lesson 7 problem solving practice discount

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). 

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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

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 BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .

A set of suggested resources or problem types that teachers can turn into a problem set

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

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 Pre-Algebra 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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Percents Applications Discount, Sale Price, and Tips Lesson Plan

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Discount, Sale Price, Tips Guided Notes with Doodles | Percents Sketch Notes

Ever wondered how to teach percent applications involving discount, sale price, and tips in an engaging way to your seventh grade students?

In this lesson plan, students will learn about calculating discount, finding sale prices, and determining tips, all using percentages. Through artistic and interactive guided notes, check for understanding questions, a doodle and color by number activity, and a maze worksheet, students will gain a comprehensive understanding of percent applications.

The lesson culminates with a real-life example that explores how calculating discounts and finding sale prices is useful in everyday situations, such as shopping or dining out. This real-life application will help students see the relevance and importance of understanding and using percentages in their daily lives.

• Standard : CCSS 7.RP.A.3
• Topic : Percents
• Grade : 7th Grade
• Type : Lesson Plans

Learning Objectives

After this lesson, students will be able to:

Calculate the discount amount and sale price of an item given the original price and the percent discount.

Solve problems involving finding the original price of an item given the sale price and the percent discount.

Determine the total cost including tips based on a percentage of the bill amount.

Apply the concepts of discount, sale price, and tips to real-life situations, such as shopping and dining out.

Prerequisites

Before this lesson, students should be familiar with:

How to convert between decimals and percents

Basic understanding of multiplication and division of integers and decimals

Colored pencils or markers

Discount, Sale Price, and Tips Guided Notes

Key Vocabulary

Introduction.

As a hook, ask students why it is important to calculate discounts, sale prices, and tips in real life situations. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce the concept of discounts. Walk through how to calculate the discount amount and the sale price. Explain the difference between the discount and the sale price. Have students fill in the steps to calculating discount and sale price. Then, have students practice using the 3 problems in the "you try" section on the page. Students will have to calculate the sale prices of the different furniture shown.

Next, use the second page of the guided notes to introduce tip calculations. Discuss the purpose of tipping and how it is typically calculated as a percentage of the total bill. Show students how to calculate the tip amount and the total amount, including the tip. Emphasize the importance of good tipping etiquette and have students fill in some services like waitressing, salons, and food delivery that often accept tips.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

After finishing the first two pages of the guided notes, have students practice finding discounts, sale prices, and tips using the maze activity (page 3). Walk around the classroom to answer any questions students may have.

Fast finishers can dive into the color by number activity (page 4) for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of calculating tips and sale price in real-life situations. Explain that understanding how to find the tip when dining at a restaurant or calculating the sale price when shopping can be useful in everyday life. Use the last page of the guided notes where students will read about a detailed example of real life applications.

Provide examples and scenarios where calculating tips and sale prices are relevant. For example, you can discuss scenarios such as:

Dining at a restaurant: Explain that when dining out, it is customary to leave a tip for the server. Show the students how to calculate a specific percentage tip based on the total bill. Discuss common tipping percentages, such as 15%, 18%, and 20%, and emphasize the importance of considering the quality of service when determining the appropriate tip.

Shopping during a sale: Explain that when there is a sale at a store, the price of an item is often reduced by a certain percentage. Show the students how to calculate the sale price of an item by applying the discount percentage to the original price. Discuss the concept of finding the better deal between items with different sale prices and comparing the savings.

Discounts and coupons: Explain that discounts and coupons are often used to reduce the price of items. Show the students how to calculate the discounted price using a specific percentage discount or a fixed amount coupon. Discuss the importance of reading the fine print to understand the terms and conditions of the discounts or coupons.

Encourage students to share their own experiences or examples of situations where they have encountered the need to calculate tips or sale prices. This will help them see the relevance and practicality of the concept in their daily lives.

Refer to the FAQ section or provide additional examples and scenarios to reinforce the concept further, if needed.

Additional Print Practice

A fun, no-prep way to practice discount, sale price, and tips is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here is an activity to try:

Discount, Sale Price, and Tips Doodle Math Activity

What is a discount? Open

A discount is a reduction in price or cost. It is usually expressed as a percentage off the original price.

How do I calculate the sale price? Open

To calculate the sale price, you need to subtract the discount amount from the original price. Here are the steps:

Step 1: Convert the discount percentage to a decimal by dividing it by 100.

Step 2: Multiply the decimal by the original price to find the discount amount.

Step 3: Subtract the discount amount from the original price to get the sale price.

How do I calculate the amount of discount? Open

To calculate the amount of discount, you need to multiply the original price by the discount percentage. Here are the steps:

How can I find the tip for a bill? Open

To find the tip for a bill, you need to multiply the bill amount by the tip percentage. Here are the steps:

Step 1: Convert the tip percentage to a decimal by dividing it by 100.

Step 2: Multiply the decimal by the bill amount to find the tip.

Can you give an example of a discount problem? Open

Sure! Here's an example:

Original price: $100

Discount percentage: 20%

To find the sale price:

Step 1: Convert the discount percentage to a decimal: 20% = 0.2

Step 2: Multiply the decimal by the original price: 0.2 * $100 = $20

Step 3: Subtract the discount amount from the original price: $100 - $20 = $80

So, the discount amount is $20 and the sale price is $80.

How do I find the total amount after adding a tip? Open

To find the total amount after adding a tip, you need to add the tip amount to the original bill. Here are the steps:

Step 1: Find the tip amount by multiplying the bill amount by the tip percentage (converted to a decimal).

Step 2: Add the tip amount to the bill amount to get the total amount.

Can you explain the concept of sale price in real-life examples? Open

Certainly! Here are some real-life examples of sale price:

A store offers a 30% discount on a $50 shirt. The sale price would be $35.

A restaurant reduces the price of a meal by 15% during a special promotion. If the original price of the meal was $100, the sale price would be $85.

An online retailer offers a 20% discount on a $200 electronic gadget. The sale price would be $160.

How can I use percentages and discounts in everyday situations? Open

Percentages and discounts are commonly used in everyday situations. Here are some examples:

Calculating how much you will save during a sale or promotion.

Determining the amount of money to tip at a restaurant or for a service.

Understanding the discount applied to a coupon or promotional code when shopping online.

Comparing prices of products with different discounts to find the best deal.

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Percentage Contexts

11.1: Leaving a Tip (5 minutes)

CCSS Standards

Building On

Building Towards

The purpose of this warm-up 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 whole-class 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

• Four-function 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 mark-up is a percentage that businesses often add to the price of an item they sell, and a mark-down 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 mark-downs discounts.

Provide access to calculators. Students in groups of 2. Give students 5 minutes of quiet work time, followed by partner then whole-class 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 whole-class 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
• Pre-printed 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.

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: Cool-down - 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:

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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Solve Problems Involving Discounts, Profits, and Commissions

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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 research-based 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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