Practice Set · Part 1
Determine the Whole Given the Part and Percent
Pick up where we left off
Where we left off
Our goal: I can determine the whole when I know a part and the percent that part represents, explain why the method works, and use it on a problem I have not seen before.
The big idea: Percent × whole = part. When the whole is unknown, divide the part by the percent in decimal form: whole = part ÷ decimal — and you can say why it is true, and where it would stop being true.
Model to copy — Watch me find the original price of the sweater
- Akela paid $42 for a sweater on sale, and that was 60% of the original price. The $42 is the part; the original price is the whole, which is 100%.
- On a double number line, I put $42 under 60%. To find a smaller step, I use 10%: if 60% is $42, then 10% is 42 ÷ 6 = $7.
- Now I count up to the whole: 100% is ten of those 10% steps, so 10 × $7 = $70.
- The equation says the same thing in one move: 0.6 × v = 42, so v = 42 ÷ 0.6 = 70. The original price was $70 — larger than the sale price, which is exactly what a discount should mean.
Start here
You did these with your group. Now do them on your own — the model above is yours to copy.
- 1
Same stepsFinish what the group started. Use the model above, step for step.
Try it together — then prove it: Sheng's car is now worth $26,600, which is 70% of what his parents paid for it. Find the original price. Name the pieces first: $26,600 is the part, 70% is the percent, and the purchase price is the unknown whole. Write the percentage statement as an equation, using the decimal form: 0.7v = 26,600. Solve by dividing both sides by 0.7: v = 26,600 ÷ 0.7 = 38,000. The car cost $38,000 when they bought it. Now prove it: say why that move had to work at all — not just that it did.Show your work - 2
Warm restartWhat is 10% of 320?
- A3.2
- B32
- C320
- D64
How do you know?
- 3
Warm restartWhat is 50% of 84?
- A50
- B34
- C168
- D42
How do you know?
- 4
Warm restartWhat is 20% of 150?
- A20
- B35
- C75
- D30
How do you know?
Practice Set · Part 2
Determine the Whole Given the Part and Percent
Keep going
You answered these out loud. Now write them.
Answer, then say how you know — the reason is the part that counts.
- 5
Think it through$42 is 60% of the original price. What was the original price?
- A$70
- B$25.20
- C$102
- D$60
Why is that the answer?
- 6
Think it throughWhich equation finds the whole when 75 minutes is 15% of the school day?
- A0.15d = 75
- B75d = 0.15
- Cd = 0.15 × 75
- Dd = 75 + 15
How do you know? Give a second reason as well.
- 7
Think it throughIf the percent given is less than 100%, the whole must be…
- ALarger than the part
- BSmaller than the part
- CEqual to the part
- DImpossible to find
Explain your thinking. What would have to change for a different choice to be right?
- 8
Back to the modelHow can you tell, before doing any arithmetic, whether the answer should be bigger or smaller than the number you were given?
Sort it again — on paper this time
Write the letter of the group each one belongs in.
- $42 is 60% of what number?
- What is 60% of $70?
- 75 minutes is 15% of the school day. How long is the day?
- 15% of a 500-minute day is how many minutes?
- A car worth $26,600 is 70% of its original price. What did it cost?
- What is 70% of $38,000?
Practice Set · Part 3
Determine the Whole Given the Part and Percent
Words and reasoning
Word bank · Banco de palabras
Use the words
Fill each blank with a word from the bank.
- Working backwards from a part and its percent finds the ___.
- How much of the base you get — your answer — is the ___.
- The full amount a percent is measured against is always ___%.
- Two parallel lines pairing amounts with their percents form a ___ ___ ___.
Explain the thinking
- 9
Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.
The mistake: A common mistake when finding the whole is multiplying by the percent instead of dividing. - 10
Say moreTo 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%?
- 11
Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Three hundred middle school students voted for one of three snacks to add to the cafeteria menu, and the graph shows the PERCENT of students who chose each snack. Today the question runs the other way: if you knew only how many students picked one snack and what percent that was, could you work back to the total?
Show your work
Practice Set · Part 4
Determine the Whole Given the Part and Percent
Show what you know
Last check
These two come from Lesson 4.4. If they are shaky, that is the lesson to revisit — not this one.
- 12
Show what you knowExplain your thinking — A sweater's sale price is $42, which is 60% of the original price. What was the original price?
- A$70, because 42 ÷ 0.6 = 70
- B$25.20, because 0.6 × 42 = 25.20
- C$102, because 42 + 60 = 102
- D$60, because the percent is 60
Explain your choice.
- 13
From Lesson 4.4Explain your thinking — What is 45% of 360?
- A162
- B45
- C315
- D180
How do you know?
- 14
From Lesson 4.4Check with a benchmark: what is 10% of 1,500?
- A150
- B15
- C1.5
- D100
How do you know?
Be honest — this tells your teacher what to do next
| I can… | Not yet | Getting there | Got it |
|---|---|---|---|
| I can determine the whole when I know a part and the percent that part represents, explain why the method works, and use it on a problem I have not seen before. | |||
| I can explain why it works: Percent × whole = part. When the whole is unknown, divide the part by the percent in decimal form: whole =… | |||
| I can justify my answer to a skeptic and connect it to a second strategy or representation. |
One question I want to ask my group next time