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Course: 7th grade > Unit 2
 Solving percent problems
 Equivalent expressions with percent problems
 Percent word problem: magic club
 Percent problems
 Percent word problems: tax and discount
 Tax and tip word problems
 Percent word problem: guavas
Discount, markup, and commission word problems
 Multistep ratio and percent problems
 Your answer should be
 an integer, like 6
 a simplified proper fraction, like 3 / 5
 a simplified improper fraction, like 7 / 4
 a mixed number, like 1 3 / 4
 an exact decimal, like 0.75
 a multiple of pi, like 12 pi or 2 / 3 pi
Curriculum / Math / 7th Grade / Unit 5: Percent and Scaling / Lesson 7
Percent and Scaling
Lesson 7 of 19
Criteria for Success
Tips for teachers, anchor problems, problem set, target task, additional practice.
Find the percent of increase or decrease given the original and new amounts.
Common Core Standards
Core standards.
The core standards covered in this lesson
Ratios and Proportional Relationships
7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Foundational Standards
The foundational standards covered in this lesson
6.RP.A.3.C — Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
 Determine the amount of increase of decrease in a situation.
 Identify the starting or original value.
 Find the percent increase or decrease by dividing the amount of change by the starting value.
Suggestions for teachers to help them teach this lesson
 Lessons 5–8 address percent increase and decrease problems. In this lesson, students find the percent that represents the amount of increase or decrease in a situation.
 Students continue to reason abstractly, making meaning of the quantities in the problems to understand their relationships before doing any calculations (MP.2).
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
2530 minutes
At the end of Quarter 1, Winston’s math grade was a 72. He made a goal to improve his grade for Quarter 2 by correcting any mistakes he made on his homework assignments. At the end of Quarter 2, Winston’s grade increased to an 80.
By what percent did Winston’s grade improve?
Guiding Questions
In the Mattapan Chess Club, each player has a specific level, either Beginner or Intermediate, that is used to pair players in competition. Last year, there were 24 players at the Intermediate level and 20 players at the Beginner level. This year the number of Intermediate players increased by 25%, and the number of Beginner players decreased by 10%.
Was there an increase or decrease in overall membership? Find the overall percent change in membership of the club.
Chess Club , accessed on Dec. 18, 2017, 9:02 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BYNCSA 4.0 . For further information, contact Illustrative Mathematics .
A set of suggested resources or problem types that teachers can turn into a problem set
1520 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson  mastery will indicate whether or not objective was achieved
510 minutes
In April, Justin sent 675 text messages on his phone. In May, he sent 621 text messages.
By what percent did the number of text messages Justin sent decrease from April to May?
Student Response
An example response to the Target Task at the level of detail expected of the students.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
 EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic A > Lesson 4 — Exercise 1, Example 3, Problem Set #2–4
 Kuta Software Free PreAlgebra Worksheets Finding Percent Change
 MARS Formative Assessment Lessons for Grade 7 Increasing and Decreasing Quantities by a Percent — Includes a great activity where students connect different amounts using percent increases or decreases
Topic A: Percent, Part, and Whole
Define percent and convert between fractions, decimals, and percentages. Solve percent problems mentally with benchmark percentages.
Find percent of a number when given percent and the whole.
7.NS.A.3 7.RP.A.3
Find the whole given a part and percent.
Find the percent given a part and the whole.
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Topic B: Percent Increase and Decrease
Find a new amount given the original and a percent increase or decrease.
7.EE.A.2 7.RP.A.3
Find the original amount given a new amount after a given percent increase or decrease.
Solve percent problems fluently, including percent increase and decrease.
Topic C: Percent Applications
Solve percent applications involving discount, tax, and tip.
7.EE.B.3 7.RP.A.3
Solve percent applications involving simple interest, commissions, and other fees.
Solve percent applications involving measurement and percent error.
Topic D: Scale Drawings
Define and identify scale images.
Define and determine scale factor between two scale images. Use scale factor to draw scale images.
7.G.A.1 7.RP.A.3
Use a scale to determine actual measurements.
Use scales in maps to find actual distances between locations.
Use scales in floor plans to find actual measurements and dimensions.
Compute actual areas from scale drawings.
Draw scale drawings at different scales.
Create a scale floor plan (optional).
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Calculating Discounts
Calculating discounts worksheets.
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Percentages
Discount and Sale Price
Related Topics: More Lessons for Grade 5 Math Math Worksheets
Examples, solutions, videos, worksheets, stories, and songs to help Grade 5 students learn how to calculate discounts and sale prices.
Finding Discounts and sales prices The video covers a onestep and a twostep process for finding a sale price, given a percent of discount. It includes four examples. Example: Find the sale price (a) Original Price = $49.50, Discount = 30% (b) Original Price = $1,348.35, Discount = 25% (c) Original Price = $19.89, Discount = 15% (d) Original Price = $189.90, Discount = 60%
Calculating Discounts Examples:
 With a SPC card you are entitled to 15% savings at Champs. If you are looking at a new pair of Nike basketball shoes that cost $125.99 and you use your SPC card, what is the sale price of the shoes?
 Tracey purchased a leather jacket from Danier for $128 on sale, when the regular price was $200. What was the rate of the discount?
 The sale price of a used Nintendo DSi after a discount o 20% was $110. What was the regular price of the Nintendo Dsi?
Percent Word Problems  Sales Tax, Discount, & Finding The Original Price Examples: A sweater that usually costs $45 is on sale for 25% off. What is the sale price?
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Grade 7  Ratios and Proportional Relationships
Standard 7.RP.A.3  Use coupons to determine the cost of an item.
Included Skills:
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
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Percentage Contexts
11.1: Leaving a Tip (5 minutes)
CCSS Standards
Building On
Building Towards
The purpose of this warmup is to help students connect their current work with percentage contexts to their prior work on percent increase and efficient ways of finding percent increase.
Consider telling students that these questions may have more than one correct answer. Students in groups of 2. 2 minutes of quiet think time followed by partner and then wholeclass discussion.
Student Facing
Which of these expressions represent a 15% tip on a $ 20 meal? Which represent the total bill?
\(15 \boldcdot 20\)
\(20 + 0.15 \boldcdot 20\)
\(1.15 \boldcdot 20\)
\(\frac{15}{100} \boldcdot 20\)
Student Response
For access, consult one of our IM Certified Partners .
Activity Synthesis
For each expression, ask a few students to explain whether they think it represents: the total bill, the tip, or neither. For each expression, select a student to explain their reasoning.
11.2: A Car Dealership (10 minutes)
Routines and Materials
Instructional Routines
 MLR6: Three Reads
 Think Pair Share
Required Materials
 Fourfunction calculators
The purpose of this activity is to introduce students to a context involving markups and markdowns or discounts, and to connect this to the work on percent increase and percent decrease they did earlier. The first question helps set the stage for students to see the connection to markups and percent increase. Look for students who solve the second question by finding 90% of the retail price, and highlight this approach in the discussion.
Tell students that a markup is a percentage that businesses often add to the price of an item they sell, and a markdown is a percentage they take off of a given price. If helpful, review the meaning of wholesale (the price the dealership pays for the car) and retail price (the price the dealership charges to sell the car). Sometimes people call markdowns discounts.
Provide access to calculators. Students in groups of 2. Give students 5 minutes of quiet work time, followed by partner then wholeclass discussion.
A car dealership pays a wholesale price of $ 12,000 to purchase a vehicle.
The car dealership wants to make a 32% profit.
 By how much will they mark up the price of the vehicle?
 After the markup, what is the retail price of the vehicle?
Attribution: Cars , by Pexels. Public Domain. Pixabay. Source .
 During a special sales event, the dealership offers a 10% discount off of the retail price. After the discount, how much will a customer pay for this vehicle?
Are you ready for more?
This car dealership pays the salesperson a bonus for selling the car equal to 6.5% of the sale price. How much commission did the salesperson lose when they decided to offer a 10% discount on the price of the car?
Anticipated Misconceptions
It is important throughout that students attend to the meanings of particular words and remain clear on the meaning of the different values they find. For example, "wholesale price," "retail price," and "sale price" all refer to specific dollar amounts. Help students organize their work by labeling the different quantities they find or creating a graphic organizer.
For the first question, help students connect markups to percent increase.
Select students to share solutions to the second question. Highlight finding 90% of the retail price, and reinforce that a 10% discount is a 10% decrease.
Ask them to describe how they would find (but not actually find) . . .
 "The retail price after a 12% markup?" (Multiply the retail price by 0.12, then add that answer to the retail price. Alternatively, multiply the retail price by 1.12.)
 "The price after a 24% discount?" (Multiply the retail price by 0.24, then subtract that answer from the retail price. Alternatively, multiply the retail price by 0.76.)
11.3: Commission at a Gym (10 minutes)
 MLR3: Clarify, Critique, Correct
The purpose of this activity is to introduce students to the concept of a commission and to solve percentage problems in that context. Students continue to practice finding percentages of total prices in a new context of commission.
Monitor for students who use equations like \(c = r \boldcdot p\) where \(c\) is the commission, \(r\) represents the percentage of the total that goes to the employee, and \(p\) is the total price of the membership.
Tell students that a commission is the money a salesperson gets when they sell an item. It is usually used as an incentive for employees to try to sell more or higher priced items than they usually would. The commission is usually a percentage of the price of the item they sell.
Provide access to calculators. Students in groups of 2. Give students 2 minutes of quiet work time. Partner then wholeclass discussion.
For each gym membership sold, the gym keeps $ 42 and the employee who sold it gets $ 8. What is the commission the employee earned as a percentage of the total cost of the gym membership?
If an employee sells a family pass for $ 135, what is the amount of the commission they get to keep?
Students may find the percentage of an incorrect quantity. Ask them to state, in words, what they are finding a percentage of.
Students may not understand the first question. Tell them that a membership is sold for a certain price and the money is split with \$42 going to the gym and \$8 going to the employee.
Select students to share how they answered the questions.
During the discussion, draw attention to strategies for figuring out which operations to do with which numbers. In particular, strategies involving equations like \(c = r \boldcdot p\) where \(c\) is the commission, \(r\) represents the percentage of the total that goes to the employee, and \(p\) is the total price of the membership.
11.4: Card Sort: Percentage Situations (10 minutes)
 MLR8: Discussion Supports
 Preprinted slips, cut from copies of the blackline master
Optional activity
This activity gives students an opportunity to practice various vocabulary terms that come along with percentages. Students are asked to sort scenarios to different descriptors using the images, sentences or questions found on the scenario cards. The questions found on the scenario cards are intended to help students figure out which descriptor the scenario card belongs under.
As students work on the task, identify students that are using the vocabulary: tip, tax, gratuity, commission, markup/down, and discount. These students should be asked to share during the discussion.
Arrange students in groups of 2. Distribute the sorting cards, and explain that students will sort 8 scenarios into one of 6 categories. Demonstrate how students can take turns placing a scenario under a category and productive ways to disagree. Here are some questions they might find useful:
 Which category would you sort this under?
 What do you think this word means?
 What words can we use as clues about where to sort this card?
Your teacher will give you a set of cards. Take turns with your partner matching a situation with a descriptor. For each match, explain your reasoning to your partner. If you disagree, work to reach an agreement.
Students should use the question at the bottom of the card to help them if they get stuck sorting the scenarios.
Ask identified students to share which situations they sorted under each word. Ask them:
 "What made you decide to put these situations under this descriptor?"
 "Were there any situations that you were really unsure of? What made you decide on where to sort them?"
Consider asking some groups to order the situations from least to greatest in terms of the dollar amount of the increase of decrease and asking other groups to order them in terms of the percentage. Then, have them compare their results with a group that did the other ordering.
Answer students’ remaining questions about any of these contexts. Tell students there is a copy of this chart at the end of the lesson that they can use as a reference tool during future lessons. Allow them a space to take notes on their own to remember it or details from one of the activity examples.
paid to:  how it works:  

sales tax  the government  added to the price of the item 
gratuity (tip)  the server  added to the cost of the meal 
interest  the lender (or account holder)  added to the balance of the loan, credit card, or bank account 
markup  the seller  added to the price of an item so the seller can make a profit 
markdown (discount)  the customer  subtracted from the price of an item to encourage the customer to buy it 
commission  the salesperson  subtracted from the payment the store collects 
Lesson Synthesis
In this lesson, we studied lots of different situations where people use percentages.
 “What are some situations in life in which people encounter percentages?”
 “Give examples of situations where you would encounter tax, tip, markup, markdown, commission.” (Lots of possible answers.)
 “When an item is marked down 10%, why does it make sense to multiply the price by 0.9?” (Since there is 10% off of the price, the new cost is 90% of the original.)
 “When an item is marked up 25%, why does it make sense to multiply the price by \(1.25\) ?” (Since the item now costs 100% plus an extra 25%, the new item costs 1.25 times the original.)
11.5: Cooldown  The Cost of a Bike (5 minutes)
Student lesson summary.
There are many everyday situations where a percentage of an amount of money is added to or subtracted from that amount, in order to be paid to some other person or organization:
goes to  how it works  

sales tax  the government  added to the price of the item 
gratuity (tip)  the server  added to the cost of the meal 
interest  the lender (or account holder)  added to the balance of the loan, credit card, or bank account 
markup  the seller  added to the price of an item so the seller can make a profit 
markdown (discount)  the customer  subtracted from the price of an item to encourage the customer to buy it 
commission  the salesperson  subtracted from the payment that is collected 
For example,
 If a restaurant bill is \$34 and the customer pays \$40, they left \$6 dollars as a tip for the server. That is 18% of $34, so they left an 18% tip. From the customer's perspective, we can think of this as an 18% increase of the restaurant bill.
 If a realtor helps a family sell their home for \$200,000 and earns a 3% commission, then the realtor makes \$6,000, because \((0.03) \boldcdot 200,\!000 = 6,\!000\) , and the family gets \$194,000, because \(200,\!000  6,\!000 = 194,\!000\) . From the family's perspective, we can think of this as a 3% decrease on the sale price of the home.
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(F) Analyze and compare monetary incentives, including sales, rebates, and coupons.
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
This number sense lesson focuses on solving problems involving discounts, profits, and commissions. The lesson includes researchbased strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem and identify the percent discount and original price, or percent profit and original cost, or percent commission and sale amount. Then, they calculate and interpret the discounted price, selling price, or commission. In addition to the lesson, there are eleven pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Lesson 7: Markup and Markdown Problems. Student Outcomes. Students understand the terms original price, selling price, markup, markdown, markup rate, and markdown rate. Students identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multistep markup and markdown problems.
Discount, markup, and commission word problems. The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of $ 113.00 , and Jessica's Furniture Store marks up all furniture by 45 % . At what price should the manager sell the couch? Learn for free ...
Tips for Teachers. Lessons 58 address percent increase and decrease problems. In this lesson, students find the percent that represents the amount of increase or decrease in a situation. Students continue to reason abstractly, making meaning of the quantities in the problems to understand their relationships before doing any calculations (MP.2).
Since the reduced price is less than the original price, the 40% discount on the reduced price would be less than a 40% discount on the original price. $50 (.25) = $12.50 first discount $ 50  $12.50 = $37.50 first sale price. $37.50 (.40) = $15.00 second discount $37.50  $15.00 = $22.50 final price The cost of the jeans is $22.50.
View L27_Problem_Solving.pdf from MTH 114 at St. John's University. NAME _ DATE _ PERIOD _ Lesson 7 ProblemSolving Practice Discount 36 1. PRETZELS The Spanish club sold hot pretzels as a
Guided Practice • Select twothree problems to guide students through using your school's designated curriculum and text. Engage in a class discussion (0.82) around problemsolving and productive struggle (0.64). Discuss mental math percent patterns. Independent Practice/Homework • Students begin assignment in class and finish for homework.
In this lesson, practice using percents to solve markdown and markup problems. Practice writing and solving equations, given real world problems involving percent of a discount or selling price.
Lesson Notes. In this lesson, students use algebraic equations to solve multistep word problems involving markups and markdowns. This lesson extends the mathematical practices and terminology students were exposed to in Module 1, Lesson 14. New finance terms such as retail price, consumer, cost price, and wholesale price are introduced.
This number sense lesson focuses on solving problems involving markups and discounts. The lesson includes researchbased strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem, identifying the original price and the percent. Then, they identify if it is a markup or discount, and convert the percent markup or discount to a decimal ...
Try our worksheets with percentage problems to practice calculating discounts until you master this skill. Over 4,500 free worksheets available to learn and practice math. Designed by experts and adapted to the demands of each country and school grade. Welcome!
Previous Lesson. 9.3 Markups and Discounts: Next Lesson Need a tutor? Click this link and get your first session free! Packet. m7_unit_9_Packets.pdf: File Size: 3318 kb: File Type: pdf: Download File. Practice Solutions. m7_9.3_practice_solutions.pdf: File Size: 133 kb: File Type: pdf: Download File. Corrective Assignment.
OF means to multiply. 5. Multiply the decimal by the price. This is what you save. 6. Subtract your savings from the original price to find the current price. How to find the discount. Finding Discounts. The video covers a onestep and a twostep process for finding a sale price, given a percent of discount.
Finding Discounts and sales prices The video covers a onestep and a twostep process for finding a sale price, given a percent of discount. It includes four examples. Example: Find the sale price (a) Original Price = $49.50, Discount = 30% (b) Original Price = $1,348.35, Discount = 25% (c) Original Price = $19.89, Discount = 15%
Percent of a Number: Tax, Discount, Tip  Grade 7  Practice with Math Games. Unlock harder levels by getting an average of 80% or higher. Earn up to 5 stars for each level The more questions you answer correctly, the more stars you'll unlock! Each game has 10 questions. Green box means correct.
A Premium account gives you access to all lesson, practice exams, quizzes & worksheets ... Problem solving  use your understanding of the formula for finding percentage discounts to correctly ...
Preparation Lesson Practice. View Student Lesson. 11.1: Leaving a Tip (5 minutes) CCSS Standards. Building On. 6.EE.A.2.b; ... Use this routine to support reading comprehension of this word problem, without solving it for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., A car dealership ...
This number sense lesson focuses on solving problems involving discounts, profits, and commissions. The lesson includes researchbased strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem and identify the percent discount and original price, or percent profit and original cost, or percent commission and sale amount. Then, they ...
California Standards Practice (STP) Vocabulary Review Lesson Resources Extra Examples Group Activity Cards ... Mathematics. Home > Chapter 7 > Lesson 7. California Mathematics: Concepts, Skills, and Problem Solving, Grade 6. Chapter 7, Lesson 7: Sales Tax and Discount. Extra Examples; Group Activity Cards; Personal Tutor; SelfCheck Quizzes ...
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Group Activity Cards Personal Tutor ... Mathematics. Home > Chapter 7 > Lesson 7. North Carolina Math Connects: Concepts, Skills, and Problem Solving, Course 2. Chapter 7, Lesson 7: Sales Tax and Discount. Extra Examples; Group Activity Cards; Personal Tutor; Self ...
Unit 5, Lesson 14: Solving Problems with Rational Numbers. 1. A furniture store pays a wholesale price for a mattress. Then, the store marks up the retail price to 150% of the wholesale price. Later, they put the mattress on sale for 50% of of the retail price. A customer just bought the mattress on sale and paid $1,200. a.
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NAME DATE PERIOD Lesson 7 Problemsolving Practice Discount 1. The Spanish club sold hot pretzels as a fundraiser. The pretzels normally sold for $2.00, but near the end of the sale the price was. We are not affiliated with any brand or entity on this form. 4,4. 98,753 Reviews. 4,5.
When a person must file a Lesson 7 Problem Solving Practice Discount Answer Key, studying regulations and guides on how to complete a form correctly and what it should include may take a lot of time and effort. However, if you find the right Lesson 7 Problem Solving Practice Discount Answer Key template, finishing a document will stop being a ...