opportunity to connect ideas in this cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. Give students the following prompt: “Elisa and Dan each are calculating the sale prices of a tablet device at two different stores. What is the sale price at each store?” Have students complete the table and ask them show a one-step calculation to find each sale price.
Store OrPirgicinae l DiPescounrcentt SalePrice Computer Deals $280 15% $238 Today’s Computers $315 25% $236.25 280 × 0.85 = 238; 315 × 0.75 = 236.25
Focus | Coherence | Rigor
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7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.
Math Talk
Language Support
EL
PROFESSIONAL DEVELOPMENT
Linguistic Support
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Academic/Content Vocabulary
increase or decrease – In this lesson, percents are used to solve markup and markdown problems. Point out to English learners the words that cue them to whether the change is increase or decrease. Words that cue an increase: markup (noun), mark up (verb), profit
Words that cue a decrease: markdown (noun), mark down (verb), loss, discount
Word that cues neither an increase nor a decrease:
break even
Rules and Patterns
co- – Point out to English learners any prefixes, suffixes, etc. to help them figure out the meanings of words in word problems. The prefix co-, meaning with, appears in the word coefficient in this lesson.
Common words with the prefix co- include coworker, co-author, co-star, co-exist, coed. Notice that some words have a hyphen after the prefix co- and while others do not.
Leveled Strategies for English Learners
Emerging Visual cues, like bar models, can help students at this level of English proficiency
understand an abstract idea or concept. Have students draw and label a bar model to demonstrate how to solve a markup problem.
Expanding Have pairs of students review and discuss the steps in Example 1 of the lesson before
solving one of the word problems in Independent Practice.
Bridging Pair students at this level of English proficiency to discuss and review the steps in
Example 1 of the lesson. Then have them explain the difference between how to solve a markup vs. markdown problem.
To help English learners answer the question posed in Example 1 Math Talk, give them a model to begin their answer with:
It makes sense to write the retail price as the sum of _______ because _______. A good reason for writing the retail price as the sum of _______ is _______.
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Emerging 2.I.6c. Reading/viewing closely – Use knowledge of morphology, context, reference materials, and visual cues to determine the meaning of unknown and multiple-meaning words on familiar topics.
Expanding 2.I.6c. Reading/viewing closely – Use knowledge of morphology, context, reference materials, and visual cues to determine the meaning of unknown and multiple-meaning words on familiar and new topics.
Bridging 2.I.6c. Reading/viewing closely – Use knowledge of morphology, context, reference materials, and visual cues to determine the meaning, including figurative and connotative meanings, of unknown and multiple-meaning words on a variety of new topics.
5.2
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Rewriting Percent Expressions
Engage
ESSENTIAL QUESTION
How can you rewrite expressions to help you solve markup and markdown problems?
Sample answer: Markups are 1 plus a percent of the cost, and markdowns are 1 minus a percent of a price. Either can be rewritten as a single term.
Motivate the Lesson
Ask: Did you ever want to figure out the sale price of an item before you got to the check-out counter? Begin the lesson to find out how to do this.
Explore
Multiple Representations Mathematical Practices
Explain that a certain pack of gum costs $1 and that you have 100% of what it costs to buy that gum. Show students four quarters. Explain that you plan to sell the pack of gum to make a profit. You plan a markup of 50%. Ask how much 50% of $1 is. Show the original cost, four quarters, in one hand and the markup, two quarters, in your other hand. Explain that the retail price is now $1.50.
Explain
EXAMPLE 1
Focus on Modeling Mathematical Practices
Point out to students that the part of the model in Step 1 labeled as s is equivalent to 1s and represents 100% of the original cost. The part labeled 0.42s shows 42% of the original cost, the amount being added to the original cost, while the entire model represents 142% of the original cost.
Questioning Strategies Mathematical Practices
•How could you use a mathematical property to add 1s+ 0.42s? Use the Distributive Property to write 1s+ 0.42s as (1 + 0.42)s.
•How could you use the expression to help you determine the retail price of a skateboard that cost the store $50? Substitute $50 for s in 1.42s. 1.42 × $50 = $71
YOUR TURN
Avoid Common Errors
Students may think that tripling a cost means a 300% markup. A cost x tripled is 3x. Breaking apart 3x into the cost plus the markup yields x+ 2x. So, you must add 200% of x or 2x to x
to get triple the cost, 3x.
Talk About It
Check for Understanding
Ask: Why will 1.1c work as an expression for a 10% markup, no matter what is being sold? c is a variable that can stand for any original cost. 1.1 is a constant that represents 100% plus 10%.
Interactive Whiteboard
Interactive example available online ADDITIONAL EXAMPLE 1
A shoe store buys a pair of boots from a supplier for b dollars. The store’s manager decides on a markup of 35%. Write an expression for the retail price of a pair of boots. 1.35b my.hrw.com
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Thestudentisexpectedto: Expressions and Equations—7.EE.2Understandthatrewritinganexpressionindifferent formsinaproblemcontextcanshed lightontheproblem andhow thequantitiesinitarerelated.
Ratio and Proportional Relationships—7.RP.3
Useproportional relationshipstosolvemultistepratioand percentproblems.Also 7.EE.3
Mathematical Practices
Math On the Spot my.hrw.com Math Trainer Online Practice and Help Personal my.hrw.com Animated Math my.hrw.com p -0.2p p 0.2p
2. Rick buys remote control cars to resell. He applies a markup of 10%.
a. Write two expressions that represent the retail price of the cars.
b. If Rick buys a remote control car for $28.00, what is his selling price?
3. An exclusive clothing boutique triples the price of the items it purchases for resale.
a. What is the boutique’s markup percent?
b. Write two expressions that represent the retail price of the clothes.
YOUR TURN
Calculating Markdowns
An example of a percent decrease is a discount, or markdown. A price after a markdown may be called a sale price. You can also use a bar model to represent the price of an item including the markdown.
A discount store marks down all of its holiday merchandise by 20% off the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23.
Use a bar model.
Draw a bar for the regular price p.
Then draw a bar that shows the discount: 20% of p, or 0.2p.
The difference between these two bars represents the price minus the discount, p- 0.2p. EXAMPLE 2 STEP 1 7.EE.2, 7.RP.3, 7.EE.3 1c+ 0.1c, 1.1c 1c+ 2c; 3c $30.80 200% Unit 2 148 © Hough ton Mifflin Har cour t P ublishing Compan y
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Math On the Spot
my.hrw.com s+0.42s 0.42s s ESSENTIAL QUESTION L E S S O N
5.2
Rewriting Percent
Expressions
Calculating Markups
A markup is one kind of percent increase. You can use a bar model to represent the retail price of an item, that is, the total price including the markup.
To make a profit, stores mark up the prices on the items they sell. A sports store buys skateboards from a supplier for s dollars. What is the retail price for skateboards that the manager buys for $35 and $56 after a 42% markup?
Use a bar model.
Draw a bar for the cost of the skateboard s. Then draw a bar that shows the markup: 42% of s, or 0.42s.
These bars together represent the cost plus the markup, s+ 0.42s. Retail price = Original cost + Markup
= s + 0.42s
= 1s + 0.42s
= 1.42s
Use the expression to find the retail price of each skateboard.
s=$35 Retail price = 1.42($35) = $49.70
s=$56 Retail price = 1.42($56) = $79.52 Reflect
1. What If? The markup is changed to 34%; how does the expression for the retail price change?
EXAMPL EXAMPLE 1
STEP 1
STEP 2
STEP 3
How can you rewrite expressions to help you solve markup and markdown problems?
Why write the retail price as the sum of two terms?
as one term?
Math Talk
Mathematical Practices
Why write the retail price 7.EE.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Also7.RP.3, 7.EE.3 7.EE.2, 7.RP.3, 7.EE.3 Sample answer: Two terms shows the original cost and the markup. One term allows for quicker calculation.
The expression would change to 1s+ 0.34s or 1.34s.
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PROFESSIONAL DEVELOPMENT
Math Background
Not explored in this lesson is a not-so-subtle distinction between the amount used as the basis for a markup and the amount used as the basis for a markdown. As presented in the lesson, a markup is generally based on the cost of an item to the retailer. However, not covered in this lesson, a markdown is generally based on the retail price of an item after a markup has been applied. This means that if an item costing $100 is marked up 20%, it will retail for $120. If this item is later placed on sale at a 20% markdown, the sale price is not $120 - $20, but $120 - (20% of
Integrate Mathematical Practices MP.5
This lesson provides an opportunity to address this Mathematical Practice standard. It calls for students to use bar models to model the relationship between a mathematical expression and a real-world context regarding either a markup or a markdown. This gives students the opportunity to read a real-world situation and use that information to write an algebraic expression to represent retail and sale prices. Finally, the students use the expression they write to solve problems regarding markups and
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Questioning Strategies Mathematical Practices
•In Step 1, how do you know how much of the 1p bar to shade to show 0.2p? The amount shaded does not need to be a specific amount, just a portion of the bar to represent 0.2p.
•How does the bar model for a markdown differ from the bar model for a markup? For a markup, the bar model for the expression is longer than the original cost. For a markdown, the bar model for the expression is shorter than the retail price.
Connect Vocabulary EL
Remind students that both percents in Example 2 are rational numbers. 20% is equivalent to 0.2 or __ 102 , and 80% is equivalent to 0.8 or __ 108 .
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Engagewiththe Whiteboard
Have a student volunteer draw the model in part a. Discuss whether the model needs to be drawn to scale for it to be helpful in solving the problem.
Focuson Math Connections Mathematical Practices
Point out that the Distributive Property also works for subtraction. So, 1b- 0.24b= (1 - 0.24)b= 0.76b.
Elaborate
TalkAbout ItSummarizethe Lesson
Ask: How does a bar model showing the expression for a sale price compare to one showing the expression for a retail price? Both show the original price and the percent markup or markdown. The bar model for the retail price shows the percent markup added to the bar model, while the sale price shows the percent markdown subtracted from the bar model.
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Engagewiththe Whiteboard
To the right of each row, have students volunteer to write the expression that could be used to find the retail price in Exercises 2–7 and write the expression that could be used to find the sale price for Exercises 8–11 on the write-on lines.
Avoid Common Errors
Exercise 1c Remind students that once $32 has been substituted for s in the expression 1.35s, they do not need to add $32 to the value of the expression again.
Exercises 2–7 Remind students that the markup is an amount found by multiplying the cost by the percent markup. The retail price is the cost plus the markup.
Integrating LanguageArts EL
Encourage English learners to ask for clarification on any terms or phrases that they don’t understand.
Interactive Whiteboard
Interactive example available online
ADDITIONAL EXAMPLE 2
A pet store marks down all of its grooming products by 15% off the regular selling price of p. Write an expression for the sale price. 0.85p
my.hrw.com
AnimatedMath Explore Markups and Markdowns
Students discover how markups and markdowns relate to the original cost using virtual manipulatives.
Guided Practice
1. Dana buys dress shirts from a clothing manufacturer for s dollars each, and then sells the dress shirts in her retail clothing store at a 35% markup. (Example 1)
a. Write the markup as a decimal. b. Write two expressions for the retail price of the dress shirt. c. What is the retail price of a dress shirt that Dana purchased for $32.00? d. How much was added to the original price of the dress shirt? List the markup and retail price of each item. Round to two decimal places
when necessary. (Example 1)
Item Price Markup % Markup Retail Price
2. Hat $18 15% 3. Book $22.50 42% 4. Shirt $33.75 75% 5. Shoes $74.99 33% 6. Clock $48.60 100% 7. Painting $185.00 125%
Find the sale price of each item. Round to two decimal places when necessary. (Example 2)
8. Original price:$45.00; Markdown:22% 9. Original price:$89.00; Markdown:33%
10. Original price:$23.99; Markdown: 44% 11. Original price:$279.99, Markdown:75%
12. How can you determine the sale price if you are given the regular price and the percent of markdown?
CHECK-IN ESSENTIAL QUESTION
?
0.35s $2.70 $9.45 $25.31 $24.75 $48.60 $231.25 $20.70 $31.95 $59.06 $99.74 $97.20 $416.25 1s+0.35s, 1.35s $43.20 $11.20 $35.10 $70.00 $59.63 $13.43Write the percent of markdown as a decimal, subtract the product of this decimal and the regular price from the regular price.
Unit 2
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Saleprice = Original price - Markdown
= p - 0.2p
= 1p - 0.2p
= 0.8p
Usetheexpressiontofindthesalepriceofeachdecoration.
p = $16 Saleprice = 0.8($16) = $12.80
p = $23 Saleprice = 0.8($23) = $18.40
Reflect
4. Conjecture Comparethesingletermexpressionforretail priceaftera markupfrom Example 1 andthesingletermexpressionforsaleprice afteramarkdownfrom Example 2. Whatdoyou noticeaboutthe coefficientsinthetwoexpressions?
STEP 2
STEP 3
5. Abicycleshopmarksdowneachbicycle’ssellingpricebby 24% for a holidaysale.
a. Drawabarmodel torepresenttheproblem.
1b-0.24b
1b
0.24b
b. Whatisasingletermexpressionforthesaleprice? 6. Janesellspillows. Forasale, shemarksthemdown5%.
a. Writetwoexpressionsthatrepresentthesalepriceofthepillows.
b. Iftheoriginal priceofapillowis $15.00, whatisthesaleprice? YOUR TURN Isa 20% markupequal toa 20% markdown? Explain. Math Talk Mathematical Practices
Amarkupincludesacoefficientgreaterthan 1 and a markdownincludesacoefficient lessthan 1.
Theamountof a 20% markup anda 20% discountare thesame, but oneisadded andtheother issubtracted. 0.76b 1p− 0.05p, 0.95p $14.25 149 Lesson5.2 © H ough to n Miff l in H ar cour t Pu b l ishing Compan y Kinesthetic Experience
Have students write expressions that could be used to calculate a 10% increase and a 10% decrease in a distance. Then have each student stand on a start line, toss his/her uniquely decorated cotton ball, measure the distance to the nearest centimeter, and record the data in a table like the one shown below. Then have students use their expressions to calculate a distance that would be 10% more and 10% less than their original distance. Next, have each
student throw his/her cotton ball a second time, trying to throw exactly 10% more or less than their original distance. Finally, have students calculate the percent more or less the cotton ball actually went than their original distance.
Cooperative Learning
Have each student “secretly” think of a percent markup or markdown for a hat. Then on an index card, have each student write a one-term expression that could be used to find the retail price or sale price for the hat. Have students exchange cards and decide if the expression they were just given is a markup or a markdown.
decision is correct. Students then trade the completed cards with a third person who will determine if the bar model and conclusion about the expression are correct.
Additional Resources Differentiated Instruction includes: •Reading Strategies
•Success for English Learners EL •Reteach
•Challenge PRE-AP
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Math Trainer Online Assessment and Intervention Personal Online homework assignment available my.hrw.com
Evaluate
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Concepts & Skills Practice
Example 1 Calculating Markups Exercises 1–7, 15, 16 Example 2 Calculating Markdowns Exercises 8–11, 13–15
AdditionalResources Differentiated Instruction includes: •Leveled Practice Worksheets
Lesson Quiz available online
5.2 LESSON QUIZ
Fred buys flags from a manufac-turer for f dollars each and then sells the flags in his store for a 26% markup.
1. Write the markup as a decimal.
2. Write an expression for the retail price of a flag.
3. What is the retail price of a flag for which Fred paid $40?
4. How much was added to the cost of the flag?
List the sale price of each item. Round to two decimal places when necessary.
5. Original price: $25; Markdown: 12%
6. Original price: $16.45; Markdown: 33%
my.hrw.com
Focus | Coherence | Rigor
7.RP.3, 7.EE.2, 7.EE.3
7.RP.3, 7.EE.2, 7.EE.3
Exercise Depth of Knowledge (D.O.K.) Mathematical Practices
13 2 Skills/Concepts MP.4 Modeling
14 2 Skills/Concepts MP.2 Reasoning
15 3 Strategic Thinking MP.7 Using Structure
16 2 Skills/Concepts MP.4 Modeling
17 3 Strategic Thinking MP.6 Precision
18 3 Strategic Thinking MP.8 Patterns
19 2 Skills/Concepts MP.7 Using Structure
20 3 Strategic Thinking MP.4 Modeling
Exercise 18 combines concepts from the California Common Core
cluster “Analyze proportional relationships and use them to solve real-world and mathematical problems.”
Answers 1. 0.26 2. 1f+ 0.26f or 1.26f 3. $50.40 4. $10.40 5. $22 6. $11.02
Work Area 16. RepresentReal-WorldProblems Haroldworksatamen’sclothingstore,
whichmarks upitsretail clothingby 27%. Thestorepurchasespantsfor $74.00, suit jacketsfor $325.00, anddressshirtsfor $48.00. Howmuchwill Haroldchargeacustomerfortwopairsofpants, threedressshirts, anda suit jacket?
17. AnalyzeRelationships Yourfamilyneedsasetof 4 tires. Whichofthe followingdealswouldyou prefer? Explain.
(I) Buy 3, getonefree (II) 20% off (III) 1 __ 4 off
18. CritiqueReasoningMargopurchasesbulk teasfromawarehouseand marks upthosepricesby 20% forretail sale. Whenteasgo unsoldfor morethantwomonths, Margomarksdowntheretail priceby 20%. She saysthatsheisbreaking even, thatis, sheisgettingthesamepriceforthe teathatshepaidforit. Isshecorrect? Explain.
19. Problem Solving Gradymarksdownsome $2.49 pensto $1.99 foraweek andthenmarksthemback upto $2.49. Findthepercentofincreaseand thepercentofdecreasetothenearesttenth.Arethepercentsofchange thesameforbothpricechanges? Ifnot, whichisagreaterchange?
20. Perseverein Problem SolvingAtDanielle’sclothingboutique, ifan itemdoesnotsell foreightweeks, shemarksitdownby 15%. Ifitremains unsoldafterthat, shemarksitdownanadditional 5% eachweek until she canno longermakeaprofit. Thenshedonatesittocharity.
Rafael wantstobuyacoatoriginallypriced $150, buthecan’taffordmore than $110. IfDaniellepaid $100 forthecoat, duringwhichweek(s) could Rafael buythecoatwithinhisbudget? Justifyyouranswer.
FOCUS ON HIGHER ORDER THINKING
resultinadiscountof 25%, whichisbetterthan 20%.
Eitherbuy 3, getonefreeor _ 14 off. Eithercasewould
No; sheistakinga loss. Hercostfortheteaist, sothe retail priceis 1.2t. Thediscountedpriceis 0.8 × 1.2t,
or 0.96t, whichis lessthant.
No; firstchange: 20.1% decrease; secondchange: 25.1%
increase. Thesecondpercentchangeisgreater.
11 or 12 weeks; after 11 weeks, thepriceis $109.32,
after 12 weeks, thepriceis $103.85, andafterthat Danielledonatesthecoat.
$783.59
Unit 2
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Independent Practice
5.2
13. Abookstoremanagermarksdownthepriceofolderhardcoverbooks, whichoriginallysell forbdollars, by 46%.
a. Writethemarkdownasadecimal. b. Writetwoexpressionsforthesalepriceofthehardcoverbook.
c. Whatisthesalepriceofahardcoverbook forwhichtheoriginal retail
pricewas $29.00? d. Ifyou buythebook inpartc, howmuchdoyou savebypayingthe
saleprice? 14. Raquela’scoworkermadepricetagsforseveral itemsthataretobe
markeddownby 35%.Matcheach RegularPricetothecorrect SalePrice, ifpossible.Notall salestagsmatchanitem.
RegularPrice $3.29 SalePrice $2.01 RegularPrice $4.19 SalePrice $2.45 RegularPrice $2.79 SalePrice $1.15 RegularPrice $3.09 SalePrice $2.72 RegularPrice $3.77 SalePrice $2.24 15. CommunicateMathematical Ideas Foreachsituation, giveanexample
thatincludestheoriginal priceandfinal priceaftermarkupormarkdown.
a. Amarkdownthatisgreaterthan 99% but lessthan 100%
b. Amarkdownthatis lessthan 1%
c. Amarkupthatismorethan 200% 7.RP.3, 7.EE.2, 7.EE.3
Sampleanswer: original price: $100; final price: $0.50 Sampleanswer: original price: $100; final price: $99.50 Sampleanswer: original price: $100; final price: $350
1b− 0.46b, 0.54b 0.46b $15.66 $13.34 151 Lesson5.2 © Hough
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Activity available online my.hrw.com
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PRE-APActivity A shirt is on sale now for $20. Starting today, a morning sales clerk decreases the price by 30%, and then an afternoon sales clerk increases the price by 20%. This pattern continues for several days. Provided the shirt is never purchased, on which day is the shirt marked down to about 75% off the price it is now?
75% off the current price would make the shirt’s sale price $5. On the morning of Day 6, the shirt will be priced at $4.90.