Determine the Whole Given the Part and Percent
I can determine the whole when I know a part and the percent that part represents.
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🎯 Content Objective / Objetivo de contenido
I can determine the whole when I know a part and the percent that part represents.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Akela paid $42 for a sweater, and that was 60% of the original price. BEFORE computing: will the original price be more or less than $42? How do you know?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Whole Finder
Every percent problem has three pieces: the part, the whole, and the percent. So far the whole has always been handed to you. Today it is the missing piece — a sale price without the original price, a car's current value without its sticker price. Your job is to work backwards to the whole.
Concept Launch
💡 Working backwards to the whole
When you know a part and the percent it represents, the whole is what is missing. A double number line, a ratio table, or an equation will each get you there — the equation is the fastest once you trust it.
Finding the Whole Given Part & Percent. Formula: Whole = Part ÷ Percent. 1. Identify the given part and the percentage it represents. 2. Convert the percent to a decimal or fraction. 3. Divide the part by the percent decimal to find the total whole (100%)
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Determine the Whole Given the Part and Percent Hallar el total dados la parte y el porcentaje |
Working backwards from a part and its percent to find the whole amount it came from. Trabajar al revés a partir de una parte y su porcentaje para hallar el total del que proviene. |
$42 is 60% of what? → $70 | |
| Part Parte |
The amount you already know — the piece of the whole that the percent describes. La cantidad que ya conoces: el pedazo del total que describe el porcentaje. |
The $42 sale price is the part | |
| Whole Total |
The full amount the percent is measured against. The whole is always 100%. La cantidad completa contra la que se mide el porcentaje. El total siempre es 100 %. |
The original price is the whole = 100% | |
| Double number line Recta numérica doble |
Two lines lined up — dollars on one, percents on the other — so matching marks show the same amount two ways. Dos rectas alineadas —dólares en una y porcentajes en la otra— para que las marcas correspondientes muestren la misma cantidad de dos formas. |
$0, $7, $42, $70 above 0%, 10%, 60%, 100% | |
| Equation Ecuación |
A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown. Una oración matemática con signo de igual. Aquí dice porcentaje × total = parte, con el total desconocido. |
0.7v = 26,600 — the percent times the unknown whole equals the part | |
| Percent Porcentaje |
A ratio comparing a number to 100. To compute with it, write it in decimal form: 60% = 0.6. Una razón que compara un número con 100. Para calcular con él, escríbelo en forma decimal: 60 % = 0.6. |
60% = 0.6 · 70% = 0.7 |
Which Word Fits?
Working backwards from a part and its percent finds 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
Akela paid $42 for a sweater, and that was 60% of the original price. BEFORE computing: will the original price be more or less than $42? How do you know?
👂 Listen For
Students reason from 60% < 100% to whole > part, without computing anything.
Extend: What if the $42 had been 150% of the original price? Which way would the comparison flip, and why?
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
In each problem, one number is the part and one is the percent. Sort what each problem asks you to find.
✍️ Explore Discourse
How can you tell, before doing any arithmetic, whether the answer should be bigger or smaller than the number you were given?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
To find the whole when 60% is $42, one strategy finds 10% first. Why is 10% such a useful stepping stone, and how does it get you to 100%?
👂 Listen For
Students explain WHY dividing by 6 gives 10% (60% is six 10%-steps), not just the arithmetic.
Extend: Show that the equation 0.6 × v = 42 tells the same story in one move. Where did the 10%-steps go inside v = 42 ÷ 0.6?
Practice Check A
A car is now worth $26,600, which is 70% of its purchase price. What was the purchase price?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Which statement correctly names the pieces of "18 students is 30% of the class"?
✍️ 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
Sort each label into the correct box.
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 Whole Given Part & Percent. Formula: Whole = Part ÷ Percent. 1. Identify the given part and the percentage it represents. 2. Convert the percent to a decimal or fraction. 3. Divide the part by the percent decimal to find the total whole (100%)" — and it works because ___.
Because Determine the Whole Given the Part and Percent means ___, but a tricky part is ___, so I have to ___.
A common mistake with Determine the Whole Given the Part and Percent is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Part to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Finding the Whole Given Part & Percent. Formula: Whole = Part ÷ Percent. 1. Identify the given part and the percentage it represents. 2. Convert the percent to a decimal or fraction. 3. Divide the part by the percent decimal to find the total whole (100%) because ___
Finding the Whole Given Part & Percent. Formula: Whole = Part ÷ Percent. 1. Identify the given part and the percentage it represents. 2. Convert the percent to a decimal or fraction. 3. Divide the part by the percent decimal to find the total whole (100%) but ___
Finding the Whole Given Part & Percent. Formula: Whole = Part ÷ Percent. 1. Identify the given part and the percentage it represents. 2. Convert the percent to a decimal or fraction. 3. Divide the part by the percent decimal to find the total whole (100%) so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Fill in the table using today's strategy.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
$20 is 50% of what number?
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
Sheng's parents bought a new car last year. Its value today is $26,600, which is 70% of what they paid for it.
✍️ Connection Reasoning
What did the car cost when they bought it, and how does your method show it?
The $26,600 is the ___ and the purchase price is the ___. Written as an equation, 0.7v = ___. Dividing both sides by ___ gives v = ___. The whole is ___ than the part, which makes sense because 70% is less than 100%.
Turn & Talk — Connect
Sheng's car is worth $26,600 today, which is 70% of what his parents paid. One partner should find the price with 10%-steps on the double number line; the other with the equation 0.7v = 26,600. Compare: where does each method show the SAME division?
👂 Listen For
Students identify that ÷7-then-×10 and ÷0.7 are the same move, and that both give a whole LARGER than $26,600.
Extend: A classmate got $18,620 by computing 0.7 × 26,600. Critique the reasoning: what question did that arithmetic actually answer?
Summarize: Determine the Whole Given the Part and Percent
Finding the Whole Given Part & Percent. Formula: Whole = Part ÷ Percent. 1. Identify the given part and the percentage it represents. 2. Convert the percent to a decimal or fraction. 3. Divide the part by the percent decimal to find the total whole (100%)
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A sweater's sale price is $42, which is 60% of the original price. What was the original price?
Bonus Exit Check
$20 is 50% of what number?
✍️ 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 reason from 60% < 100% to whole > part, without computing anything.
• Students explain WHY dividing by 6 gives 10% (60% is six 10%-steps), not just the arithmetic.
• Students identify that ÷7-then-×10 and ÷0.7 are the same move, and that both give a whole LARGER than $26,600.
• Students name the size check (whole > part for percents under 100%) — not just 'I divided.'
Common mistake: A common mistake when finding the whole is multiplying by the percent instead of dividing. For "$42 is 60% of the original price," computing 0.6 × 42 = $25.20 makes the original price SMALLER than the sale price — impossible for a discount. Since percent × whole = part, the whole is found by dividing: 42 ÷ 0.6 = $70. Whenever the percent is less than 100%, the whole must come out larger than the part, so a smaller answer is the tell.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: $38,000 — Write 0.7v = 26,600 and divide: v = 26,600 ÷ 0.7 = $38,000.
✓ Practice 2: 18 is the part, 30% is the percent, the class size is the whole — The known count is the part, the percent describes it, and the missing class size is the whole (100%).
✓ Practice 3: $40 — 50% is half, so the part is half the whole. Doubling gives the whole: 20 ÷ 0.5 = 40.
✓ Practice 4: 0.25n = 30 — Percent × whole = part, so 0.25 × n = 30.
✓ Exit ticket: $70, because 42 ÷ 0.6 = 70 — Percent × whole = part, so 0.6 × v = 42. Dividing both sides by 0.6 gives v = $70 — larger than the sale price, as a discount requires.