Introduction
Solving Percent Problems is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with solving percent problems.
What Is Solving Percent Problems?
Solving Percent Problems means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Solving Percent Problems
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: In the bar model above, the shaded region represents \(75\) students. How many students are there in total?
- A. \(100\)
- B. \(150\)
- C. \(200\)
- D. \(300\)
Why it works: Shaded portion is \(75\%\) of the total. If \(75\%\) equals \(75\) students, then \(100\%=\frac{75}{0.75}=100\) students.
Answer: \(100\)
Visual Model 2
Question: What is the discount amount on the pants?
| Item | Original Price | Discount |
|---|---|---|
| Shirt | $\(50\) | \(10%\) |
| Pants | $\(80\) | \(15%\) |
- A. \($10\)
- B. \($20\)
- C. \($15\)
- D. \($12\)
Why it works: \(15\%\) of \($80 = 0.15 \times 80 = $12\).
Answer: \($12\)
Worked Examples
Example 1
Question: The shaded portion represents apples. How many apples are there?
- A. \(40\)
- B. \(60\)
- C. \(80\)
- D. \(100\)
- \(50\%\) of \(160 = 0.50 \times 160 = 80\) apples.
Answer: \(80\)
Example 2
Question: Which store offers the larger percent discount?
| Store | Original Price | Sale Price |
|---|---|---|
| Store A | $\(50\) | $\(40\) |
| Store B | $\(60\) | $\(42\) |
- A. Store A (\(20\%\) off)
- B. Store B (\(30\%\) off)
- C. Store A (\(30\%\) off)
- D. Both offer the same discount
- Store A's discount is \(\frac{50-40}{50}=\frac{10}{50}=20\%\).
- Store B's discount is \(\frac{60-42}{60}=\frac{18}{60}=30\%\), so Store B offers the larger percent discount.
Answer: Store B (\(30\%\) off)
Example 3
Question: In an election, the shaded portion represents votes for Candidate A. How many votes did Candidate A receive?
- A. \(60\)
- B. \(100\)
- C. \(180\)
- D. \(120\)
- \(40\%\) of \(300 = 0.40 \times 300 = 120\) votes.
Answer: \(120\)
Real-World Word Problems
Problem 1
Question: A sweater originally costs \($40\). It is on sale for \(25\%\) off. What is the sale price?
- A. \($10\)
- B. \($15\)
- C. \($30\)
- D. \($50\)
Why it works: \(25\%\) of \($40\) is \(0.25\times40=$10\). Sale price is \($40-$10=$30\).
Answer: \($30\)
Problem 2
Question: A jacket costs \($80\) after a \(20\%\) discount. What was the original price?
- A. \($96\)
- B. \($160\)
- C. \($120\)
- D. \($100\)
Why it works: If the discount is \(20\%\), the customer pays \(80\%\) of the original price. So \(0.80 \times \text{original} = $80\). Original \(= $80 \div 0.80 = $100\).
Answer: \($100\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Sarah scored \(45\) correct answers out of \(60\) questions on a math test. What percent of the questions did she answer correctly?
- A. \(55\%\)
- B. \(65\%\)
- C. \(75\%\)
- D. \(85\%\)
Question 2
What is \(15\%\) of \($200\)?
- A. \($20\)
- B. \($25\)
- C. \($30\)
- D. \($35\)
Question 3
A restaurant bill comes to \($45\). The customer wants to leave a \(20\%\) tip. How much is the tip?
- A. \($4.50\)
- B. \($9.00\)
- C. \($18.00\)
- D. \($27.00\)
Question 4
Out of \(250\) students at a school, \(30\%\) participate in sports. How many students participate in sports?
- A. \(50\)
- B. \(70\)
- C. \(75\)
- D. \(100\)
Question 5
A game costs \($60\). During a sale, it is discounted by \(35\%\). What is the sale price?
- A. \($21\)
- B. \($25\)
- C. \($39\)
- D. \($45\)
Question 6
If a book's price increases from \($20\) to \($24\), what is the percent increase?
- A. \(20\%\)
- B. \(25\%\)
- C. \(30\%\)
- D. \(40\%\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(75\%\)
To find the percent: \(\frac{45}{60}=\frac{3}{4}=0.75=75\%\).
Question 2
Answer: \($30\)
\(15\% \times $200 = 0.15 \times 200 = $30\).
Question 3
Answer: \($9.00\)
\(20\%\) of \($45 = 0.20 \times 45 = $9.00\).
Question 4
Answer: \(75\)
\(30\%\) of \(250 = 0.30 \times 250 = 75\) students.
Question 5
Answer: \($39\)
\(35\%\) of \($60 = 0.35 \times 60 = $21\). Sale price is \($60 - $21 = $39\).
Question 6
Answer: \(20\%\)
Increase is \($24 - $20 = $4\). Percent increase is \(\frac{4}{20} = 0.20 = 20\%\).
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Solving Percent Problems becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
