Mathematics · 7th Grade · The World of Ratios and Proportions · Weeks 1-9

Markup and Markdown

Students will calculate markup and markdown prices, understanding their application in retail.

• Common Core State Standards
• CCSS.Math.Content.7.RP.A.3

About This Topic

Markup and markdown are the pricing mechanisms behind every retail transaction, and understanding them requires the same proportional reasoning students have been building throughout this unit. Under CCSS 7.RP.A.3, students learn that markup is the amount added to an item's cost to set its selling price, while markdown is a reduction from the selling price , each expressed as a percentage, but applied to different base amounts.

The retail context provides a natural hook for authentic problem-solving. A product costs a store $40 to purchase; the store marks it up 60% to set the retail price. Later, the item goes on a 25% markdown. Students must track which amount serves as the base , the cost price for markup, the retail price for markdown , and recognize that these operations are not symmetric: a 50% markdown does not return the price to cost.

Active learning approaches using real or simulated products help students develop accurate intuition about what markup and markdown mean in practice. When students run a simulated classroom store, they discover that profitable pricing requires understanding both the proportional structure and the practical consequences of each percentage decision.

Key Questions

1. Differentiate between markup and markdown in pricing strategies.
2. Analyze how a store determines the selling price of an item after markup.
3. Evaluate the impact of a markdown on a product's original price.

Learning Objectives

• Calculate the selling price of an item after a given markup percentage is applied to its cost.
• Determine the original selling price of an item given its sale price and the markdown percentage.
• Compare the final selling price of an item after a markup and subsequent markdown to its original cost.
• Explain the difference between the base amount used for calculating markup versus markdown.
• Analyze the impact of a 50% markdown on an item's price and explain why it does not return the price to the original cost.

Before You Start

Calculating Percentages

Why: Students must be able to accurately calculate a percentage of a given number to find the markup or markdown amount.

Finding the Whole Given a Part and a Percent

Why: Students need this skill to determine the original selling price when only the sale price and markdown percentage are known.

Basic Operations with Decimals

Why: Calculations involving percentages often require multiplication and addition/subtraction with decimals.

Key Vocabulary

Cost Price	The amount a retailer pays for an item before adding any markup.
Selling Price	The price at which a retailer offers an item for sale to customers.
Markup	The amount added to the cost price of an item to determine its selling price, usually expressed as a percentage of the cost.
Markdown	A reduction in the selling price of an item, usually expressed as a percentage of the original selling price.
Profit Margin	The difference between the selling price and the cost price, often expressed as a percentage of the selling price.

Watch Out for These Misconceptions

Common Misconception

A 40% markup means the customer pays 40% of the original cost.

What to Teach Instead

A 40% markup means the selling price is 140% of the cost , the customer pays the full cost plus an additional 40%. Students who confuse 'percent of' with 'percent on top of' regularly underestimate selling prices. Visual percent bar models that show 100% + 40% help distinguish the two interpretations.

Common Misconception

A 50% markdown brings the price back to the original cost.

What to Teach Instead

A 50% markdown from retail cuts the price in half from retail , not back to cost. Whether this is still profitable depends on the original markup. If an item was marked up 100% from cost, a 50% markdown returns it exactly to cost. But if it was marked up only 30%, a 50% markdown means selling below cost. Classroom store simulations make this asymmetry concrete.

Common Misconception

Markup and markdown percentages use the same base.

What to Teach Instead

Markup is calculated on the cost price (what the store paid). Markdown is calculated on the selling price (what the store charges retail). Using the wrong base produces incorrect results. Multi-step problems requiring students to explicitly label which price they are working from build the habit of identifying the base before calculating.

Active Learning Ideas

Simulation Game: The Classroom Store

Each group manages a fictional product line, receiving a wholesale cost and a target markup percentage to set retail prices. Groups then face a clearance event and must decide on a markdown percentage that still lets them turn a profit. They calculate their results and present their pricing strategy with full mathematical justification.

50 min·Small Groups

Think-Pair-Share: Markup or Markdown , Which Base?

Show four pricing problems, two involving markup (calculated from cost) and two involving markdown (calculated from retail price). Students individually identify the base for each calculation, then pair to compare reasoning. The class discussion focuses on why the choice of base matters and how confusing the two leads to pricing errors.

20 min·Pairs

Error Analysis: The Pricing Mistake

Present a scenario where a store clerk calculated a 30% markup using the retail price as the base instead of the cost. Students find the error, calculate the correct selling price, and determine how much profit was lost due to the mistake. They then write a one-sentence rule to help remember which base to use for markup.

25 min·Pairs

Gallery Walk: Price Tags

Post eight product cards around the room, each showing a cost and either a markup percentage or a markdown scenario. Students calculate the final selling price for each and write a sentence interpreting what the percent means in context , for example, confirming whether a sale price still generates a profit above cost.

30 min·Small Groups

Real-World Connections

• Clothing stores frequently use markdowns to clear out seasonal inventory. For example, a department store might offer a 40% markdown on winter coats in February to make space for spring merchandise.
• Electronics retailers calculate markups to determine the retail price of new gadgets. A computer store buys a laptop for $600 and applies a 50% markup to set the selling price for consumers.
• Online marketplaces like Amazon use dynamic pricing algorithms that can involve both markups and markdowns based on demand, competitor pricing, and inventory levels.

Assessment Ideas

Exit Ticket

Provide students with a scenario: 'A store buys a T-shirt for $10 and marks it up by 75%. Later, they put it on a 20% markdown sale.' Ask students to calculate: 1. The selling price after markup. 2. The sale price after the markdown. 3. The final profit.

Quick Check

Present students with two problems: A) An item costs $50 and is marked up by 30%. What is the selling price? B) An item sells for $80 after a 20% markdown. What was the original selling price? Have students show their work and identify which base amount was used for each calculation.

Discussion Prompt

Pose the question: 'If a store marks an item up by 50% and then marks it down by 50%, is the final price the same as the original cost? Why or why not?' Facilitate a class discussion where students use specific examples to justify their reasoning.

Frequently Asked Questions

What is the difference between markup and markdown?

Markup is the amount added to an item's cost to establish the selling price, expressed as a percent of cost. Markdown is a reduction from the selling price, expressed as a percent of selling price. They use different bases, which is why they are not simply the reverse of each other , the arithmetic of one does not undo the other.

How do I calculate a selling price with a 35% markup?

Multiply the cost by 1.35. The 1 represents the full cost (100%) and the 0.35 is the 35% added on top. For a $60 item: 1.35 × $60 = $81 selling price. Alternatively, calculate 35% of $60 = $21 and add to the cost: $60 + $21 = $81. Both methods give the same result , the multiplier approach is faster once students understand why it works.

Can a store still make a profit after a markdown?

It depends on the markup. If a $40 item was marked up 60% to $64, then marked down 20% ($12.80 off), the sale price is $51.20 , still $11.20 above cost. As long as the sale price exceeds the cost, the store makes a profit. At cost they break even; below cost they take a loss. The original markup determines how much room there is to discount.

How does active learning improve students' understanding of markup and markdown?

Retail pricing requires tracking multiple percentage steps on different bases , easy to lose without a meaningful context. Running a simulated store where students make real pricing decisions and must check whether they would turn a profit engages students in exactly the multi-step proportional reasoning CCSS 7.RP.A.3 requires. Group discussion surfaces confusion about base amounts and turns it into a teachable moment rather than a silent, repeated mistake.