Teacher Guide: Percent Applications

@ Learning Objective 5-10 min lesson

Students will: Solve real-world problems involving percent increase, percent decrease, tax, tip, discount, and simple interest using appropriate formulas and strategies.

Why this matters for FAST: Percent applications are heavily tested on FAST. Students must calculate tax, tip, discounts, and simple interest, as well as find percent change. These problems require converting between percents and decimals and applying the correct operations.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Calculators
Sample receipts/menus
Colored pencils
Sale advertisement flyers

! Common Misconceptions to Address

Misconception #1: Adding the Percent Directly

Students think "20% tip on $50" means adding 20 to get $70. They forget to convert percent to decimal and multiply.

How to Address:

"Percent means 'per hundred.' 20% = 20/100 = 0.20. To find 20% of $50, we MULTIPLY: 0.20 x 50 = $10. The tip is $10, so total is $50 + $10 = $60."

Misconception #2: Confusing Percent Increase with New Amount

Students confuse the INCREASE (how much it went up) with the NEW VALUE (the final amount).

How to Address:

"If a price goes from $80 to $100, the INCREASE is $20, but the percent increase is 20/80 = 25%. We divide by the ORIGINAL, not the new amount!"

Misconception #3: Using Wrong Base for Percent Decrease

Students use the sale price instead of the original price when calculating percent discount.

How to Address:

"Percent change is always based on the ORIGINAL amount. If something was $100 and is now $75, the discount is $25. The percent decrease is 25/100 = 25%, NOT 25/75."

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Review converting percents to decimals: "How do we write 15% as a decimal? Move the decimal two places left: 15% = 0.15. How about 7.5%? That's 0.075."

2

Introduce Key Formulas (2 min)

Essential Percent Formulas

Tax/Tip/Markup: Amount = Original x Rate

Discount: Discount = Original x Rate; Sale Price = Original - Discount

Percent Change: (New - Original) / Original x 100

Simple Interest: I = P x r x t

3

Tax, Tip, and Markup Examples (2 min)

Example: Restaurant Bill

Meal cost: $45.00

Tax (7%): 0.07 x $45 = $3.15

Tip (18%): 0.18 x $45 = $8.10

Total: $45 + $3.15 + $8.10 = $56.25

SAY THIS:

"Always convert the percent to a decimal first, then multiply by the original amount. Add the result to get the total, or keep it separate if asked for just the tax or tip amount."

4

Discount and Sale Price (2 min)

Example: 30% Off Sale

Original price: $80

Discount: 0.30 x $80 = $24

Sale price: $80 - $24 = $56

Shortcut: 100% - 30% = 70%, so Sale = 0.70 x $80 = $56

5

Simple Interest (2 min)

Simple Interest Formula: I = P x r x t

I = Interest earned | P = Principal (starting amount) | r = Rate (as decimal) | t = Time (in years)

Example: Savings Account

Principal: $500, Rate: 4%, Time: 3 years

I = 500 x 0.04 x 3 = $60

Total after 3 years: $500 + $60 = $560

6

Guided Practice (2-3 min)

Work through these together:

A shirt costs $40. If it's 25% off, what's the sale price? ($30)
A population grew from 2,000 to 2,500. What's the percent increase? (25%)
Find the simple interest on $1,200 at 5% for 2 years. ($120)

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"A jacket originally costs $60. It's on sale for 20% off. What is the sale price?"

A) $12 B) $20 C) $40 D) $48

Correct answer: D) $48. Discount = 0.20 x $60 = $12. Sale price = $60 - $12 = $48. (Or: 80% of $60 = 0.80 x 60 = $48)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Percent of a number: word problems Find the percent: tax, tip, and more Sale prices: find the percent markdown Percent increase and decrease Simple interest Multi-step percent problems

^ Differentiation & Extension

For struggling students: Focus on one type at a time. Use visual models (100-grids) to show percents. Always have students write the percent as a decimal first before calculating.

For advanced students: Introduce compound scenarios (discount THEN tax). Have them compare deals: "Which is better: 20% off then 10% off, or 30% off once?"

For home: Send Parent Activity sheet. Families can calculate tips at restaurants and find sale prices while shopping.