Find and Compare with Percentages
I can find the percent of a number using an equation or a model.
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🎯 Content Objective / Objetivo de contenido
I can find the percent of a number using an equation or a model.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
On Discount Day the claw machine is 25% off its 60-ticket price. In '25% of 60,' which number is the base (the number right after 'of'), and what part are you trying to find?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Arcade Builder Challenge
It's Discount Day at the arcade! Different games are offering percent-off deals on ticket prices. The claw machine is 25% off its usual 60-ticket price, and the racing game is 40% off 80 tickets. You need to calculate the discounts to figure out how many tickets each game actually costs!
Concept Launch
💡 How do I find the percent of a number?
A percent is a piece of a whole. The whole is called the base — it is the number right after the word “of,” and “of” means multiply. Your answer is the piece you get, called the part.
Finding the Percent of a Number. Formula: Part = Percent × Whole. 1. Identify the percent and the whole (base amount). 2. Convert the percent to a decimal or simplified fraction. 3. Multiply the decimal/fraction by the whole to calculate the part
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Percent of a Number Porcentaje de un número |
A part of a number found by multiplying the number by the percent written as a decimal. Una parte de un número que se halla multiplicando el número por el porcentaje escrito como decimal. |
25% of 80 = 0.25 × 80 = 20 | |
| Percent Porcentaje |
A way to compare a number to 100, shown with the % sign. Una manera de comparar un número con 100, con el signo %. |
30% means 30 out of 100 | |
| Base Base |
The whole amount you start with — the number right after the word “of.” La cantidad total con la que empiezas: el número que va después de la palabra “de”. |
25% of 80 → the whole is 80. | |
| Part Parte |
How much of the base (the whole) you get. It is your answer. Cuánto obtienes de la base (el total). Es tu respuesta. |
25% of 80 = 20 → the part is 20 (20 out of the 80). | |
| Equation Ecuación |
A number sentence with an equal sign. The percent one is: part = percent × base. Una oración numérica con signo de igual. La de porcentaje es: parte = porcentaje × base. |
part = percent × base — like 20 = 0.25 × 80. | |
| Discount Descuento |
Money taken off the first price to make it cheaper. Dinero que se quita del precio original para que sea más barato. |
$40 shirt at 25% off: discount = $10 |
Which Word Fits?
A part found by multiplying a number by a percent in decimal form is the ___ ___ ___ ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
On Discount Day the claw machine is 25% off its 60-ticket price. In '25% of 60,' which number is the base (the number right after 'of'), and what part are you trying to find?
👂 Listen For
Students identify 60 as the base, the 25% discount as the part to find, and connect 'of' to the base.
Extend: Without computing exactly, will the discount be more or less than half of 60? Use a benchmark to estimate and explain.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Find the percent of each number. Use the equation: Part = Percent × Base. Convert the percent to a decimal first.
✍️ Explore Discourse
What steps do you follow every time you find the percent of a number?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
What steps did you follow every time to find the percent of a number in the discount table?
👂 Listen For
Students describe the equation part = percent x base, converting the percent to a decimal first (e.g., 0.40 x 80 = 32).
Extend: Compare finding 25% of 60 with the decimal 0.25 versus dividing 60 into 4 equal parts. Why do both methods give the same part?
Practice Check A
An arcade prize costs 240 tickets. If you have a coupon for 15% off, how many tickets do you save?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A student scored 72 out of 90 on a test. What percent did they score?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Equivalent Ratio Sort
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Each arcade game shows a percent of a number. Sort each one into the correct result bin.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Finding the Percent of a Number. Formula: Part = Percent × Whole. 1. Identify the percent and the whole (base amount). 2. Convert the percent to a decimal or simplified fraction. 3. Multiply the decimal/fraction by the whole to calculate the part" — and it works because ___.
Because Percent of a Number means ___, but a tricky part is ___, so I have to ___.
A common mistake with Percent of a Number is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Percent to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Finding the Percent of a Number. Formula: Part = Percent × Whole. 1. Identify the percent and the whole (base amount). 2. Convert the percent to a decimal or simplified fraction. 3. Multiply the decimal/fraction by the whole to calculate the part because ___
Finding the Percent of a Number. Formula: Part = Percent × Whole. 1. Identify the percent and the whole (base amount). 2. Convert the percent to a decimal or simplified fraction. 3. Multiply the decimal/fraction by the whole to calculate the part but ___
Finding the Percent of a Number. Formula: Part = Percent × Whole. 1. Identify the percent and the whole (base amount). 2. Convert the percent to a decimal or simplified fraction. 3. Multiply the decimal/fraction by the whole to calculate the part so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Find the percent of each number. Use the equation: Part = Percent × Base. Convert the percent to a decimal first.
| Game | Original Tickets | Discount % | Discount as Decimal | Discount Amount |
|---|---|---|---|---|
| Claw Machine | 60 | 25% | 0.25 | 15 |
| Racing Game | 80 | 40% | ||
| Skee-Ball | 50 | 30% | ||
| Air Hockey | 120 | 15% | ||
| Dance Pad | 90 | 20% | ||
| Pinball | 200 | 5% |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is 20% of 150?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
The arcade is donating 12% of Saturday's ticket sales to charity. They sold 1,500 tickets on Saturday. The manager says they will donate 180 tickets. A student says it should be 18 tickets.
✍️ Connection Reasoning
Who is correct, and how do you know?
The ___ is correct because 12% of 1,500 = ___ × 1,500 = ___. The mistake was ___.
Turn & Talk — Connect
The arcade donates 12% of Saturday's 1,500 ticket sales. The manager says 180 tickets, a student says 18. Who is right, and how do you know?
👂 Listen For
Students compute 0.12 x 1,500 = 180 and explain the student likely used 0.012 (divided by 1,000) instead of 0.12.
Extend: Estimate first: 10% of 1,500 is easy to find. Use that to check whether 180 is reasonable for 12%, and explain your reasoning.
Summarize: Find and Compare with Percentages
Finding the Percent of a Number. Formula: Part = Percent × Whole. 1. Identify the percent and the whole (base amount). 2. Convert the percent to a decimal or simplified fraction. 3. Multiply the decimal/fraction by the whole to calculate the part
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
What is 45% of 360?
Bonus Exit Check
What is 20% of 150?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students identify 60 as the base, the 25% discount as the part to find, and connect 'of' to the base.
• Students describe the equation part = percent x base, converting the percent to a decimal first (e.g., 0.40 x 80 = 32).
• Students compute 0.12 x 1,500 = 180 and explain the student likely used 0.012 (divided by 1,000) instead of 0.12.
• Listen for students naming a specific strategy tied to 6.AT.4 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Find the Percent of a Number is multiplying by the percent number itself instead of its decimal form — for example, finding 30% of 80 by computing 30 × 80 = 2,400 instead of 0.30 × 80 = 24. Always divide the percent by 100 to get the decimal, then multiply that decimal by the base.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 36 tickets — 15% of 240 = 0.15 × 240 = 36 tickets saved.
✓ Practice 2: 80% — 72/90 simplifies to 8/10, and 10 × 10 = 100, so 8 × 10 = 80. That makes 72/90 = 80/100 = 80%.
✓ Practice 3: 30 — 20% = 0.20. Multiply: 0.20 × 150 = 30.
✓ Practice 4: 42 — 50% = 0.50. Multiply: 0.50 × 84 = 42. (Or simply divide by 2: 84 ÷ 2 = 42.)
✓ Exit ticket: 162 — 45% = 0.45. Multiply: 0.45 × 360 = 162. A student who answers 45 wrote the percent number itself instead of finding the part. A student who answers 315 subtracted the percent number from the base (360 − 45) instead of multiplying. A student who answers 180 rounded 45% up to 50% before multiplying (0.50 × 360). Always convert the exact percent to a decimal, then multiply by the base.