Materials & Prep
Prepare the board with a four-column organizer labeled Original amount, Percent, Change, and New amount. Copy the independent practice and exit ticket. No special materials are needed beyond the usual classroom setup.
Opening
Ask“A $50 item is marked down 20%. Which is the sale price: $10, $40, or $50?” Have students silently choose and write one sentence explaining what the 20% is taken of. Do not confirm the answer yet.
ConnectBriefly recall that finding a percent of a number means multiplying the percent as a decimal by that number. Ask students to predict whether the number used should be the price before or after the markdown. Keep both predictions visible for later revision.
Mini-lesson
ModelUse the board organizer for a $50 item with a 20% markdown. The original price is the base because it is the amount before the change.
Worked example
Original amount: $50 Percent: 20% = 0.20 Change: 0.20 × 50 = $10 New amount: 50 - 10 = $40
Think aloud“The markdown is 20% of the original $50, not 20% of the sale price. The $10 is the decrease, so I subtract it from the original price. The sale price is $40.” Return to the opening choices and confirm $40.
ConfrontIf I incorrectly take 20% of the new price, I calculate 0.20 × 40 = $8. That would make the discount only $8, so the result does not match a 20% markdown of the original $50. The same error happens when students use a tip-inclusive total as the base.
ExplainFor a decrease, calculate the change as a percent of the original amount, then subtract. For an increase such as a tip, calculate the change as a percent of the bill before the tip, then add. The sentence frame is: “The percent is % of , the original or before-change amount.”
Guided practice
Work through the first problem together, asking students to name each quantity before calculating.
Problem A: A $60 jacket is marked down 30%.
ExpectedThe discount is 0.30 × 60 = $18, and the sale price is 60 - 18 = $42. The 30% is taken of the original $60.
Turn and talk“A restaurant bill is $40 and the tip is 15%. What is the tip, and what is the total?” Partners must use the sentence frame before sharing.
ExpectedThe tip is 0.15 × 40 = $6, and the total is 40 + 6 = $46. The tip is 15% of the $40 bill before the tip.
Check for understandingDisplay “A $60 item becomes $42 after a markdown. Is the markdown 30% of $60 or 30% of $42? Explain.” Students hold up 1 for the original amount or 2 for the new amount, then justify with the organizer. Listen for students identifying the original price as the base.
Partner problem solving
Have pairs solve both problems and explain the base in a complete sentence.
Problem 1: A $90 pair of shoes has a 20% markdown. Find the markdown amount and sale price.
Problem 2: A $45 bill receives a 20% tip. Find the tip and total.
ExpectedFor Problem 1, 0.20 × 90 = $18 and 90 - 18 = $72. For Problem 2, 0.20 × 45 = $9 and 45 + 9 = $54.
ScaffoldStudents who need support copy the sentence “The % is taken of the , because that is the amount before the change.” They may fill the organizer one column at a time, circling the original bill or price before calculating.
ExtensionAsk ready students to reverse the process: “A shirt costs $45 after a 25% markdown. What was the original price?” Expected: The original price was 45 / 0.75 = $60, so the markdown was $15. Students must explain why $45 is not the base for finding the original price.
Independent practice
Students solve independently and show the original amount, percent, change, and new amount.
- An $80 backpack is marked down 25%. Find the discount and sale price.
- A $50 bill receives a 12% tip. Find the tip and total.
- A price drops from $70 to $56. Find the percent decrease and state what amount the percent is taken of.
Expected1. 0.25 × 80 = $20, and 80 - 20 = $60. 2. 0.12 × 50 = $6, and 50 + 6 = $56. 3. The decrease is 70 - 56 = $14, and 14 / 70 × 100 = 20%, taken of the original $70.
CirculateAsk, “What is the original or before-change amount in your problem?” before helping with computation. Watch for students using the new sale price or tip-inclusive total as the base.
Closing check
Exit ticketSolve both and write one sentence for each naming the base.
- A $60 bill receives a 15% tip. Find the tip and total.
- A $90 item is marked down to $72. Find the percent decrease and state what amount the percent is taken of.
Expected1. The tip is 0.15 × 60 = $9, the total is 60 + 9 = $69, and the percent is taken of the original $60 bill. 2. The decrease is 90 - 72 = $18, and 18 / 90 × 100 = 20%, taken of the original $90 price.