Teacher Guide: Discounts and Tax Together
Learn how to calculate the final price when both a discount and sales tax apply to a purchase.
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Class quiz
10 questions on Taxes & Tips. Students join with a name, you see everyone's score.
For Teachers
- Determine the correct order for applying discounts and sales tax
- Calculate final prices using step-by-step or multiplier methods
- Explain why tax is applied after discounts
- Compare prices across different discount and tax scenarios
- • Understanding of percentages and converting to decimals
- • Ability to calculate percent of a number
- • Familiarity with sales tax calculations
- • Basic understanding of discounts and percent off
- 1. Have you ever been surprised by a total at checkout? What might have caused the difference from what you expected?
- 2. Why do you think the government requires tax to be calculated on the discounted price?
- 3. If two stores have the same item but different discounts and prices, how would you decide where to buy?
- 4. A store advertises '50% off plus no tax!' Is this always a better deal than a smaller discount with tax?
Discount and tax percentages can be combined (e.g., 20% off + 10% tax = 10% increase)
The order doesn't matter since it's all multiplication
For Struggling Students:
- • Use simpler percentages (10%, 20%, 50%) that are easy to calculate mentally
- • Break every problem into four steps: original price, discount amount, sale price, tax amount, final price
- • Provide a visual flowchart showing the order of operations
For On-Level Students:
- • Practice with realistic percentages (15%, 25%, 7.5% tax)
- • Compare deals between two stores
- • Work backwards: Given a final price, find the original
For Advanced Students:
- • Multiple discounts (e.g., 20% off then additional 10% loyalty discount)
- • Calculate the 'effective' single discount rate when combining discount and tax
- • Analyze how different tax rates affect the savings from a discount
- 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)
Use proportional relationships to solve multistep ratio and percent problems
- 7.EE.B.3 (CCSS.MATH.CONTENT.7.EE.B.3)
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers
- visualPrice Breakdown Chart
Shows how price changes at each step: original, after discount, after tax
- activityStore Comparison Challenge
Compare final prices at different stores with varying discounts and tax rates
- worksheetShopping Scenarios
Real-world problems involving sales, coupons, and taxes
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
Worked Examples
A jacket costs 80 dollars and is 25% off. Sales tax is 8%. What is the final price?
Calculate the discount amount
dollars discount → 20 dollars off
Find the discounted price
dollars → 60 dollars
Calculate tax on discounted price
dollars tax → 4.80 dollars tax
Add tax to get final price
dollars → 64.80 dollars
Answer: The final price is 64.80 dollars
Common Mistakes
Applying tax first, then the discount
Why it's wrong: This incorrectly calculates tax on the full price instead of what you actually pay. It also violates how stores legally must calculate tax.
Correct: Always apply the discount first. Tax is calculated on the sale price, not the original price.
Adding the discount and tax percentages together
Why it's wrong: Thinking '25% off and 8% tax = 17% off total' is wrong because you can't combine these operations.
Correct: Discount and tax must be applied separately in sequence: discount first, then tax on the result.
Forgetting that tax applies to the discounted price
Why it's wrong: Some students calculate the discount correctly but then add tax based on the original price.
Correct: The tax base is always the price you're actually paying after any discounts.
Why It Matters
- Smart Shopping: Know exactly how much you'll pay at checkout before you get there
- Budget Planning: Calculate whether a sale item fits your budget after tax
- Comparing Deals: Determine which store offers a better final price
- Avoiding Surprises: No more shock when the total is higher than expected
Real World Applications
Black Friday Shopping
During major sales events, stores offer deep discounts. Knowing how to calculate the final price helps you budget.
Example:
A 200 dollar TV is 40% off on Black Friday. With 6% sales tax, the final price is dollars.
You have 100 dollars to spend. A jacket originally costs 120 dollars and is 30% off. Sales tax is 5%.
Can you afford the jacket?
Step 1: Write the mathematical expression
Calculate:
Online Shopping
E-commerce sites automatically apply discounts and taxes. Understanding the math helps you verify charges.
Example:
A 50 dollar order with a 20% coupon code and 9% tax: dollars.
An online store shows a 90 dollar item with a 15% promo code. Your state has 8% sales tax.
What will you pay at checkout?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1When both discount and tax apply, always calculate discount first, then tax
- 2Tax is calculated on the discounted price, not the original price
- 3Use multipliers for faster calculation:
- 4This order is required by law and reflects what you actually pay
Frequently Asked Questions
Why do we apply the discount before the tax?
Does the order matter mathematically?
What if I have multiple discounts?
Glossary
- Discount
- A reduction in the original price, usually expressed as a percentage (e.g., 25% off)
- Sales tax
- A government-imposed tax on purchases, calculated as a percentage of the sale price
- Multiplier
- A decimal used to calculate percent changes in one step (e.g., 0.75 for 25% off)
- Sticker price
- The original price shown on a product before any discounts